o V Marine Biological Laboratory RprpivPfl July 29, 1950 Accession No. & Qven By McGraw-Hill Book Co., Inc, Place ^ew York City 0 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS With Applications to Biology and Medicine e I ISOTOPIC TRACERS AND NUCLEAR RADIATIONS With Applications to Biology and Medicine by William E. Siri with contributions by Ellsworth C. Dougherty Cornelius A. Tobias Rayburn W. Dunn James S. Robertson Patricia P. Weymouth Division of Medical Physics, Department of Physics, and Radiation Laboratory, University of California FIRST EDITION McGRAW-HILL BOOK COMPANY, INC. NEW YORK TORONTO LONDON 1949 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS WITH APPLICATIONS TO BIOLOGY AND MEDICINE Copyright, 1949, by the McGraw-Hill Book Company, Inc. Printed in the United States of America. All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. PRINTED BY THE MAPLE PRESS COMPANY, YORK, PA. pMGAl PREFACE The recent very rapid developments in nuclear physics and the parallel progress in tracer techniques have made it imperative to compile from the vast accumulation of data and experimental procedures some of the material that appears to be most essential to applications of isotopic tracers and nuclear radiations. For the most part, such information is to be found at the present time only in widely scattered literature. Nuclear physicists, to be sure, have access to this information by virtue of their familiarity with the technical literature in the field, but even for the nuclear physicist it is often necessary to refer to many different sources for much of the explicit data he requires. The situation is very much worse for those who are less familiar with nuclear physics but who plan to employ isotopic tracers and high-energy radiations in their research. For such persons, Seaborg and Perlman's "Table of Isotopes" has been literally the only comprehensive source for some of the essential information. Until recently the compilation of a volume of this kind would have been somewhat futile, since there was too little data that was firmly established and a compilation, once made, would have had to be completely revised and considerably extended six months later. Now, however, it is felt that at least an effort can be made in this direction with the accumulated information derived from the extensive research during and since the war. While it is impossible to present in a single volume the vast amount of material that biologists and physicists in this field would like to have immediately avail- able, it is hoped that the present book, despite its obvious limitations, may find some justification in attempting to provide some of the information for which there seems a pressing demand. Based on the experience of our laboratory, it was felt that an urgent need could be satisfied if the present volume were prepared in the form of a ready reference in which fundamental data and descriptions of processes and instru- ments were available in compact form. On the other hand the book was expanded beyond a simple compilation of data and formulas in order to make it more intelligible to those who are less conversant with the terminology and details of nuclear physics and tracer methods. In general, descriptions of processes and instruments have been made rather elementary and with the intention of noting only the essential principles and those data which are important in practice. The biological and medical aspects of tracer methods, presented by VI PREFACE Dr. Ellsworth C. Dougherty in Part III, is in the form of a survey of those isotopes which have already been used and those which, because of their convenient physical properties and biological significance, may reasonably be employed in future research. No effort has been made to present an exhaustive and detailed account of the biological and medical research since several excellent reviews have already been published, particularly those of Hevesy, Kamen, and Lawrence and Hamilton. The need for a book covering the fields of tracer methods and nuclear radiations, sufficiently technical to be of use in the laboratory, was early recognized by Col. A. P. Gagge of the Aeromedical Laboratory at Wright Field, Ohio. It was at his suggestion and with the enthusiastic support of Dr. John H. Lawrence that initial preparation of the present volume was undertaken. The first draft, written for the Army Air Forces, was com- pleted in November, 1947, and printed shortly afterward in a limited edition which appeared as A. F. Technical Report No. 5669. Despite the great numbers of errors and omissions, there seemed sufficient interest in this report to justify a comprehensive revision. The original manuscript, conse- quently, was completely rewritten and extended in scope for the present edition. Much of the credit for the existence of the book must be given Colonel Gagge and the Army Air Forces, for whose early interest and support we are fully appreciative. From its beginning through to completion, preparation of the book has had the active interest and indispensable support of Dr. Lawrence, to whom the authors owe a great debt of gratitude. The chapters submitted by the contributing authors, Drs. Ellsworth C. Dougherty, Cornelius A. Tobias, James S. Robertson, Rayburn W. Dunn, and Patricia P. Weymouth, have greatly extended the scope and usefulness of the book. Without their assistance it is doubtful that, even if completed, the book would have served a useful function. We wish especially to thank Dr. Dougherty for the time and effort required for his preparation of the entire biological section of the book, Part III. In addition to the authors cited above we wish to thank Dr. R. L. Dobson for preparing Sec. 19.2 and Dr. M. C. Fishier who began the initial compilation of the bibliography of isotope literature. To aid in identification, the name of each author has been placed at the head of the chapter he submitted. We wish also to acknowledge our indebtedness to Drs. G. T. Seaborg and I. Perlman for permission to use their table of isotopes, to Dr. R. Serber for permission to include the range-energy data calculated by Walter Aron and B. G. Hoffman of the Radiation Laboratory ©f the University of California, and to the authors and publishers who readily gave permission to reprint many of the graphs and tables. A considerable portion of the labor in preparing the manuscript was borne PREFACE vu by Miss Jean Smith and Mrs. Frances Schaefer, who typed the greater part of the manuscript, and by Ellis H. Myers, who assisted in preparing the diagrams and graphs. We are especially grateful to Miss M. J. Brandenburg, who not only typed a large part of the manuscript, but also read the entire manuscript and proof, offering many important suggestions and corrections. Many others have been very helpful in the preparation of the manuscript. Among these we wish especially to express our sincere thanks to Drs. R. R. Newell, B. J. Moyer, A. C. Helmholz, and H. B. Jones for critically reading parts of the manuscript and making many corrections and suggestions. William E. Siri Berkeley, Calif. June, 1949 CONTENTS Preface v Foreword xiii Part I. Isotopes and Nuclear Radiations 1. Properties of Nuclei 3 1.1. Stable isotopes — 1.2. Mass defect — 1.3. Packing fraction — 1.4. Binding energy — 1.5. Nuclear spin — 1.6. Magnetic dipole moment — 1.7. Electric quadrupole moment. 2. Gamma Rays 32 2.1. Properties — 2.2. Photoelectric effect — 2.3. Scattering of gamma rays — 2.4. Pair production — 2.5. Secondary particle production — 2.6. Internal conversion. 3. Beta Particles 49 3.1. Physical properties — 3.2. Absorption processes — 3.3. Ionization energy loss — 3.4. Radiative collision losses — 3.5. Specific ionization — 3.6. Relative stopping power — 3.7. Nuclear excitation — 3.8. Absorption of beta particles of homogeneous energy — 3.9. Absorption of inhomogeneous beta-particle beams — -3.10. Scattering of beta particles by nuclei — 3.11. Beta decay — 3.12. Selection rules for beta decay — 3.13. K capture. 4. Protons, Deuterons, and Alpha Particles 76 4.1. Physical properties — 4.2. Energy loss of fast charged particles — 4.3. Stopping- formula corrections — 4.4. Stopping formula for high-energy particles — 4.5. Rela- tive stopping power — 4.6. Atomic stopping power — 4.7. Mass stopping power — 4.8. Range of heavy charged particles— 4.9. Specific ionization — 4.10. Delta rays — 4.11. Straggling of charged particles — 4.12. Scattering of charged particles — 4.13. Alpha decay. 5. Neutrons 121 5.1. General properties — 5.2. Neutron processes — 5.3. Elastic scattering of neu- trons— 5.4. Interaction of slow neutrons with nuclei — 5.5. Interaction of fast neu- trons with nuclei — 5.6. Neutron diffusion. 6. Fission 148 6.1. Mechanism of fission — 6.2. Fission probability — 6.3. Stability of heavy nuclei — 6.4. Fission fragments — 6.5. Absorption and range of fission fragments — 6.6. Radioactive chains — 6.7. Prompt neutrons — 6.8. Delayed neutrons — 6.9. Alpha particles — 6.10. Fission induced by other radiations — 6.11, Fission of elements below thorium. ix 64409 x CONTENTS 7. Radioactivity 163 7.1. Summary of radioactivity — 7.2. Law of radioactive decay — 7.3. Fluctuations — 7.4. Simple decay — 7.5. Growth of radioactivity — 7.6. Radioactive substance produced by parent of long half -life — 7.7. Parent and daughter substance of com- parable half-lives — 7.8. Decay of nth. component in a radioactive chain — 7.9. Radioactivity units — 7.10. Decay schemes — 7.11. The natural radioactive series. — 7.12. Seaborg and Perlman table of isotopes. Part II. Methods and Instruments 8. Indirect Methods for Measuring Deuterium 263 8.1. Introduction — 8.2. Phyical properties of deuterium oxide and water — 8.3. Preparation and purification of water samples for analysis — 8.4. Refractive index — 8.5. Pycnometer — 8.6. Free float — 8.7. Falling drop — 8.8. Diffusion gradient. 9. Mass Spectrographs 279 9.1. Aston mass spectrograph — 9.2. Dempster mass spectroscope — 9.3. 60-degree (Nier-type) mass spectrometer — 9.4. Mattauch double-focusing spectrograph — 9.5. Dempster double-focusing spectrograph — 9.6. Bainbridge-Jordan double- focusing mass spectrograph — 9.7. Trochoidal trajectory mass spectrograph — 9.8. Ion sources — 9.9. Detector requirements — 9.10. Photographic plates — 9.11. Electrical devices — 9.12. Mass spectrometer recording systems — 9.13. Mass spec- trometer errors — 9.14. Hydrogen — 9.15. Carbon — 9.16. Nitrogen — 9.17. Oxygen. 10. Geiger-Miiller Counters 304 10.1. General properties — 10.2. Non-self-quenching counters — 10.3. Self-quenching counters — 10.4. Pulse and voltage characteristics — 10.5. Filling gases — 10.6. Counter tube life — 10.7. Low-voltage counter tubes — 10.8. Active gas-filled counters — 10.9. Neutron counters — 10.10. Slow neutron counters — 10.11. Fast neutron counters — 10.12. Accuracy of counting measurements — 10.13. Average deviation — 10.14. Standard deviation — 10.15. Probable error — 10.16. Counter resolving time — 10.17. Coincidence correction for high counting rates — 10.18. Coincidence counting corrections — 10.19. Counting efficiency — 10.20. Averaging effect of scaling circuit — 10.21. Quenching circuits — 10.22. Scaling circuits — 10.23. Discriminators — 10.24. Recording circuits — 10.25. Coincidence circuits — 10.26. Counting rate meter. 11. Proportional Counters 341 11.1. General features and use — 11.2. Theory of operation. 12. Ionization Chambers 344 12.1. Description — 12.2. Applications — 12.3. Charge measuring instruments — 12.4. Statistics of measurements. 13. Standardization of Radioactive Samples 358 13.1. Introduction — 13.2. General methods — 13.3. Primary alpha-particle stand- ards— 13.4. Standards for beta and gamma emitters — 13.5. Standardization by coincidence measurements — 13.6. Long-life beta standards — 13.7. Beta-particle standardization by direct measurement of the charge of the particles — 13.8. Indi- rect standardization by calorimetric measurement of the total energy — 13.9. Ionization measurement of beta and gamma rays — 13.10. Standardization of beta- CONTENTS xi counter geometry— 13.11. Secondary beta- and gamma-ray standards — 13.12. Standardization of neutrons and protons. 14. The Radioautograph 381 14.1. Introduction — 14.2. Techniques for preparing radioautographs — 14.3. Radio- autographic emulsions. 15. Theory of Tracer Methods 388 15.1. Introduction — 15.2. Isotopic dilution — 15.3. Tracer problems involving first- order reactions — 15.4. A more general theory of tracer methods. 16. Internal Dosimetry 403 16.1. Physical principles of dosimetry — 16.2. Units of dose — 16.3. Calculation of beta-particle dose — 16.4. Absorption of gamma rays in tissue — 16.5. Gamma-ray dose calculations — 16.6. Calculation of radioactivity density in tissue — 16.7. Geo- metrical factor. 17. The Preparation of Thin Films of Radioactive Elements by Electrolysis .... 438 17.1. General considerations — 17.2. Apparatus — 17.3. Anodes — 17.4. Cathodes — ■ 17.5. Electrodeposition — 17.7. The electrolysis eurrent and voltage. 18. The Treatment of Biological Tissues for Recovery of Radioactive Elements. . . 445 18.1. Introduction — 18.2. Dry ashing — 18.3. Wet ashing. 19. The Safe Handling of Radioactive Materials 450 19.1. Introduction — 19.2. Medical considerations — 19.3. Laboratory design — 19.4. Special laboratory equipment — 19.5 Safety procedures — 19.6. Radiation shields — ■ 19.7. Radiation monitoring — 19.8. Shipping regulations. 20. The Electrostatic Generator 472 20.1. Description — 20.2. Construction and operation. 21. The Cyclotron 476 21.1. Description — 21.2. Ion paths — 21.3. Ion source — 21.4. Cyclotron targets — 21.5. Synchro-cyclotron. 22. The Betatron 489 22.1. Description — 22.2. Electron injection and beam extraction — 22.3. Orbital oscillations — 24.4. Focusing. 23. The Synchrotron 493 23.1. Description — 23.2. Motion of particles — 23.3. Energy loss by radiation — ■ 23.4. Synchrotron operation. Part III. Biological and Medical Applications of Isotopes 24. General Critique of the Biological Application of Isotopes 503 24.1. Introduction — 24.2. Survey of useful isotopes — 24.3. Isotopes as tracers — 24.4. Differential behavior and effects of isotopes. xii CONTENTS 25. Elements Constituting Major Organic Metabolites 514 25.1. Introduction— 25.2. Carbon— 25.3. Hydrogen — 25.4. Oxygen— 25.5. Nitro- gen— 25.6. Sulfur — 25.7. Phosphorus. 26. Elements Constituting Major Mineral Metabolites 520 26.1. Introduction — 26.2. Sodium — 26.3. Potassium — 26.4. Calcium — 26.5. Mag- nesium— 26.6. Chlorine. 27. Trace Elements Known to Be Essential in Animals and Plants 524 27.1. Introduction— 27.2. Iron— 27.3. Iodine — 27.4. Manganese — 27.5. Copper— 27.6. Zinc— 27.7. Cobalt— 27.8. Molybdenum— 27.9. Boron— 27.10. Aluminum— 27.11. Silicon— 27.12. Vanadium 28. Elements Not Known to Be Essential to Life 530 28.1. Introduction — 28.2. Possible micronutrient elements — 28.3. Elements of importance to pharmacology and toxicology — 28.4. Noble gases — 28.5. Rare- earth elements (lanthanide series) and other elements in fission — 28.6. New rare- earth elements (actinide series) — 28.7. Other elements. 29. Isotopes in Therapy and Diagnosis 537 29.1. Introduction— 29.2. Radiophosphorus — 29.3. Radioiodine — 29.4. Radio- sodium — 29.5. Radiocolloids — 29.6. Other isotopes 30. Bibliography 552 30.1. General references — 30.2. Americium — 30.3. Antimony — 30.4. Argon — 30.5. Arsenic— 30.6. Astatine— 30.7. Barium— 30.8. Bismuth— 30.9. Boron— 30.10. Bro- mine—30.11. Calcium— 30.12. Carbon— 30.13. Cerium— 30.14. Cesium— 30.15. Chlorine— 30.16. Cobalt— 30.17. Columbium— 30.18. Copper— 30.19. Curium— 30.20. Deuterium— 30.21. Fluorine— 30.22. Gold— 30.23. Hydrogen— 30.24. Iodine —30.25. Iron— 30.26. Krypton— 30.27. Lanthanum— 30.28. Lead— 30.29. Lithium — 30.30. Magnesium — 30.31. Manganese — 30.32. Mercury — 30.33. Molybde- num— 30.34. Neptunium — 30.35. Nitrogen — 30.36. Oxygen — 30.37. Phosphorus — 30.38. Plutonium — 30.39. Polonium — 30.40. Potassium — 30.41. Praseodymium— 30.42. Prometheum — 30.43. Protactinium — 30.44. Radium and radon — 30.45. Rubidium— 30.46. Ruthenium— 30.47. Selenium— 30.48. Sodium— 30.49. Stron- tium—30.50. Sulfur— 30.51. Tellurium— 30.52. Thorium— 30.53. Tritium— 30.54. Uranium — 30.55. Xenon — 30.56. Yttrium — 30.57. Zinc— 30.58. Zirconium. Index 643 FOREWORD The advent of the cyclotron and the nuclear reacting pile has heralded what may be regarded, when viewed by future historians, as the beginning of an entirely new and spectacularly successful era of scientific development. For the physicist, high-energy accelerators have provided the means for unraveling the next and, as yet, the most difficult phase in our progressive understanding of the actual nature of matter. They have made the nucleus accessible to investigation in much the same way that the optical spectro- graph permitted an exhaustive study of the atom. The impact of radio- active materials and the half-dozen readily available nuclear radiations on medical research and the biological sciences has been no less profound than for the physical sciences. The rapidly developing tracer techniques have provided a research tool whose power of analysis has only begun to be fully utilized in biology. Although only a few' isotopes and nuclear radiations have as yet found a justifiable place in medical investigation, it is difficult at present to predict the medical applications that doubtless will be developed. In some respects, one of the important results of the development of artificial radioactivity has been the dissolution of the remaining barriers between the biological and physical sciences. Serious students of physics have now found a real challenge in the problems of biology and medicine. They are joining with the biologist in increasing numbers to form efficient research teams with virtually no limits to the fields of experience and knowl- edge from which they can draw. This book is an example of the concerted effort of physicists, biologists, and chemists. The data and the physical principles and methods so necessary to the intelligent use of tracers and nuclear radiations are to be found for the most part only in the literature of the physical sciences. In that form it is almost inaccessible to the biologist, and it is often inconveniently scattered for the physicist. With this problem in mind, the present volume was prepared in an effort to present the necessary data and methods in compact form. Having observed with considerable interest the development of the book from its beginnings, I feel certain it will serve an important function in supplementing the combined experience of research groups by providing a long needed technical reference. For those persons yet unfamiliar with the physical and biological literature in this field, it would appear to provide much of the fundamental material with which he must familiarize himself before attempting intelligent and useful investigations with isotopic tracers and nuclear radiations. John H. Lawrence xiii PART I Isotopes and Nuclear Radiations a CHAPTER 1 PROPERTIES OF NUCLEI 1.1. Stable Isotopes. Examination of the charge, mass, and abundance of existing isotopes has led to a set of empirical rules governing the structure of stable nuclei so far as the allowed numbers of protons and neutrons in a stable nucleus are concerned [l,2].x They are understood in a qualitative way from elementary considerations of the binding energies for various combina- tions of neutrons and protons and are strongly supported by the behavior of the radioactive isotopes. The fundamental requirement for stability of nuclei is satisfied when the binding energy is a maximum or, alternatively, the exact mass is a minimum for a given total number of nuclear particles. This may be regarded as equivalent to filling the lowest proton and neutron quantum levels in the nucleus. If the transformation of a proton to a neutron results in a greater binding energy or smaller exact atomic weight, the nucleus is unstable and the transformation will occur through K capture or positron emission. Con- versely, positron decay will reduce an excess number of neutrons to protons until the most stable configuration is reached, i.e., until lower lying proton levels are filled. On this basis the isotope rules can be explained and are borne out by the modes of decay of the radioactive isotopes. Formulation of the isotope rules is simplified with the aid of several designa- tions expressing the relation between numbers of neutrons and protons. Nuclei with the same number of protons Z but different atomic weights, or A — Z, are referred to as isotopes; nuclei with the same number of neutrons, A — Z, but different Z are isotones; and nuclei with the same A but different Z are isobars. Nuclei with even numbers of both protons and neutrons will be designated by (E, E) and those with even protons and odd neutrons by (E, O). Similar definitions hold for the designations (O, E) and (O, O). I. In a first approximation, nuclei contain equal numbers of protons and neutrons, i.e., Z = A/2. For the light elements this rule is followed exactly for the most abundant isotope. This can be understood if it is assumed that the nuclear force binding a neutron and proton (pn) is somewhat greater than the attraction between like particles (pp) and (nn). If the reverse were true, one would expect nuclei to consist wholly of neutrons, or neglecting electro- static repulsion, wholly of protons. Further, if forces between like particles 1 The numbers in brackets refer to the references at the end of the chapter. The refer- ences for this chapter appear on page 14. 3 4 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 (pp) and (nn) exist, they must be nearly equal in magnitude. Assuming that (nn) were greater than (pp), the maximum binding energy and, hence, greatest stability would occur for nuclei with a greater proportion of neutrons. Actually a variation in Z = A/2 of approximately 10 per cent does occur among the isotopes of light elements, but this appears to be insufficient to conclude that a significant difference exists between (nn) and (pp). The most stable configurations with respect to the purely nuclear forces, therefore, are equal numbers of protons and neutrons. In apparent variance with this, however, is the increase in the proportion of neutrons with increas- ing atomic weight where, in the heaviest stable isotopes, the ratio of the neutrons to protons reaches a value of 1.6. In these nuclei, however, the repulsive, long-range electrostatic field of the proton becomes a significant factor. The nuclear forces (np), (nn), and (pp) exhibit the property of saturation due to their short range and the finite size of the nucleons. A single particle, therefore, is unaffected by the intrinsically nuclear forces of more distant members of the nucleus, and the total binding energy is then proportional to the number of particles, A. The electrostatic field, on the other hand, does not show the property of saturation, and consequently each proton is affected by the presence of all other protons in the nucleus. Taken together the protons contribute a total electrostatic energy proportional to Z(Z - \)/R or Z(Z — l)A~tt which tends to diminish the effective total binding energy of the nucleus. In the lightest nuclei the electrostatic energy is less than 0.3 mev per particle, whereas the nuclear forces amount to approximately 8.5 mev per particle. For greater atomic weights the electro- static energy increases rapidly, and the most stable configuration for a given number of particles is one with a greater proportion of neutrons. A balance between the numbers of neutrons and protons for a given atomic weight is achieved which provides the maximum total binding energy. 2. (E, E) nuclei are the most stable. This fact is apparent from both the number and the relative abundance of such nuclei. Of the 278 known stable isotopes, this type includes 164, and where several isotopes of an element of even A exist the most abundant are (E, E). This is reasonable on the basis of Pauli's exclusion principle. Two particles can occupy the same state, i.e., with identical spatial coordinates, if their spins are different. Pairs of particles in nearly the same quantum state, it can be assumed, form closed shells in which they are strongly bound. If an odd particle is added to the nucleus, it forms an unclosed shell and is weakly bound by interaction with the closed shells. 3. (E, O) and (O, E) nuclei are about equally stable but less so than (E, E). Stable nuclei of these types are found to occur in about equal numbers; 58 are (E, 0) and 51 are (O, E). A single proton or neutron added to an (E, E) nucleus is less strongly bound through interaction with completed shells at Sec. 1.1] PROPERTIES OF NUCLEI 5 lower quantum levels as indicated under Rule 2. Nevertheless, such nuclei are stable against K capture or beta emission when the odd particle is added to the next lowest level. The type of stable nucleus that can be formed by the addition of a particle to an (E, E) nucleus of given atomic weight then depends upon the next lowest level to be filled. If this is a proton level but a neutron is added instead, the nucleus is unstable against beta decay and the neutron is transformed to a proton. 4. (0, 0) nuclei, with the exception of H2, Li6, B10, and N14, are unstable. The existence of only four such stable isotopes indicates immediately the relative instability of this type of nucleus in all but the lightest elements. If each proton-neutron pair occupies the same quantum state, the resulting nucleus is stable and the numbers of protons and neutrons are equal. If, however, the number of neutrons is greater by two or more, they will lie in successively higher levels above the last filled proton level and will transform by beta emission to the lower lying proton level to form nuclei of the type (0, 0). Thus, nuclei of this type are stable only if the numbers of protons and neutrons are equal. This condition carv be found, however, only for the lightest elements where the electrostatic forces are still small. In heavier elements, stable nuclei containing equal numbers of protons and neutrons cannot exist since the electrostatic repulsion then diminishes the nuclear binding energy as compared with nuclei with the same total number of particles but with a greater proportion of neutrons. 5. For any even Z, there exists only one or at the most two stable isotopes of odd A; if two, they differ by two mass units. Many isotopes of even A may exist. 6. For any odd Z, there exists only one or, at most, two isotopes; if two, they differ by two mass units. 7. For any even A, only two stable isobars may exist and they differ in charge by two units and are even in Z. 8. For any odd A , only one stable nucleus exists (no isobars) and its Z may be even or odd. A qualitative proof of rules 5, 6, 7, and 8 follows from energy considerations for the various possible combinations of protons and neutrons. A nucleus of mass A is stable only for that combination of protons and neutrons which provides the maximum binding energy or, alternatively, the minimum exact mass. This can be estimated from the principal terms in the binding-energy formula „ . . (A - 2Z)2 Z2 E = a A — b - A A* £ is a maximum when the last two terms are equal in magnitude and opposite in sign. This requires that {A — 2Z)/Z ~ A'& or that the excess of neutrons over protons increase as A^ for stable nuclei. Further, the binding energy of ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 nuclei of the same A varies as Z2 and is represented therefore by a parabola about the most stable value of Z located at or near the apex. For odd A , Z may be even or odd with equal probability as shown by the nearly equal numbers of these stable nuclei. The only isobar that is stable -4 -3 -2 -I Z +1 + 2 +3 +4 Fig. 1. Schematic diagram representing the cross section of the nuclear energy surface at odd and even isobars, (a) Cross section at odd nuclei. Only the nucleus at Z is stable, all others move toward this value of Z (and N) by /3_, /3+, and K transformation, (b) Cross section at even nuclei. Nuclei at Z + 1 and Z — 1 are stable since transition from one to the other is energetically impossible. All other nuclei are unstable, as indicated by arrows. is the one lying nearest the apex of the parabola. All other isobars are unstable and move toward the apex either by K capture or positron or nega- tron emission until the stable Z is reached, as shown in Fig. 1. Stated alternatively, isobars with neutrons in energy states higher than the next Sec. 1.3] PROPERTIES OF NUCLEI 7 unoccupied proton level will transform by beta emission until the lowest levels are filled. The converse holds for isobars with an excess of protons compared with the stable configuration. Such nuclei capture electrons or undergo positron emission transforming protons to neutrons in order to fill lower lying neutron levels. The binding energy of nuclei with even A must be represented by two parabolas on the same E axis: one containing (0, O) nuclei and a lower curve containing (E, E) nuclei, as shown in Fig. 1. From the possible combination of A particles, (Z, N), (Z - 1, N + 1), (Z - 2, N + 2) etc., and (Z + 1, N — 1), (Z + 2, N — 2) etc., which can form isobars, those with odd Z lie on the upper curve and can always transform to a nucleus on the lower curve by beta emission or K capture. By the same processes, isobars lying far up on the Z-even curve can cross to a lower level on the Z-odd curve. By successive transformations of this kind the isobar is brought finally to one of two possible stable nuclei occupying the lowest levels on the Z-even curve. If two points are stable, they must differ by two charge units. These nuclei cannot transform into each other despite a possible energy difference since either beta emission or K capture would take them first to a higher level on the Z-odd curve, which is energetically impossible, and no process is known for the simultaneous transformation of two charge units without also a change in mass. An exception to this is found only in the light nuclei H2, Li6, B10, and N14. Here, the Z-even and Z-odd curves are nearly superimposed because the contribution of the electrostatic field to the binding energy is negligible. The lowest state, therefore, lies at the apex of the Z-odd curve and Z = A - Z = N. 1.2. Mass Defect. Mass spectrographic measurements of the exact weight of nuclei indicate a consistent variation from the integral values of atomic weight. The difference between the integral atomic weight and the exact mass of an isotope, M, relative to O16 (A = 16.00000) is referred to as the mass defect AM. AM = M - A The mass defect is positive only for elements lighter than O16 and for the very heaviest elements. In all other cases it is negative. The variation in the mass defect over the entire mass range is of the order of 0.5 per cent or less. 1.3. Packing Fraction. The packing fraction/ or mass defect per elemen- tary particle is a quantity most frequently employed in experimental practice to express the deviation of the exact isotope weight from the integral atomic mass number. It is defined by the relation M - A AM f ~ A A 8 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Values of the known packing fractions are given in Table 2 and plotted in Fig. 2. The smooth curve is given by a semiempirical formula calculated by- Fowler [3]. / = -79.0 + 4.0^ + 242.1 £2 + ™* + 7.42 ^^ X 10"* where I = A — 2Z 1.4. Binding Energy. The exact atomic mass of an atom is in all cases less than the mass of an equivalent number of free neutrons and protons plus Z electrons. This mass difference is given by AM = M(A,z) - 1.008132Z - 1 .00893 U - Z) where 1.008132 is the mass of a proton plus one electron and 1.00893 is the neutron mass. The apparent decrease in the mass of elementary particles bound in a nucleus is exactly equivalent to the total binding energy of the particles. From Einstein's law of equivalence of mass and energy, the bind- ing energy is then E = AMc2. One mass unit (mass of 016/16) energy equivalent is 1 MU = 931.05 mev = 1.49 X 10"3 erg from which the binding energy of a nucleus may be calculated when its exact mass is known. A semiempirical formula for calculating the binding energy or the mass defect has been derived which is based mainly on the liquid-drop model of the nucleus [1,6,7]. The total binding energy of a nucleus of atomic weight A and charge Z may be expressed as the sum of a volume energy, a surface energy, a symmetry (or isotopic spin) energy [7], a coulomb or electrostatic energy, and a somewhat uncertain term involving the fluctuations associated with the even-odd combination of nuclear particles. Evaluation of explicit expressions for the terms has not yet been possible, but the factor to which each term is proportional is readily found as indicated below. With but few exceptions (deuterium and lithium notably) the average binding energy per nucleon in light and medium nuclei is approximately 8.5 mev. In the heaviest nuclei (Z > 82) the binding energy decreases to approximately 6 mev per particle. Over the greater part of the mass range of nuclei the total binding energy is roughly proportional to the number of nucleons or to the nuclear volume. Each particle is influenced by the short- range attractive fields of only those particles next to it and will remain unaffected by more distant particles in the nucleus. To a first approxi- mation then, saturation of the intrinsically nuclear forces leads to a volume energy that is proportional to the number of particles, A. Particles lying at the surface of the nucleus would not be expected to Sec. 1.4| PROPERTIES OF NUCLEI x o o 2 £ o I- < ,01 * N0I10VHJ 9NIX0Vd 10 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 exhibit complete saturation of their nuclear fields as do those lying deeper. The particle is bound to the nucleus by only a portion of its available energy, and the remainder cannot contribute to the total binding energy but gives rise, instead, to a surface tension analogous to that of a liquid drop. The total amount of the energy associated with the surface tension or unsaturated fields must be proportional to the nuclear surface and hence to A& if it is assumed that nuclear matter is incompressible. Referred to as surface energy, this term is deducted from the .binding energy first estimated from the nuclear volume. Since the volume-to-surface ratio increases with the radius as A1^, the relative magnitude of the surface effect in heavy nuclei is smaller than in light nuclei where it causes an appreciable reduction in the binding energy. The long-range electrostatic forces due to a uniform volume distribution of Z protons are taken into account by the third term. These fields cannot be saturated, and since their range is very much greater than nuclear dimensions, each proton is influenced by the repulsive electrostatic fields of the remaining Z — 1 protons. From electrostatics, this term is found to be proportional to Z(Z — \)/R ~ Z(Z — 1)/A^. The term is relatively unimportant in light nuclei where it amounts to but a small fraction of the energy but increases rapidly with atomic number and becomes, in the heaviest nuclei, a dominant factor in reducing the binding energy and, particularly, the stability against fission (see Fission, Chap. 6). The symmetry or isotopic-spin [7] energy term is based on the observation that the most stable nuclei are those for which Z = A/2. From the statisti- cal model of the nucleus [1,2,7] this effect is found to be proportional to P/A, where I = A — 2Z = N — Z is the isotopic number. The complete expression for the total binding energy may now be written E = aA + bA& + cZ(Z - 1)A~X + dPA~l + AE where [ O, for A odd Z even | AE = + eA~3/*, for A even Z odd _ The coefficients a, volume energy, b, surface energy, c, electrostatic energy, and d, symmetry energy, have been determined by fitting the equation to the packing-fraction curve of isotopes for which the masses have been measured with accuracy (see Table 2 and Fig. 2). Table 1 gives three sets of values based on calculations of coefficients in similar formulas for the packing fraction and exact atomic mass. The form of AE used here is based on that suggested by Deutsch [4]. For a detailed discussion of AE see reference 7. The semiempirical binding-energy formula above represents an energy surface in the form of a trough. Stable nuclei lie at points along the bottom Sec. 1.5] PROPERTIES OF NUCLEI 11 of the trough, while radioactive nuclei are found at points on the sides and move toward the bottom by emission of radiations. The packing fraction of an atom of atomic weight A and charge Z is found from the energy formula by dividing through by 9314. Similarly an esti- mate of the exact mass of the atom is obtained by dividing the formula by 931 and adding the terms 1.00893(4 - Z) + 1.00812Z. The detailed structure of the observed packing-fraction curve for stable isotopes is not accounted for by the semiempirical formula since it is evaluated Table 1. Semiempirical Binding Energy Coefficients Values, mev Reference a b c d e -14.66 -15.30 -13.97 15.4 16.75 13.0 0.602 0.69 0.58 20.54 22.55 38.63 33.5 Mattauch [2] Fowler [3] Deutsch [4] by an averaging process and no terms of short period are included. A closer fit to the fluctuations in the actual curve must await more detailed informa- tion on nuclear structure. The total binding energy is an important criterion of nuclear stability. At least the lightest nuclei are stable against spontaneous radioactive decay only when their binding energy is greater, i.e., their mass is less, than that for any combination of lighter nuclei containing the same total number of protons and neutrons. An important application of binding energy is found in the calculation of the exact atomic mass of radioactive nuclei. In the case of beta decay, the energy released (rest mass plus kinetic energy) is exactly equivalent to the difference in the atomic masses of the initial and final atoms, i.e., E = c2(Mz — Mz+i). When a positron is emitted, however, the residual atom is lighter by the equivalent energy carried off by the particle together with its rest energy plus the rest energy of an orbital electron which is also lost. E = c2(Mz — MZ-i — 2m), where m is the mass of the positron. Similarly, when an alpha particle is emitted, the energy release is E = c2{MA,z — Af(4_4,z_2) — 2m). It must be kept in mind, however, that when gamma radiation is emitted its energy must also be taken into account. 1.5. Nuclear Spin. The resultant angular momentum or spin of a nucleus is observed in all instances to be either half-integer or integer multiples of h/2ir. In particular, the spins of all nuclei with even atomic weight are integral multiples of h/2ir, while for nuclei of odd atomic number, the spins are 12 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 half-integer value. In most stable, unexcited nuclei the spin is less than 4///27T, and for all nuclei of the even-even type it is zero. The resultant angular momentum of a nucleus is presumably the vector sum of the orbital angular momenta of all the particles and the intrinsic spin of each particle, added according to the vector rules of quantum theory. The orbital angular momentum is always an integer multiple of h/2ir if the same quantum condi- tions hold here as for the orbital electrons. The vector sums therefore are also integers. The spin of both the neutron and proton are known from experimental evidence to be one-half, and if two such particles occupy the same quantum state, their spins must be orientated parallel or antiparallel. The contribution of the particle spins to the total nuclear spin will therefore be an integer or half-integer for even or odd numbers of particles, respectively. A sufficiently detailed and consistent model of the nucleus has not yet been formulated which will provide the exact magnitude of the spin for a nucleus containing a prescribed number of protons and neutrons. But the qualita- tive conclusions outlined above regarding the origin and the necessary magni- tudes of nuclear spin are borne out by experiment. Further, if the spin of a stable isotope (Z, A) is known, it is safe to conclude that the spin of a stable nucleus with which it is isotopic will differ by one-half the number of excess neutrons, i.e., i = (i0/2)(A — A0), where i0 is the known spin for the isotope of atomic weight A0, and A, the atomic weight of a stable isotopic nucleus. The spin of a radioactive nucleus, on the other hand, will depend on its state of excitation and will differ from the ground state, usually by integral units of spin. If a beta particle, for example, is emitted, the nuclear spin always changes by an integral value, including zero, since the ejected beta particle and neutrino each have an intrinsic spin of one-half. In any nuclear reaction, spin and angular momentum must be conserved as well as mass and energy. Known values of nuclear spins in units of h/2x are given in Table 3 page 22 for stable nuclei. 1.6. Magnetic Dipole Moment. Assuming the particles within a nucleus to be in motion, it is to be expected that a magnetic field will be produced by the current distribution of at least the charged particles. A single proton moving in a circular orbit with a frequency v and angular momentum lh/2ir represents a circulating current of magnitude equal to i — ev and produces a field equivalent to a magnetic shell with a magnetic moment of leh . The unit n0 is referred to as the nuclear magneton. Because of the relative magnitudes of the masses of the electron and proton it is smaller than the Bohr magneton by the factor 1,840. Sec. 1.7] PROPERTIES OF NUCLEI 13 Without a more detailed knowledge of the structure and the motions of particles in nucleus, the magnetic moment must be determined experi- mentally. Both the proton and neutron themselves have a magnetic moment which also must be determined experimentally because the charge distribu- tion in elementary particles is not known. Although the magnetic moment of the electron is determined directly by its spin and angular momentum, this is not true of the proton and neutron, neither of which have magnetic moments of one nuclear magneton, the value suggested by the ratio of their masses to that of the electron. This discrepancy between nuclear angular moments and the corresponding magnetic moments is taken into account by the formal introduction of a nuclear g factor which is defined as the ratio of the magnetic moment in units of nuclear magnetons, n0, to the angular momentum in units of h/2ir. Thus, the magnetic moment in units of nuclear magnetons is n = ig, where i is the nuclear spin in units of h/2ir. Most experimental methods give the nuclear g factor directly, and if the spin is known, ju is given the simple product as indicated above. Known experimental values of n are given'in Table 3. 1.7. Electric Quadrupole Moment. From the theory of electrostatics it is known that the potential field of an arbitrary charge distribution can be expressed in a series of terms of the form v = — + -Pi (cos e) + ±p, (cos e) + • • • r r- r where P< (cos 6) are Legendre polynomials. At large distances compared with the dimensions of the charge distribution, only the first term, represent- ing a spherically symmetric or coulomb field, is important since all other terms diminish as 1/r2 or faster. Thus, at distances large compared with the nuclear radius the electrostatic field is equivalent to a point source of charge eZ. The second term, representing an electric dipole, does not exist for nuclei since it vanishes for radially symmetric charge distributions containing charge of only one sign. The third term, representing the electric quadrupole, may, however, exist for nuclei in which protons are not distributed throughout the nucleus with strict spherical symmetry. A small contribution to the electric field is then made by the quadrupole moment which in effect alters the spherically symmetric form of the stronger coulomb field but only within a distance of a few times the nuclear radius. It is reasonable to assume in a first approxi- mation that the asymmetry takes the simplest form of distortion of a sphere which is that of an ellipsoid of rotation. Then from electrostatics the nucleus will be cigar-shaped or a prolate spheroid when q is positive, and platter-shaped or an oblate spheroid when q is negative. 14 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 REFERENCES FOR CHAP. 1 1. Bethe, H. A., and R. F. Bacher: Rev. Mod. Phys., 8, 82 (1936). 2. Mattauch, J., and S. Fluegge: "Nuclear Physics Tables," 1946. 3. Fowler, W. A.: Private communication. Coefficients determined from data of Mattauch, and Duckworth and Dempster by the method of least squares to give best fit to packing-fraction data. 4. Deutsch, M.: "Science and Engineering of Nuclear Power,"Vol. 1, C. Goodman, ed., Addison-Wesley Press Inc., Cambridge, Mass., 1947. 5. Heisenberg, W.: Rapport du VII Congres Salvay, Paris, 1934. 6. Weizsacker, C. F. V.: Physik. Z., 96, 431 (1935). 7. Feenberg, E.: Rev. Mod. Phys., 19, 239 (1947). Sec. 1.7] PROPERTIES OF NUCLEI 15 Table 2. Atomic Weight and Natural Abundance of Isotopes An asterisk (*) indicates that the isotope is radioactive. The relative abundances of most medium and heavy elements are subject to some uncertainty since values reported by various investigators differ by as much as 50 per cent for the rare isotopes and as much as 10 per cent for the more abundant. Isotop e Abundance, Atomic weight O16 = 16 000000 Packing fraction Chemical atomic Z El. A per cent \_j x \-j * wv/v/x/v * Error X 105 mu X 104 mu weight 1 H 1 99 . 9844 1.008123 + 0.6 81.2 1.00785 2 0.0156 2.014708 ± 1.1 73.6 2 He 3 4 1.3 X lO^4 ~ 100. 3.01700 ± 4. 4 . 00390 ± 3 . 56.7 9.8 4 . 003 3 Li 6 7.39 6.01697 ± 5. 20.3 6.940 7 92.61 7.01822 ± 6. 26.0 4 Be 9 100. 9.01503 ± 6. 16.4 9.02 5 B 10 18.83 10.01677 ± 8. 16.7 10.82 11 81.17 11.01244 ± 19. 11.3 6 C 12 98.9 12.00382 ± 4., 3.2 12.010 13 1 1 13.007581 ± 2.5 5.8 7 N 14 99.62 14.00751 ± 4. 5.4 14.008 15 0.38 15.004934 + 3. 3.3 8 0 16 99.76 16.000000 0.0 16.00000 17 0.04 17.00450 ± 6. 2.7 18 0.20 18.0049 ± 40. 2.7 9 F 19 100. 19.00452 + 17. 2.4 19.00 10 Ne 20 90.00 19.99877 ± 10. -0.6 20.183 21 0.27 20 . 99963 + 22 . -0.2 22 9.73 21.99844 ± 36. -0.7 11 Na 23 100. 22.99618 ± 31. -1.7 22.997 12 Mg 24 78.60 23.9924 + 60. -3.2 24.32 25 10.11 24.9938 ± 90. -2.5 26 11.29 25.9898 ± 50. -3.9 13 Al 27 100. 26.9899 ± 80. -3.7 26.97 14 Si 28 92.28 27.9866 ± 60. -4.6 28.086 29 4.67 28.9866 ± 60. -4.5 15 P 30 31 3.05 100. 29.9832 ± 90. 30.9842 ± 50. -5.7 -5.2 30.98 16 S 32 95.1 31.98089 ± 7. -6.0 32.06 33 0.74 32.9800 + 60. -5.2 34 4.2 33.97710 + 35. -6.5 17 CI 36 35 0.016 75.4 35.978 ± 100. 34.97867 + 21. -6.1 -6.1 35 . 457 18 A 37 36 24.6 0.307 36.97750 ± 14. 35.9780 + 100. -6.1 -6.8 39.944 38 0.061 37.974 ± 250. -6.8 19 K 40 39 99.632 93.44 39.97504 ± 26. 38.9747 -6.5 39.096 40* 0.012 39.9760 ± 100. -6.0 20 Ca 41 40 42 6.55 96.96 0.64 40.974 39.9753 ±150. 41.9711 -6.3 -6.2 -6.8 40.08 16 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Table 2. Atomic Weight and Natural Abundance of Isotopes — (Continued) Isotop e 4 1 1 Atomic weight Packing Chemical Abundance, O16 = 16.000000. Error X 10B mu fraction X 10" mu atomic weight Z El. A per cent 20 Ca 43 44 46 48 0.15 2.06 0.0033 0.-185 42.9723 -6.3 21 Sc 45 100. 44.9689 + 100. -6.8 45.10 22 Ti 46 7.95 45.9661 ± 100. -7.4 47.90 47 7.75 46.9647 ± 100. -7.5 48 73.45 47.9651 ± 50. -7.3 49 5.51 48.9646 ± 60. -7.2 50 5.34 49.9646 ± 40. -7.6 23 V 51 100. 50.9577 ± 50. -8.3 50.95 24 Cr 50 4.49 49.96443 ± 3.9 -7.11 52.01 52 83.75 51.95589 ± 4.4 -8.47 53 9.55 52.95527 ± 4.4 -8.44 54 2.38 53.95427 + 4.8 -8.47 25 Mn 55 100. 54.965 -6.4 54.93 26 Fe 54 5.81 53.95774 ± 4.8 -7.83 55.84 56 91.66 55.95340 ± 2.7 -8.32 57 2.20 56.95485 ± 5.2 -7.92 58 0.33 57.95091 ± 4.9 -8.46 27 Co 59 58 100. 67.76 -7.0 58.94 28 Ni 57.95939+ 40. 58.69 60 26.16 59.94951 + 31. -8.4 61 1.21 60.9537 ± 150. -7.6 62 3.66 61.94928+ 40. -8.2 64 1.16 63.94712 ± 56 -8.4 29 Cu 63 69.09 62 . 956 Mean 63.542 65 30.91 64.955 -8.13 30 Zn 64 48.89 63.95365 + 6.6 -7.24 65.38 66 27.81 65.94676 + 4.2 -8.07 67 4.07 66.94826 + 3.8 -7.71 68 18.61 67.94885 +6.5 -7.53 70 0.620 69.9461 ± 17. -7.69 31 Ga 69 61.2 68.955 -6.5 69.72 71 38.8 70.953 -6.6 32 Ge 70 72 20.55 27.37 72.60 73 7.61 74 36.74 76 7.67 33 As 75 74 76 100. 0.87 9.02 74.91 34 Se 78.96 Sec. 1.7] PROPERTIES OF NUCLEI 17 Table 2. Atomic Weight and Natural Abundance of Isotopes — {Continued) Isotop e Abundance, per cent Atomic weight O16 = 16.000000. Error X 105 mu Packing fraction X 104 mu Chemical atomir Z El. A weight 34 Se 77 78 80 7.58 23.52 49.82 35 Br 82 79 9.19 50.53 79.94438±5.0 -7.04 79.916 81 49.47 80.94228+3.8 -7.12 36 Kr 78 80 0.342 2.223 77.945 -7.0 83.7 82 11.50 81.939 -7.5 83 11.48 84 57.02 83.938 -7.3 86 17.43 85.939 -7.1 37 Rb 85 87* 72.8 27.2 85.48 • 38 Sr 84 86 0.56 9.86 87.63 87 7.02 88 82.56 39 Y 89 90 91 100. 51.51 11.27 88.92 40 Zr 91.22 92 17.14 94 17.30 96 2.78 41 Cb 93 92 94 100. 15.86 9.12 92.91 42 Mo 95.95 95 15.70 94 . 945 -5.8 96 16.50 95 . 946 -5.6 97 9.45 96.945 -5.8 98 23.75 97.944 -5.7 100 9.63 43 Tc 99 44 Ru 96 98 5.68 2.22 95.946 -5.7 101.7 99 100 12.81 12.70 98.944 -5.7 101 16.98 102 31.34 104 18.27 45 Rh 103 102 104 100. 0.8 9.3 -5.2 102.91 46 Pd 106.7 103.946 18 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Table 2. Atomic Weight and Natural Abundance of Isotopes — (Continued) Isotope Abundance, Atomic weight O16 = 16.000000. Packing fraction Chemical atomic Z El. A per cent Error X 105 mu X 104 mu weight 46 Pd 105 22.6 104.945 -5.2 106 27.2 105.945 -5.2 108 26.8 • 107.943 -5.2 110 13.5 109.942 -5.2 47 Ag 107 51.35 106.948 -4.8 107.880 109 48.65 108.947 -4.8 48 Cd 106 108 1.215 0.875 112.41 110 12.39 111 12.75 112 24.07 113 12.26 114 28.86 116 7.58 49 In 113 115 4.23 95.77 114.76 50 Sn 112 114 0.90 0.61 118.70 115 0.35 116 14.07 115.942 -5.0 117 7.54 118 23.98 117.939 -5.1 119 8.62 118.938 -5.2 120 33.03 119.94 -6. 122 4.78 121.944 -4.6 124 6.11 123.943 -4.6 51 Sb 121 123 57.25 42 . 75 121.76 52 Te 120 122 0.091 2.49 127.64 123 0.89 124 4.63 125 7.01 126 18.72 128 31.72 130 34.46 53 I 127 124 126 100. 0.094 0.088 126.92 54 Xe 131.3 128 1.90 129 26.23 128.946 -4.2 130 4.07 131 21.17 Sec. 1.7] PROPERTIES OF NUCLEI 19 Table 2. Atomic Weight and Natural Abundance of Isotopes — {Continued) Isotope Atomic weight Packing Chemical Abundance, O16 = 16 000000 fraction atomic Z El. A per cent Error X 106 mu X 104 mu weight 54 Xe 132 134 136 26.96 10.54 8.95 131.946 -4.4 55 Cs 133 100. 132.91 56 Ba 130 0.101 137.36 132 0.097 134 2.42 135 6.59 136 7.81 137 11.32 138 71.66 57 La 138 139 0.089 99.911 -3.2 138.92 138.955 58 Ce 136 138 0.193 0.250 ' 140.13 140 88.48 142 11.07 59 Pr 141 142 143 100. 27.27 12.26 140.92 60 Nd 144.27 144 23.95 145 8". 27 146 17.06 145.960 -2.8 148 5.66 147.961 -2.7 150 5.53 149.967 -2.2 61 Pm 144 150.43 62 Sm 3.16 147 15.07 148* 11.27 149 13.85 150 7.47 152 26.63 154 22.53 63 Eu 151 153 47.77 52.23 152.0 64 Gd 152 154 0.21 2.14 156.9 155 14.86 154.977 -1.5 156 20.61 155.976 -1.5 157 15.66 156.976 -1.5 158 24.75 160 21.77 65 Tb 159 100. 159.2 20 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Table 2. Atomic Weight and Natural Abundance of Isotopes — (Continued) Isotope A 1_ J Atomic weight Packing Chemical Abundance, O16 = 16.000000 Error X 106 mu fraction X 10* mu atomic weight Z El. A per cent 66 Dy 156 158 0.0524 0.0902 162.46 160 2.294' 161 18.88 162 25.53 163 24.97 164 28.18 67 Ho 165 100. 0.1 1.5 164.935 68 Er 162 167.2 164 166 32.9 167 24.4 168 26.9 170 14.2 69 Tm 169 100. 0.06 4.21 169.4 70 Yb 168 173.04 170 171 14.26 172 21.49 173 17.02 174 29.58 176 13.38 71 Lu 175 97.5 2.5 174.99 176* 72 Hf 174 0.18 5.30 178.6 176 177 18.47 178 27.10 179 13.84 180 35.11 73 Ta 181 100. 0.135 26.41 180.88 74 W 180 183.88 182 183 14.40 184 30.64 186 28.41 75 Re 185 37.07 62.92 186.31 187 76 Os 184 0.018 1.59 190.2 186 187 1.64 188 13.3 189 16.1 Sec. 1.7] PROPERTIES OF NUCLEI 21 Table 2. Atomic Weight and Natural Abundance of Isotopes — {Continued) Isotope Abundance, Atomic weight Packing Chemical O16 = 16.000000. Error X 105 mu fraction X 104 mu atomic weight Z El. A per cent 76 Os 190 26.4 190.038 2.0 192 41.0 192.038 2.0 77 Ir 191 38.5 191.040 2.1 193.1 193 61.5 193.941 2.1 78 Pt 192 0.78 195.23 194 32.8 194.040 2.0 195 33.7 195.040 2.0 196 25.4 196.039 2.0 198 7.23 198.044 2.2 79 Au 197 100. 197.039 2.0 197.2 80 Hg 196 198 199 0.15 10.12 17.04 200.61 200 23.25 200.028 1.4 201 13.18 202 29.54 204 6.72 81 Tl 203 29.1 203.057 2.8 204.39 205 70.9 205.057 2.8 82 Pb 204 206 207 1.5 23.6 22.6 204.058 2.8 207.21 208 52.3 208.057 2.7 83 Bi 209 100. 209 . 055 2.6 209.00 84 Po 85 At 86 Rn 222* 222 87 Fa 88 Ra 223* 224* 226.05 226* 89 Ac 227* 100. 90 Th 232* 100 232.12 5.2 232.12 91 Pa 231* 92 U 234* 235* 0.006 0.720 238.07 238* 99.274 238.14 5.6 93 Np 238* 94 Pu 239* 95 Am 241* 96 Cm 242* 22 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Table 3. Spin, Magnetic Moment, and Quadrupole Moment of Stable Isotopes An asterisk * indicates that the isotope is radioactive. A dagger t indicates that the quadrupole moment is in megacycles. The letters and numbers in brackets refer to the references given at the end of the table. Isotope Spin t„ Units of h Magnetic moment, y.,, Units of he/lMc Quad. mom. 10-" cm2 Z El. A 0 n 1 y% -1.9103 ± 0.0012 [F3.P2.H7.A1.A3] 1 H 1 Yi [H8.K1] 2.7896 [K2.M15] ^n/Mp _ -0.6847 + 0.0004 2 1 [MIS] 0.85647 + 0.0003 [A3.K3] y.d/y.p = 0.30702 ± 0.0001 H'/ft* = 3.25719 ± 0.00002 [B7] 2.73 [K2] 2 He 3 M 4 0 [B5] 0.0 3 Li 6 1 [M2] 0.8213 [R2.R3.M8] 7 H [H2.G5.S6.F2] 3.2532 [R2,R3,M8J4] 4 Be 9 % -1.176 [K13] 5 B 10 l 0.597 ± 0.003 [M9] 11 H 2.686 ± 0.005 [M9] 6 C 12 0 [B17] 13 H 0.701 ± 0.004 [H3] 7 N 14 l [01] 0.402 + 0.002 [M18.K14] 15 X [K12.W3] -0.280 ± 0.003 [Zl] 8 0 16 17 18 0 0 [B17] 9 F 19 x [Gl.Cl] 2.622 + 0.014 [R2.R3.M8] 10 Ne 20 21 22 0 0 11 Na 23 % [Jl,G3,El,Rl] 2.216 + 0.011 [K14] 12 Mg 24 25 26 0 0 13 Al 27 % [H6.M10] 3.628 ± 0.010 [M10] 14 Si 28 29 30 0 0 15 P 31 X [J6.A2] ±1.1314 ± 0.0013 [P3] 16 S 32 33 34 36 0 0 0 [B5] 17 CI 35 *A [T7] 1.365 ± 0.005 [K15] -84 + 4t [T7] 37 X [T7] -1.135 ± 0.005 [K15] -64 ± 4t [T7[ 18 A 36 38 40 0 0 0 19 K 39 X [M6.F2] 0.391 ± 0.002 [K14] 40* 4 - 1 . 290 41 X [Ml] 0.217 ± 0.001 [M1.K14] 20 Ca 40 42 43 0 0 Sec. 1.7] PROPERTIES OF NUCLEI 23 Table 3. Spin, Magnetic Moment, and Quadrupole Moment of Stable Isotopes- (Conlinued) Isotope Spin »',, Units of h Magnetic moment, iio Units of he/lMc Quad. mom. 10-" cm' Z El. A 20 Ca 44 46 48 0 0 0 21 Sc 45 7A [S14.K7] 4.8 [K10] 22 Ti 46 47 48 49 50 0 0 0 23 V 51 A [K9] 24 Cr 50 52 53 54 0 0 0 25 Mn 55 A [W2.F1] 3.0 . [Fl] 26 Fe 54 56 57 58 0 0 0 27 Co 59 A [K8,M11,R5] 2-3 [Mil] 28 Ni 58 60 61 62 64 0 0 0 0 29 Cu 63 % [R81 2.5 [S21.S26] -0.1 ± 0.1 [S21] 65 H [R8] -2.6 [S21.S26] ^,66/^63 = i .04 -0.1 ± 0.1 [S21] 30 Zn 64 66 0 0 67 A [LI] 0.9 [LI] 68 0 70 0 31 Ga 69 H [J1.C6] 2.0165 ± 0.0035 [P3] 0.20 [R6] 71 A [J1.C6] 2.5611 ± 0.0030 [P3] ^71/^89 = 1.270 0.13 [R6] 32 Ge 70 72 73 74 76 0 0 0 0 33 As 75 H [T8.C7.C3] 1.5 [C3.S22] 0.3 [S221 34 Se 74 76 77 78 80 82 0 0 0 0 0 [W5] 35 Br 79 H [T1.T7] 2.61 [T1.S2] 720 ± 10f [T7] 81 A [T1.T7] 2.61 [T1.S2] ^79^81 = 1.0 556 ± 10f [T7] 24 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Table 3. Spin, Magnetic Moment, and Quadrupole Moment of Stable Isotopes — {Continued) Isotope Spin »"0 Units of h Magnetic moment, /i„ Units of he/2Mc Quad. mom. 10~24 cm' Z El. A 36 Kr 78 0 80 0 82 0 83 % [Kll] -0.967 [K17] 0.15 [K11.S26] 84 0 86 0 37 Rb 85 SA [K16J8.M19] 1.345 ± 0.005 [K14] 87* % [H10.M20.H9] 2.741 ± 0.009 [K14] 38 Sr 84 86 0 0 87 % [H5] -1.1 Q [H5] 88 0 1 39 Y 89 H >0.1 40 Zr 90 91 92 94 96 0 0 0 0 41 Cb 93 % [B6] 5.3 [M24] 42 Mo 92 94 95 96 97 98 100 0 0 0 Yl 0 0 43 Tc 99 44 Ru 96 98 99 100 101 102 104 0 0 0 0 0 45 Rh 103 X [F5] 46 Pd 102 104 105 106 108 110 0 0 0 0 0 47 Ag 107 H tJ3] -0.10 [J3] 109 H [J3] -0.19 [J3] Mi09/Ali07 = 1 . 93 48 Cd 106 108 110 0 0 0 111 Yi [S5.S7.S10] -0.65 [J6.B5] 112 0 113 H [S5.S7.S10] -0.65 [J9.B5] ,,113/^Ul =1.0 % Sec. 1.7] PROPERTIES OF NUCLEI 25 Table 3. Spin, Magnetic Moment, and Quadrupole Moment of Stable Isotopes — {Continued) Isotope Spin i0 Units of h Magnetic moment, /i0 Units of he/lMc Z El. A 48 Cd 114 116 0 0 49 In 113 % [B1.M7] 6.4 [B1.M7] 115 % [J2.P1.M7] 5.49 [Hi] 50 Sn 112 114 0 0 115 H -0.9 [T2] 116 0 117 H [T2.S11] -0.89 [T2] 118 0 119 H [T2.S11] -0.89 [T2] 120 0 122 0 124 0 51 Sb 121 H [B3.T3.C3] 3.7 ' [C3,B5] 123 7 £ [B3.C3] 2.8 [C3.B5] M121/M123 = 1.316 52 Te 120 122 123 124 125 126 128 130 0 0 0 0 0 0 53 I 127 *A [T4.M13] 2.8122 [P3] 54 Xe 124 126 128 0 0 0 129 3-2 [K6J7] -0.9 [K6J7.B5] 130 0 131 ?2 [K6J7] 0.8 [K6J7.B5] Mi!yMi3i = -l.n 132 0 134 0 136 0 55 Cs 133 Vi [K4.C8] 2.572 ± 0.013 [K14] 56 Ba 130 132 134 0 0 0 135 ?2 [B4] 0.837 + 0.003 [H4] 136 0 137 % [B4] (0.936 ± 0.003) [H4] 138 0 57 La 139 7A [A4] 2.5 - 2.8 [A5,C4,C5] 58 Ce 136 138 140 142 0 0 0 0 59 Pr 141 H [W1J Quad. mom. 10-24 cm2 0.82 [B1.S24] -0.46 + 0. 15 [S3.S4.M14] 0 ± 0.1 [K11.S26] < 0.3 [S6.K4] 26 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 Table 3. Spin, Magnetic Moment, and Quadrupole Moment of Stable Isotopes — {Continued) Isotope Spin io Units of h Magnetic moment, \i0 Units of he/2Mc Quad. 10-:< mom. cm' Z El. A 60 Nd 142 143 144 145 146 148 150 0 0 0 0 0 61* 62 Sm 144 147 148* 149 150 152 154 0 0 0 0 63 Eu 151 % [S17] 3.4 [S17.S2] — 1.2 [S17.C21 153 % [SI 7] 1.5 [S17.S2] Mui/Mi53 = 2.24 ~2.5 [S26J 64 Gd 152 154 155 156 157 158 160 0 0 0 0 0 65 Tb 159 SA [SI 3] 66 Dy 159 160 161 162 163 164 0 0 0 67 Ho 165 % [SI 8] 68 Er 162 164 166 167 168 170 0 0 0 0 0 69 Tin 169 H [SI 5] 70 Yb 168 170 0 0 171 X [S26] 0.45 [S27] 172 0 173 y2 [S26] -0.65 [S27] M173/M171 = 1.4 3.9 + 0 4 [S26] 174 0 176 0 71 Lu 175 V2 [S19.G2] 2.6 ± 0.5 [G2] 5.9 [G2] 176 [Hll,M21,L2,S28] 3.8 ± 0.7 [S28] 6-8 [S28] Sec. 1.7] PROPERTIES OF NUCLEI 27 Table 3. Spin, Magnetic Moment, and Quadrupole Moment of Stable Isotopes- (Conlinued) Isotope Spin to Magnetic moment, y.„ Quad. mom. Units of h Units of he/2Mc 10"24 cm' Z El. A 72 Hf 174 176 0 0 177 <3A [R4] 178 0 179 <% [R4] 180 0 73 Ta 181 A [M22] 2.1 ~6 [S29] 74 W 180 182 183 184 186 0 0 0 0 75 Re 185 *2 [M4,M5,G4,Z2] 3.3 [S25.S26] 2.8 [S25.S26] 187 H [M4,M5,G4,Z2] 3.3 [S25.S26] 2.6 [S25.S26] 76 Os 184 186 187 188 189 190 192 0 0 0 H 0 0 77 Ir 191 A [V2] M191/M193 = -1.0 [V2] 193 % [V2] 78 Pt 192 194 0 0 195 A [F4,V1J5,T5] 0.6 [J5.T5.S1] 196 0 198 0 79 Au 197 («) [R7.W4] 80 Hg 196 198 0 0 0.3 [R7.W4.S16.B5] 199 lA [S8.S9] 0.547 ± 0.002 [M12] 200 0 201 3A [S8.S9] -0.607 ± 0.003 [M12] Mi99/M2oi = -0.9018 [S19] 0.5 [S301 202 0 204 0 81 Tl 203 y% [M23.M17.S31] 1.45 [S24] 205 A [M23.M17.S31] 1.45 [S24] 82 204 206 0 0 207 H [K5] 0.6 [M3,R9,S16,B5] 208 0 83 Bi 209 A [B2] 3.6 [S16.S26] -0.39 [S20] 28 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 REFERENCES FOR TABLE 3 A 1 Alvarez, L. W., and F. Bloch: Phys. Rev., 67, 111 (1940). 2 Ashley, M.: Phys. Rev., 44, 919 (1933). 3 Arnold, W. R., and A. Roberts: Phys. Rev., 71, 878 (1947). 4 Anderson, O. E.: Phys. 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The energy of a gamma photon is directly proportional to the frequency: E = hv = hc/\, where the factor of the proportionality, h, is Planck's con- stant, c is the velocity of light, and X is the wavelength. In units of mev, E = 0.012354/A where X is in angstroms. Also associated with the photon is a momentum of magnitude p = hv/c = h/\. In any process involving the interaction of a gamma photon with an atom or any elementary particle, both the energy and momentum must be distributed according to the laws of conservation among the various particles and radiations participating. In the collision of a photon with an atom, a large proportion of the momentum is transferred to the atom and the greater part of energy is transferred to an orbital electron which is ejected from the atom. Gamma-ray absorption is due almost entirely to interaction of photons with free and bound electrons in an absorbing medium. Each absorption event, involving a single photon and an electron, takes place by one of three distinct interaction processes: (1) photoelectric effect, cross section designated by t; (2) scattering (Compton effect), cross section designated by a; (3) pair formation, cross section designated by k. The relative importance of each process as well as the absolute probability for its occurrence bears a strong dependence on gamma-ray energy and the atomic number of the absorber. In principle, the total effective electronic cross section over the entire energy range is represented by the sum of t, a, and k, but in limited ranges contribu- tions from more than one process may be negligible. At very low energies only the photoelectric effect is important, particularly in heavy elements. Scattering becomes the dominant process at medium energies, and for high energies pair formation is mainly responsible for gamma-ray absorption. Again, in certain portions of the energy range, pairs of processes, either t and a or a and k, must be considered in gamma-ray absorption because the cross sections for the processes are then comparable in magnitude. The simplest problem in gamma-ray absorption and the one most fre- quently encountered in experimental arrangements is that of a well-colli- mated beam of radiation. Geometrical reduction in intensity does not enter, 32 Sec. 2.1] GAMMA RAYS 33 and photons scattered by the Compton effect are regarded as lost since they no longer contribute to the intensity of the collimated primary beam. Thus since each absorption event involves the complete removal of a single photon, the energy is not degraded as in the absorption of charged particles and the cross sections, therefore, remain constant. Consequently the reduction in energy flux, or intensity, is due wholly to the reduction in the number of photons and not the energy per photon. The rate at which the beam intensity or the number of photons decreases at any depth x in an absorber is then directly proportional to the depth. dl Tx = -^ Therefore if the absorber is homogeneous the gamma-ray intensity decreases exponentially with absorber thickness. / = I0e^x where I0 = intensity at surface y. = absorption coefficient The physical significance of the absorption coefficient is apparent from the fact that when x = 1/n the intensity is reduced to l/e of its value at the surface of the absorber. When * is measured in units of length, p is referred to as the linear-absorption coefficient and is expressed in cm""1. Other units also can be used and sometimes are found more useful. A form that is frequently used is the mass-absorption coefficient pm expressed in square centimeters per gram when x is measured in units of grams per square centi- meter. This is related to the linear-absorption coefficient by pTO = p./p, where p is the density of the absorbing material. This form of the coefficient has the advantages of being an easy and more certain quantity to measure and is independent of the physical state of the absorber. Two other forms are also important in that they relate the linear and mass coefficients to values that can be calculated. The first is the electronic coefficient pe which is simply the cross section per electron, or pe = re + ae + x-e- The second is the atomic- absorption coefficient or atomic cross section pa, which is equal to \ieZ. The relationship between the four coefficients is then ill = p/JLm = pXna = pNZfXe where N = N0/A = number of atoms per gm N0 = Avogadro's number A = atomic weight Z = atomic number Instead of expressing gamma-ray absorption in terms of absorption coeffi- cients it is sometimes more explicitly stated in units of half- value layers of 34 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 2 the particular absorber. One half-value layer is the quantity of material, either in grams per square centimeter or in centimeters, required to reduce the intensity of gamma rays of a particular energy to one-half its initial value at the surface. In terms of the absorption coefficient in corresponding units the half-value layer is T^ = 0.693 //x. The gamma-ray intensity after tra- versing n half- value layers is then I = I0 2~~n. Table 4. Mass-absorption Coefficients for Gamma Rays Data taken from "Handbook of Chemistry and Physics," 30th ed., Chemical Rubber Publishing Company, Cleveland, by permission of the publisher. Energy, Mass-absorption coefficients, cm2 per gm mev H C O Al Fe Cu Au Pb 0 . 0296 0.0465 0.0617 0.0705 0.0845 0.0951 0.1260 0.1545 0.1717 0.193 0.2470 0.3085 0.4118 0.5147 1 . 2354 2 . 4708 0.390 0.385 0.375 0.360 0.340 0.320 0.280 0.255 0.250 0.245 0.205 0.180 0.165 0.117 0.078 0.256 0.185 0.175 0.163 0.155 0.152 0.142 0.137 0.136 0.130 0.110 0.095 0.080 0.059 0.0385 0.372 0.210 0.183 0.169 0.162 0.157 0.144 0.137 0.130 1.170 0.402 0.270 0.228 0.195 0.186 0.156 0.146 0.143 0.130 0.115 0.105 0.093 0.079 0.058 0.038 8.45 2.28 1.10 0.800 0.520 0.424 0.265 0.235 0.202 0.178 0.140 0.118 0.095 0.080 0.058 11.45 3.16 1.55 1.12 0.680 0.551 0.325 0.268 0.232 0.198 0.155 0.126 0.100 0.081 0.057 0.038 28.4 8.3 4.40 3.13 7.85 6.40 3.21 2.42 2.05 1.55 0.88 32.0 10.0 4.90 3.48 2.35 6.55 3.50 2.50 2.10 1.64 1.00 0.62 0.38 0.21 0.071 0.042 It should be noted that the coefficients, cross sections, and half-value layers are constant only for a particular energy and absorbing atom. When the absorber consists of atoms with only one atomic number but the gamma radiation contains photons of several different energies, the intensity at any depth in an absorber is given by the sum of exponentials for the components. / = her™ + I2e-^x + +Ise- HsX where Ii, la, • • • In are the intensities of the 5 components at the surface and fj.1, /x2, . . . Us are the corresponding absorption coefficients. In practice, the experimental conditions involved in gamma-ray absorption are often more complicated: the energy may contain many components or may even be continuous in distribution, the absorber may contain several atomic species, and the geometry may be confused by a divergent beam. Sec. 2.2] GAMMA RAYS 35 These factors, together with the fact that scattering causes degradation of energy as well as directional divergence, make it impracticable to attempt to compute the reduction in energy flux or intensity of beams traversing absorb- ing media, and experimental measurements of the attenuation must be made. However, for the detection and measurement of gamma rays emitted by radioisotopes, the requirements of homogeneity and parallel beams can be met in the experimental arrangement and the simple exponential absorption described above is more nearly valid. Only scattered radiation remains a possible source of error, but this is largely eliminated by adequate collima- tion. Detailed calculations of gamma-ray absorption in thick slabs when single and multiple scattering are included have been given by Hirschfelder and Adams [13]. 2.2. Photoelectric Effect. Gamma rays of low energy are absorbed mainly by photoelectric ejection of orbital electrons from atoms of the absorbing medium. This is a resonance phenomenon in which the energy of a photon is transferred to a single electron, ejecting it from the atom with a kinetic energy Ee equal to the difference between the gamma energy hv and the electron's ionization potential /, or Ee — hv — I. The mechanism of the interaction is most easily explained in terms of the influence of the electric and magnetic components of the gamma ray on an electron. At very low energies only the electric component is important, and since, as in other forms of radiation, it is oriented normally to the direction of the ray, the most probable direction taken by the ejected electron is also normal to the incident gamma ray and along the electric vector. As the energy is increased, the influence of the magnetic component becomes appreciable. The electron is accelerated by the electric field as before, but it is also deflected more in the forward direction of the incident photon by the magnetic-field component. From the direction taken by the electron it is evident that the total momentum involved in the process can be preserved only if it is shared in part with the atom from which the electron is ejected. The orbital electrons most likely to participate in the photoelectric effect are those with binding energies nearest in magnitude to that of the incident photon, provided that the binding energy is less than hv. When the gamma- ray energy is considerably greater than the K x-ray absorption limit, the probability for interaction with electrons of the various atomic shells, K, L, M, . . . , decreases with increasing principal quantum number. Con- sequently the K electrons are the most likely to participate in the photo- electric effect when the gamma-ray energy is greater than the K absorption limit. When the gamma-ray energy is comparable to the K, L, . . . electron ionization potentials, the photoelectric cross section is complicated by the characteristic x-ray absorption limits. However, for energies greater than 36 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 2 the K absorption limit the cross section, or absorption coefficient, decreases rapidly and smoothly. In this region the cross section per electron may be calculated from a formula given by Grey [13,15] in a form similar to that below. re = 2.04 X 10-30Z3£7-4(1 + 0.008Z)(£7 - 0.25Ek - 0.422£|) where Z = atomic number of absorbing atoms Ey = gamma-ray energy, mev Ey = K x-ray absorption limit, mev When Ey » Ek, Te = 2.04 X 10-30Z3£7-3(1 + 0.008Z) From Te the linear-, mass-, and atomic-absorption coefficients are obtained from the relations given in Sec. 2.1. ti = pTm = pNra — pNZre When the electronic cross section is known for one substance, e.g., lead, it may be calculated approximately for another absorbing material with atomic number Z by the relation Zz Te = \Je)Vb Tcyy^Z Similar extrapolations may be made for the linear and mass coefficients. Empirical cross section formulas, equivalent to that above, have been given in the form > Te = AZn\m where A = constant X = gamma wavelength As an example, for air and water the mass-absorption coefficients are rm = 2.33X3-13 (air) rm = 2.54X3-22 (water) 2.3. Scattering of Gamma Rays. Gamma rays are scattered with loss of energy only by electrons, and all electrons, whether bound in an atom or free, have the same cross section for scattering. It is the only process in which the gamma photon is not absorbed but instead undergoes a reduction in energy and a deflection from its initial direction. Thus a collimated beam of monoenergetic gamma rays after traversing an absorber is partially degraded in energy and spread over a wide angle by scattering. Scattering is also the only process involving gamma rays in which both energy and momentum are balanced exclusively by the scattered photon and recoil electron; the atom does not participate in the interaction, and its presence is unnecessary. The effect was first described by Compton [1] who, Sec. 2.3] GAMMA RAYS 37 by considering the interaction as a classical two-body collision, derived the following relation between the scattering angle and change in wavelength (see Fig. 3): h V - X = — (1 — cos 4>) = 0.0242(1 - cos 0) angstrom m0c ° where X', X = initial and scattered wavelengths, angstroms = scattering angle The factor h/m0c = 0.0242 angstrom, known as the Compton wavelength, is the shift in wavelength for any gamma ray scattered through an angle of 90 deg. The scattering angle may take any value from 0 to tt. Furthermore it is INCIDENT PHOTON / RECOIL ELECTRON RECOIL PHOTON Fig. 3. Compton effect. A gamma photon is scattered by electrons as though it were a particle. The scattered photon consequently leaves with less energy (longer wavelength) and at a definite angle as required for conservation of energy and momentum in elastic, two-body collisions. apparent that on the average after one or two collisions, high-energy gamma rays are degraded to wavelengths in the order of a Compton wavelength. Further scattering then has lessmarked effect, and the photon is more likely- to be absorbed subsequently by the photoelectric effect. For gamma-ray energies corresponding to the soft x-ray region, Compton scattering is negligible compared with the photoelectric effect, but at higher energies, approximately 0.5 to 5 mev, it is the most important process in gamma-ray absorption. For energies greater than this the scattering coeffi- cient decreases slowly with energy and is rapidly superseded in importance by pair production. Furthermore, since the electronic cross section is independent of the atomic number of the absorber, scattering is relatively more important in light than in heavy elements as compared with the photo- electric effect and pair production, both of which exhibit strong dependence on Z. 38 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 2 A quantum mechanical treatment of scattering that is valid for all gamma- ray energies has been carried out by Klein and Nishina [2] on the basis of Dirac's relativistic theory of the electron [7]. The total electronic cross section is given as the sum of two scattering terms. The first, denoted by sae, accounts for the reduction in intensity due to loss of gamma photons scattered out of the beam. The second, denoted by aoe, is the scattering- absorption cross section arising from the loss in energy suffered by scattered photons. The total electronic scattering cross section is given in the form [2] 2tt^ 2(1 -f a)2 1 + a . .. _ . 1 + 3a 1 . . log (1 + 2a) - ,., , 0 x2 + w- log (1 + 2a) _a2(l + 2a) a3 &v ' (1 + 2a)2 ' 2a hv E where a = — ^ = jr^ = gamma-ray energy in units of m0c2 where Ey is energy, mev e = electronic charge m0 = electronic rest mass For very low and very high energies reduced expressions may be used. For low energies a < 1, ae can be expanded as [3] Sire* 3m20c4 CFe = (1 - 2a + 5.2a2 - 13.3a3 + 32.7a4 +••• ) For high energies a ^>> 1, sae reduces to 2ire m2c 1 (-T + y- ^g 2a - ~2 log 2a) 4 \4a la a- / The scattering-absorption coefficient ace is given by the equation [2] 2«H aO e o a 2(1 + a)2 1 +3a (1 + a)(l + 2a - 2a2) a2(l + 2a)2 (1 + 2a)2 + a2( 1+ 2a)2 4a2 (\ + cl 1 , 1 \ . fs,0, ~ 3(1 + 2a)3 " \~a^ ~ Ta + W) bg (1 + 2a) As for >> 1, «4/l, ry 1 \ a can be obtained by- subtraction. The linear-, mass-, and atomic-absorption coefficients may be found from the usual ratios <*l = P0~m = pN(Ta = pNZ> l37m0c2Z^^, Bethe and Heitler [4] have also shown that the exact formula approaches asymptotically the value given by the formula — 27 ) The atomic cross section and the linear- and mass-absorption coefficients for pair production are obtained from the usual relations Kl = pKm = pNKa = pNZKe When the mass-absorption coefficient is known for one substance, e.g., lead, the coefficient for any other material may be found from . v 207.2 PZ* Km - Um)Pb(82)21L3 A where p, Z, A = density, atomic number, and atomic weight, respectively, of absorber lOpb = mass-absorption coefficient for pair production in lead The explanation of the process of pair production is to be found in Dirac's relativistic theory of the electron [7]. Dirac showed that the wave equation for the electron admits negative energy states for the electron as well as those of positive energy. The lowest positive state in the continuum of positive energies must necessarily be that equivalent to the rest mass of the electron, m0c2, as required by Einstein's law. Similarly, a highest negative energy state may exist at —m0c2, and below this there exists an infinity of possible quantum states identical to the positive energy continuum. Between —m0c2 and +m0c2 there are no states in which an electron can exist. Since the existence of electrons in positive states hardly needs demonstration, it must be assumed on the basis of Pauli's exclusion principle that all negative states are filled and, hence, that all space is occupied by an infinite density of negative energy electrons. The existence of such a "sea" of electrons normally could not be demonstrated because its uniformly distributed charge forms a field-free region. However if an electron is raised to a positive energy state, the unoccupied level or "hole" left behind behaves as a posi- tively charged electron and can be detected by the ionization it produces. An electron can be ejected from a negative state only by the expenditure of energy at least equal to 2m0c2, corresponding to the transition from —m0c2 to -\-m0c2. Gamma rays with energies greater than this, therefore, can excite Sec. 2.5] GAMMA RAYS 41 an electron transition to positive energy states where it is then observed together with the "hole," or positron, as a pair of particles of identical mass but opposite charge. The energy in excess of 2m0c2 appears as kinetic energy, but it need not be shared equally by the two particles. When the positron is brought to rest by the normal processes of energy loss from ionization and radiation, it recombines with an electron, or more precisely, a positive energy electron fills the unoccupied level, and two gamma photons are emitted (annihilation radiation) each with a characteristic energy hv = m0c2. The existence of such "holes" or positrons were first observed by Anderson [8] in cosmic radiation. 2.5. Secondary Particle Production. The total radiation observed at any depth in an absorber consists of primary gamma rays together with their z UJ z SECONDARY PARTICLES / ^\ TRANSITION / X REGION GAMMA RAYS -, AIR _ "• LEAD - — AIR DISTANCE Fig. 4. Diagram indicating the change in secondary radiation intensity when gamma rays pass through media of different electronic densities — in this case, from air to lead to air. Intensity curves are not to scale. secondary radiation of electrons (photo-, Compton, and pairs) and x-rays produced as a result of these electrons. Since the range of secondary elec- trons in all absorbers is very small compared with the half -value thickness for gamma rays, the number of recoil particles formed per unit time equals the number absorbed when radiative equilibrium is reached between the primary and secondary radiation intensity. The observed secondary intensity there- fore decreases exponentially at the same rate as the gamma-ray intensity although its actual absorption coefficient is very much greater. The relative magnitudes of the intensity of the gamma-ray beam and its secondary elec- trons when they are in equilibrium depends on the atomic number and density 42 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 2 of the absorber, or more directly, on the separate absorption coefficients /j. and Ho as expressed by the relation J. = /J"> I0 (X — Ho where I, I0 = intensities of secondary and primary radiations, respectively H, fi0 = absorption coefficients of secondary and primary radiations, respectively It is seen from the expression above that if the beam of gamma rays enters a second medium more dense than the first, e.g., from air into lead, the intensity of the secondary radiation will make a transition to a higher relative intensity level before coming to equilibrium. The transition region is characterized by a very rapid increase in electron emission and reaches a maximum value at a depth in the absorber approximately equal to maximum range of the recoil electrons. From the surface of the second absorber (see Fig. 4) the variation in the secondary radiation intensity I with depth x is given by the equation I = I0 M° ( the energy involved in the transition, hv, and the atomic num- ber of the nucleus. For heavy nuclei and for gamma rays with hv > m0c2, calculations of a [9,10,11] indicate stronger conversion for magnetic dipole than for electric dipole radiation and an increase in a with multipole order. The most probable conversion under these conditions occurs in the K shell, while L, M, . . . conversion occurs with successively smaller probability for any one value of Z and Ey. Conversion in lighter elements, Z < 40, and for low-energy isomeric transitions has been calculated for both the K shell [17] and the L shell [18]. The results of these investigations indicate that, for decreasing gamma-ray energy, conversion increases rapidly with multipole order. For any one energy and kind of radiation conversion varies approxi- mately as Zz. Direct experimental evaluation of conversion coefficients usually has been obtained by beta spectrograph analysis of the beta spectrum. The line spectrum of monoenergetic conversion electrons appears as a set of peaks superimposed on the continuous background of the decay electrons when these are present. The peak positions in units of Hp indicate the energies of electrons from various shells, and the area under the peaks indicate the relative intensities of the electrons. For a radioisotope with a simple decay scheme and one strongly converted gamma ray the conversion coefficient is given unambiguously by the ratio of the number of electrons in the line spectrum to the number in the continuous portion. However, when the decay scheme is complex, the method is difficult and the results often uncertain. A second but less accurate method for determining conversion coefficients involves counter measurements of the coincidences (I3e~) and ((87) [12,14]. A sample of the isotope for which internal conversion is to be measured is placed between two thin window counters one of which, counter A, registers single events as well as twofold coincidences with counter B. With sufficient aluminum absorber placed in front of counter A to stop all electrons, single gamma events are registered in A and {J5y) coincidences by counters B and A . In the same way, but with the absorber removed, single beta events are now registered in counter A and ((3e~) coincidences by counters A and B. The recorded number of (j3e~) coincidences, Npe-, must be corrected for (J3y) and (77) coincidences as measured above. These corrections are normally small, however, since the gamma-ray efficiency of counters is ~ 0.01 whereas for beta particles the efficiency is ~ 1.0. If the decay scheme of the isotope is simple and only one gamma is con- verted appreciably, the conversion coefficient is calculated from the counting measurements above by the expression Sec. 2.6] GAMMA RAYS 45 Npe-/Np „ 2/ Nfiy/Ny"/ f€(T (l+/-'f)! where / = total conversion coefficient N$e- = number of (/3e_) coincidence counts Np = number of beta counts iV/3-y = number of (@y) coincidence counts Ny = number of gamma counts a = geometrical efficiency (per cent solid angle) of counter B e = beta particle efficiency of counter B. If/ and m0c2, traversing media of low density dE 2ve*NZ . Es log dx m„c2 2m0cir- This formula is not valid, however, for electrons with high velocities travers- ing dense materials since local polarization of the medium greatly alters the 52 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 / I / ENERGY LOSS PER ION PAIR FOR ELECTRONS (STOPPING CROSS SECTION x N) Redrawn from v.Engel 8 Steenbeck. / ao / O) ~7 01 a. p "& — / E —t o / < / w / o / & / r < / A i < / m -z ' ' -/—%-- u z / / 7 / 1- 8 / / / / / / V / / / I / / / / / / / / / 7^ f t / r r /' / / / V / / / / ,' / / / / / / . 1 , / / r / / // / / T //< '/ 1 / 1 1 / i / /I / 1 / / [ 1 ' v \ \ s \ :±5 sk \ \ ^ '• > \ \ 'S I V \ \\ \\ \ V vo \ \ ' k ^ ■> X z *~ 8 & __i o > z o 137m0c2_1/* (complete screening) where Z = atomic number of absorber e = electronic charge m0 = electronic rest mass E = energy of electron in units of m0c2 c = velocity of light In energy ranges other than those indicated above the complete expression for 4>„ should be used and integrated numerically. Neglecting the logarithmic terms in the stopping formula for ionization and in the formula above for radiative collisions, a simple but approximate formula is found for the ratio of the rates of energy loss by these two processes as a function of energy and atomic number. (dE/dx)ion EZ EZ (dE/dx)I&d ~ 1,600 mc2 == 800 where E = energy, mev A second form of radiative energy loss, known as Cerenkov radiation [20], occurs when high-speed electrons traverse dielectric media. Radiation is emitted in the frequency range for which the phase velocity in the medium is smaller than the velocity of the electron. The theory of the process, devel- oped by Frank and Tomm [21], leads to expressions for the rate of emission given also by Fermi [28] in the form For v < c ce~y2, -(f) =^(1-^ + log^1) \dx /cer tnv \ e — 1 e — 1/ where e = dielectric constant n = number of electrons per cc (8 = v/c In calculations of the total rate of energy loss from both ionization and radiation, the contribution from the Cerenkov effect given in the formula above should not be added since they are contained implicitly in Fermi's complete stopping formulas which should be used in the velocity range where the Cerenkov effect appears (see Sec. 4.4). 3.5. Specific Ionization. The total ionization produced by a beta particle is the sum of the primary ions produced directly by the particle plus the Sec. 3.6] BETA PARTICLES 55 subsequent ionization by the primary ions and that produced by Brems- strahlung or x-rays emitted from the initial particle. In general, the range of the secondary ions is a fraction of a millimeter so that the majority of ions lie close to the path of the beta particle. The total ionization, however, usually amounts to at least several times the primary ionization produced directly by the initial particle. Differentiation between primary and secondary ion- ization is possible only in the Wilson cloud chamber with properly controlled expansion. When expansion takes place just before the electron traverses the chamber, the number of drops formed per unit length of path corresponds to the specific primary ionization. Under this condition secondary ions cannot diffuse sufficiently far to form separate drops but rather coalesce into a single drop containing the primary ion. If, on the other hand, expansion is delayed, the ions can diffuse far enough from one another to form separate drops and thus indicate quantitatively the total specific ionization. The intensity of ionization is greatest (50 to 200 ion pairs per centimeter path in air) at very low beta particle velocities and decreases with greater velocity until a minimum value is reached when the energy is in the order of 1 mev. For energies greater than 1 mev, the specific ionization increases very slowly, roughly as log E, but for practical purposes, in the energy range 1 to 10 mev, it remains essentially constant at approximately 25 ion pairs per centimeter path in air at normal temperature and pressure. The average energy absorbed from a beta particle in the formation of an ion pair has been shown to be independent of velocity for energies greater than 0.01 mev. The value for air has been carefully measured, and its best value is given as 32.5 ev [22,23]. The energy absorbed per ion pair at low velocities is somewhat larger. For the energy range 300 to 60,000 ev Gerbes [24] gives the following formula for the value of W in air: S 27 W = 31.62 + ^- ev E — I where E = beta-particle energy, kev I = ionization potential (1.7 X 10-2 kev) 3.6. Relative Stopping Power. The relative stopping power 5 is defined as the ratio of the rate of energy loss in one substance to that in another sub- stance, usually air. It is seen from the stopping formula for ionization energy loss that 5 should be relatively independent of velocity but strongly dependent upon the electronic density and to some extent on the average excitation potential of the medium. Considering only the stopping power per electron, the value of Se in the range from hydrogen to copper decreases about 20 per cent [22] while, for any one substance, the variation with velocity is approx- imately 8 per cent in the energy range 0.1 to 2.0 mev [22]. 56 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 3.7. Nuclear Excitation. Energy loss by nuclear excitation and capture is negligibly small in terms of absorption of beta-particle beams for all energies that have been observed. Its principal importance is in the determination of nuclear energy levels. Theoretical as well as experimental values of the cross section for nuclear excitation are of the order of 10-7 barn. 3 8. Absorption of Beta Particles of Homogeneous Energy. A well-defined range does not exist for beta particles because of the great variation in energy loss per collision and, . to an even greater degree, because of scattering. Nevertheless, a useful experimental range can be found since the absorption curve for a beam of initially monoenergetic beta particles such as conversion electrons is roughly linear for energies greater than 0.5 mev. Hence an extra- polated range may be determined by plotting the number of particles against thickness of absorber and extending the linear portion of the curve to the axis (or background count). Experimental determination of the range of parti- cles with energies smaller than 0.5 mev by the absorption method is somewhat more difficult and less certain in its results than at higher energies. The absorption curve becomes more concave with decreasing energy and may, at low energies, be approximated by an exponential function over a considerable portion of the range. Estimation of the termination of the curve, however, is subject to considerable uncertainty, particularly if the background activity is appreciable. More accurate measurements of energy in this range are obtained with the beta spectrograph. The relationship of energy to maximum range is also found to be linear for energies greater than 0.7 mev and at least as high as 3.0 mev. In this respect the range-energy relation for monoenergetic particles is almost identical to that for heteroenergetic beams, differing by only a few per cent for corresponding maximum energies. Figure 11 gives the observed extra- polated ranges of beta particles determined with the aid of the monoenergetic electrons provided by line spectra of various radioisotopes. An empirical relation for the extrapolated range in aluminum, fitting these data within ±5 per cent over the energy range from 0.5 to 3 mev, is [4] R = 0.52£ - 0.9 mg/cm2 where E = energy, mev The range in aluminum for energies less than 0.2 mev is given approximately by the relation proposed by Libby [26]. R = K5o£5/* gm/cm2 3.9. Absorption of Inhomogeneous Beta-particle Beams. The absorption curve for beta particles of inhomogeneous energy decreases more rapidly than the curve observed for monoenergetic beams of the same maximum energy. The shape and range of such curves is of particular importance in its applica- Sec. 3.9] BETA PARTICLES 57 .020 .015 2 o .010 UJ o z < cr .005 1.0 1.5 2.0 ENERGY IN MEV Fig. 11. Extrapolated range of monoenergetic beta particles in aluminum. (Reprinted from the "Science and Engineering of Nuclear Power," Vol. I, by permission of Addison- Wesley Press, Inc., Cambridge, Mass.) 58 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 tion to beta particles emitted from radioisotopes for which the energy dis- tribution is continuous from zero to a well-defined maximum value. The observed absorption curve for beta particles from these sources is sometimes roughly logarithmic and often can be represented by an exponential function over the greater part of its range. Unlike similar curves for gamma rays, however, it has a finite and definite termination. The exponential character of the absorption can be interpreted only as a fortuitous effect due to a com- bination of the Fermi energy distribution of the emitted particles, scattering, and absorption by radiative and ionization energy loss. When the absorp- tion curve does appear as a straight line when plotted on semilogarithmic graph paper, the beta intensity / (e.g., counts per minute) at a depth x in an absorber is given by / = I0e-»x where I0 = initial intensity (or counts) with no absorber fj. = absorption coefficient, cm x = depth of absorber, cm A form sometimes more convenient is found in terms of the mass-absorption coefficient a = p/p, where p is the absorber density in grams per cubic centimeter. The absorber thickness x is then measured in grams per square centimeter and a expressed in square centimeters per gram. This coefficient is relatively insensitive to the atomic number Z of the absorber since the number of electrons per unit mass decreases slowly with increasing atomic weight and for light elements is therefore essentially constant. An empirical relation for the mass-absorption coefficient, valid for the light elements and with a probable error in energy of 0.2 mev, is [4] 22 a 171.33 J-'m where Em = maximum energy, mev and in terms of the half-value thickness d (where I = 0.5Io) the relation is d = 0.693a = 0.032£i;33 These expressions are valid only when a considerable portion of the absorption curve appears, within the experimental error, as a straight line when plotted on semilogarithmic graph paper. More often, when plotted on semilogarithmic graph paper with the absorber thickness as the linear abscissas, the absorption curve is found to be concave toward the origin or otherwise distorted and cannot be represented by a simple exponential function. The shape of the curve depends on the initial energy distribution of the beta particles and is also strongly influenced by the geometry of the counting arrangement. For this reason an absorption Sec. 3.9] BETA PARTICLES 59 1000 100 coefficient is often of little use, and even when the absorption does appear to be exponential the counter geometry should be specified. A more definite quantity of universal adoption is the maximum range in aluminum. It is less subject to the influence of scattering and does not depend on the shape of the absorption curve. Under certain conditions the range can be estimated from the plotted absorption curve, as shown in Fig. 12. The thickness of aluminum in milligrams per square centimeter just sufficient to stop all beta particles is the indicated range. From this value the true range is obtained by add- ing the equivalent absorber thickness of the air path between the source and the counter, the counter window, and the self-absorption in the source. When the absorber is a substance of low atomic weight, these corrections are given with sufficient accuracy by adding the products of the density of air, window, etc., and the path length in each. Normally when thin sources are used, the corrections do not total more than about 10 mg per cm2 equivalent of aluminum. This method for measuring range is reliable only when the absorption curve can be followed through a reduction in intensity by a factor of 100 or more before reaching the level 10 cr l \V Background mg/cm Aluminum Fig. 12. Absorption curve of beta particles. R0 is the extrapolated range and R the maximum range. The absorption curve above is characteristic of the curves ob- tained for beta particles emitted from radio- active isotopes. For monoenergetic beta particles the relative intensity scale would be linear. of background activity due to radiations other than the beta particles. Consequently the method cannot be used with accuracy for isotopes that also emit gamma rays. Their contribution to the counting rate, assuming a gamma-ray efficiency of ~ 1 per cent, may amount to several per cent of the total, and since they are not appreciably attenuated by beta-particle absorbers, the gamma rays tend to mask the last portion of the beta absorp- tion curve. Similarly when the source activity is less than several hundred times the background, it is often difficult to estimate with accuracy where the absorption curve terminates. These difficulties are eliminated in a method of analysis developed by Feather [5] which is now generally adopted as the standard procedure for accurate range determinations. In addition to its accuracy as compared with other methods, it is applicable to complex as well as to simple spectra, to isotopes that emit gamma rays, and to relatively weak sources. 60 rSOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 The Feather method consists in comparing the absorption curve of the beta emitter being investigated with the curve for an isotope with a simple beta spectrum for which the range is known accurately, such as RaE (476 + 2 mg of aluminum per square centimeter [5]). The absorption curve for RaE, measured with aluminum-foil absorbers and corrected for air and window thickness and with the background subtracted, is plotted on semilogarithmic graph paper with range scaled along the abscissa. The total range (476 mg 10,000 1,000 z 2 ac Q. 100 RANGE IN MG/CM — n— i r .5 .6 .7 .8 .9 1.0 FRACTION, RANGE OF STANDARD 0 .1 .2 D C < — .7 •8 o .1.0 Fig. 13. Feather method for determining the range of beta particles by comparing the absorption curve with that of beta particles for which the range is accurately known (e.g., RaE for which R = 476 mg/cm2). per cm2) is then divided into 10 equal parts, and horizontal lines are drawn through corresponding points on the absorption curve, as shown in Fig. 13. Without altering the counter and sample geometry, a similarly corrected curve is obtained for the test material and plotted on the same graph starting also from the same ordinate for zero absorber thickness. The intersections of the previously drawn horizontal lines when referred to the abscissa give a set of fractional ranges differing from those of RaE. Each of the fractional ranges is then divided by its corresponding decimal fraction (0.1 — 0.9), and the resulting estimates of range are plotted against the same fraction, as illustrated by Fig. 14. A curve drawn through the points thus plotted may then be extrapolated to the point R (abscissa of 1.0) which is the actual range in aluminum. In practice the horizontal lines obtained with the RaE absorption curve are ruled on a vertical scale with the divisions marked 0 to 10 to match the corresponding fractional range. The scale may then be used Sec. 3.10] BETA PARTICLES 61 for any beta absorption curve which is measured with the same counting arrangement and plotted on the same kind of graph paper. The rest of the procedure is followed as before. The Feather analysis can be extended to complex spectra provided that the difference in the maximum energies of the components is sufficiently great to allow the absorption curve to be broken down into components. The relation between range and maximum energy of beta particles emitted from radioisotopes is linear within experimental errors for ener- gies greater than 0.8 mev and at least as high as 3.0 mev. On the basis of range measurements made by the method above and corresponding energies determined with the beta spectrograph, Feather [5] proposed as the range-energy relation for beta particles in aluminum the expression .2 .3 .4 .5 .6 .7 FRACTIONAL RANGE - — A 10 R = 543£ - 160 mg/cm5 Fig. 14. Beta-particle range determina- tion by the Feather method. The curve of partial ranges is extrapolated to full range (1.0) to obtain the actual beta-particle range given by the ordinate A. where E — energy, mev, > 0./ The constants were redetermined by Glendenin and Coryell [25] with more extensive data, and they give the relation as R = 542£ - 133 mg/cm2 For energies less than 0.8 mev the range-energy curve bends toward the origin in a way that cannot be represented accurately with a single function. For energies less than 0.2 mev, Libby [26] finds that the range is accurately represented by the formula R Hso- ?tt In the range from 0.15 to 0.8 mev, the range is given by [12] R = 407£138 mg/cm2 mg/cm2 The portion of the curve for energies less than about 0.7 mev is essentially the same for monoenergetic and heteroenergetic beta-particle beams with the same maximum energy. The formulas above therefore can be used in either case. 3.10. Scattering of Beta Particles by Nuclei. The elastic scattering of beta particles has presented a difficult problem both in theory and in measure- ment. Because of the small mass of the electron compared to a nucleus, 62 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 large deflections in a single collision may occur frequently, particularly for beta particles of low energies scattered by heavy elements. For this reason, the effects of elastic scattering should never be underestimated in the evalua- tion of measurements on beta particles. Single elastic collisions of slow electrons with nuclei can be calculated from Rutherford's formula [6] since elastic collisions involve only interaction of the coulomb fields of the electron and nucleus. For collisions of high-speed beta particles where relativistic effects are important, a formula has been given by Mott [7] for the intensity (or number) of beta particles scattered into the solid angle doi at an angle 9 from the initial direction. l7/«2ZV/i o^\ 1 P2 i o 7 cos2 (0/2)' n(9) = n0N I ^ s ) (1-0) . ia/1 ~ ■ ,an + T(3aZ . )' ' \2m0v2/ |_ sin4 9/2 sin2 6/2 sm6 (8/2) which for small angles and all values of Z reduces to n = n0N ( ^-, ) (1 - /32) cosec4 Q- \2m0v2/ 2 and for large angles and small Z is » ■ n°N {&} (1 - ^ 0 - "* si,,: !) cosec< \ where a = 2ire-/hc = \\zi n = number of particles per cm2 scattered into solid angle dco at angle 9 n0 = initial number of particles per cm2 in beam N = number of atoms per cc Z — atomic number of scatterer m0 = electronic mass In all cases the scattering coefficient is proportional to Z-(\ — /32)/V. These formulas apply only to very thin foils in which the probability of more than one collision is small. A criterion for determining if single scattering can be expected in an experimental arrangement has been given by Wentzel [8] which provides that the minimum observed angle of deflection 9 and the foil thickness / must be chosen so that 9 > 4

9 where the scattered beam is detected. For aluminum the maximum thickness for single scattering is Sec. 3.11] BETA PARTICLES 63 approximately 2/jl (0.54 mg per cm2). In a more recent study of scattering, Williams [27] gives as the criterion for multiple scattering the expression 1 « nn Z t 2ir(3mlc2 where / is in centimeters. Single deflections of low-energy beta particles through large angles (> 90 deg) may be expected with a finite but very small probability in "thin" foils but in "thick" layers where multiple scattering is important an appreciable fraction of an incident beam of particles is back-scattered, or deflected, through more than 90 deg. The coefficient of reflection Re may be defined by the ratio Ir/I0 where IQ is the incident beta intensity and Ir is the back- scatter intensity. For most substances the reflection coefficient has a value between 0.1 and 0.5 depending upon the atomic number and density. This effect is particularly important in measurements of radioactive samples and in the preparation of standards. The observed activity or counting rate is profoundly affected by the backing material. The back- scatter from platinum and lead, for example, is found to be 20 to 50 per cent greater than from aluminum, depending to some extent upon the counter geometry and beta-particle energy. 3.11. Beta Decay. The emission of beta particles (negatrons and posi- trons) occurs only during the decay of an unstable nucleus and is a slow process compared with the primary process in which an excited nucleus is formed by bombardment. The -latter process takes place in less than 10-10 sec, whereas the probable time for beta-particle emission is usually a second or longer. When an excited nucleus is formed by bombardment with heavy particles, it contains an excess of either protons or neutrons as compared with a stable nucleus of the same mass number. If the replacement of a proton with a neutron leads to a smaller atomic weight (greater binding energy), the transformation will occur according to the scheme P -> « -f (P+) + n° Conversely, if the replacement of a neutron with a proton results in a more stable nucleus, the transformation is A7 -> P + 08") + n° In both cases the excess energy (mass) is carried off by the neutrino n° and beta particle. If a negatron is emitted, the nuclear charge increases by one unit; if a positron is emitted, the charge decreases by one unit. In calculating the exact mass reduction by these processes, the exact atomic weights (neutral atom) can be used in negatron emission since the loss of the rest mass of the beta particle is exactly compensated by the gain of an orbital electron. In 64 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 positron emission, however, a correction for twice the rest mass must be made since both the positron and an orbital electron are lost. The emission of the hypothetical neutrino, first postulated by Pauli, is required for the conservation of energy, spin, and statistics. The emission of a beta particle corresponds to a transition in the excited nucleus involving a discrete quantity of energy; yet the emitted particles are observed to possess any energy ranging from zero up to the total transition energy, Em&%. It is necessary to assume, therefore, that the neutrino carries off an amount of energy in each instance equal to the difference between the beta-particle kinetic energy and the transition energy. Furthermore, beta emission always results in a change of spin i of the residual nucleus by integral units of h/2ir, i.e., 0, ± 1, + 2, • ■ ■ , while the intrinsic spin of the beta particle is only a half unit. It must be assumed, therefore, that the neutrino spin is also one-half. A similar observation holds for the statistics in that residual nucleus remains unaltered while the emitted electron obeys Fermi statistics. The properties of the neutrino deduced from these observations are then Mass : 0 or < n), (n — > p), Fermi [10] developed a theory of beta decay analogous to that for the emission of light from an atom. The theory provides a means of calculating the probability of the transformation in terms of the mean life for decay, the energy distribution of the particles and a set of selection rules for determining if a transition is allowed or forbidden. Assuming the neutrino mass to be negligible, the probability of emitting per unit time a beta particle with energy between E and E + dE is given by Fermi's theory in the form PdE = £-3 \Q\*f(Z, E)pE(E2 - 1)X(E0 - E)2 dE where E = energy of electron in units of m0c2 — mc2/m0c2 E0 = maximum energy in units of m0c2 g = constant p = momentum of electron The factor Q is a matrix element involving the proper functions Un for the neutron and Um for the proton to which it is transformed, integrated over-all space and spin coordinates Q = jUtUme-2-i^"°+^)-T/hdv Sec. 3.11] BETA PARTICLES 65 If the proton or neutron that is transformed remains in nearly the same quantum state after beta emission, Q is nearly unity. If the initial and final quantum states are markedly different, Q is smaller than unity, and it is zero when a transition between two states is impossible; i.e., the transformation of a proton or neutron in state n to a neutron or proton in state m is forbidden. For most light elements in which comparatively few states exist at ordinary levels of excitation, it can be regarded generally as unity (or zero if it is energetically impossible). The factor f(Z, E) includes the relativity correc- tion and the appropriate wave function of the electron in the presence of the strong coulomb field of the nucleus. In light elements /(Z, E) is of the order of unity; for Z = 0,/(O, E) = 1. In heavy nuclei, however, this factor increases the probability for beta emission by an order of magnitude over that for light nuclei emitting beta particles of the same maximum energy. The Fermi theory provides for a continuous distribution in kinetic energy for the ejected particles from zero to a maximum energy corresponding to the total transition energy for the particular nucleus and the specific transition. The most probable beta energy is found to be E0/2, and near both zero kinetic and the maximum energy very few particles are to be expected. A difference in the numbers of positrons and beta particles should be found in the low-energy end of the spectrum for medium and heavy elements because of the strong effect of the nuclear coulomb field. Fewer low-energy positrons will be observed since, once formed, they derive additional energy from the repulsive electrostatic field. Conversely, a greater number of slow negative particles are observed because faster particles lose energy to the field and are then observed at relatively lower energy. Measurements of beta-energy spectra are sometimes complicated in radio- isotopes in which two or more beta particles are emitted or when conversion electrons (line spectra) are present (see Gamma Rays, Chap. 2). When a nucleus can decay by one of several possible beta transitions, the observed energy distribution is a superposition of the several Fermi curves [11]. Conversion electrons, on the other hand, can be readily identified since they form peaks with small energy spread and often high intensity super- imposed on the continuous distributions. An approximate expression for the energy distribution when E0 < 2 mev has been given in the form [12] PdE = AEHl + 2E)(1 + E)»(Eo - E)2 dE where A = constant for each isotope A form more useful for plotting experimental data is to be found in the reduced equation given by Kurie [13]. 66 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 = A - B{E + 1) GT where iV = number of particles observed in each successive momentum = interval E = energy in units of m0c2 A, B = experimental constants In terms of the number N1 of particles per unit energy range, the "Kurie plot" is Jef) =c~de (, where p = momentum in units of m0c for energy E C, D = experimental constants Plotting (N/F)W or (Nl/pEF)Vl against E, a straight line of negative slope is obtained if the particles follow a Fermi distribution in energy. The intercept on the energy ordinate corresponds to E0 = %mv2 + m0c2. The theoretical mean life r for beta decay is found by integrating the probability of emission per unit time over the whole range of energy. i-P,« j*° PdE = g>\Q\>F(Z,E0) where Pt = total probability that a particle of any energy is emitted per unit of time F(Z, E0) = f^EiE* - 1)»(JE - EYf{Z, E) dE The exact form of the function F{Z, E0) is inconveniently complicated for calculation, but approximations valid over certain ranges of Z and E0 have been suggested [14,15,16]. In all cases the probable life for beta emission decreases rapidly with increasing maximum energy, E0. 3.12. Selection Rules for Beta Decay. Nuclear transitions of the form w— >P or P-^n involved in beta emission are classed as allowed, first, second, or higher order forbidden depending upon the relative probability of the process. Empirically, a transition is classed by comparison of the magni- tude of its half-life and energy with those of beta emitters of nearly the same atomic number. The product of the half-life T and the function F, defined in the preceding section, is roughly constant for a particular class of transition within each of the three groups formed by light, medium, and heavy nuclei. Division of nuclei into at least three groups is necessary since the product FT increases also with atomic number independent of the forbiddenness of a transition. Sec. 3.13] BETA PARTICLES 67 This is due mainly to the more pronounced effect of the coulomb field with increasing Z. The orders of magnitude of FT for allowed, first and second forbidden transitions in light, medium, and heavy nuclei are given in Table 5 [15]. Table 5. Values of the Product FT ix Beta Decay Transition FT Light Medium Heavy Allowed . . 3 X 103 2 X 10s 5 X 107 5 X 104 2 X 106 1 X 108 2 X 105 1st forbidden . . 1 X 107 2d forbidden ~ 109 Theoretical selection rules for beta decay are based on the form of the matrix element Q which determines the change in state accompanying beta emission. For many light beta emitters, Q ~ 1 since the residual proton remains in nearly the same state as the initially transformed neutron. This is much less likely in heavy nuclei where the level density is much greater. If the change in state is considerable, Q « 1 and the transition is to some degree, first, second, or higher order, forbidden. The principal changes in state to affect the probability of transition are the change in total angular momentum AJ of the nucleus and the parity change of the proper function. The selection rules originally proposed by Fermi are Allowed: 1st forbidden: 2d forbidden: AJ = 0 no parity change AJ = 0, ±1, (0 — > 0 forbidden) parity change i/= +1,±2, (loO forbidden) no parity change A second set of selection rules proposed by Gamow and Teller [17] and based on a different choice of matrix element Q appears to find better support from the experimental data in certain instances. The simplest results of the G-T rules, without reference to the matrix elements, are Allowed : A J 1st forbidden: A J 0, ±1, (0 -* 0 forbidden) 0, ±1, ±2, (0 ->0 forbidden and }/2 — * }/2 forbidden) 2d forbidden: AJ = ±2, ±3, (0 *> 2 forbidden) 0 -> 0 no parity change parity change no parity change 3.13. K Capture. The inverse process to normal beta decay is the absorp- tion by the nucleus of an orbital electron accompanied by the emission of a neutrino [18]. Once in the nucleus the electron does not retain its intrinsic form but is essential, as in positron emission, to the transformation of a proton to a neutron. The electron absorbed is one of the two K electrons since they 68 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 spend more time within and near the nucleus than do the L and M electrons and, hence, have a higher probability for capture when the process is ener- getically possible. K capture leads to a nucleus one charge unit less and to an atomic weight that is smaller than the initial atom by only the mass equiva- lence of the increase in binding energy. The energy of the absorbed K electron has a definite value which is given by its rest energy minus its atomic binding energy, i.e., E0 = (1 — a2Z2)^ in units of m0c2. Thus the neutrino must be ejected with a kinetic energy just equal to the sum of the total electron energy, and the nuclear transition energy and is therefore monoenergetic. Its value is given by En = Ez — -E(z-i) + Ee — 1 = E0 + Ee where E0 = transition energy in units of m0c2 Ez = energy equivalent of exact atomic weight of initial nucleus in units of m0c2 -E(z-i) = energy equivalent of exact atomic weight of final nucleus in units of m0c2 Although K capture frequently competes with positron emission in the same transition, it is in some instances the only process energetically possible. Thus, only K capture is possible if the transition involves less energy than that equivalent to the rest mass of an electron (0.5 mev), i.e., when 1 — Ec < Ez — E(z-i) < 2 (units of m0c2) However, both positron emission and K capture are possible when E0 > 1. The theoretical treatment and calculation of mean life and the transition probability is essentially the same as for beta decay. The probability of a transition depends principally, as in beta decay, on the accompanying change in total angular momentum AJ of the nucleus, i.e., A/ = 0, allowed; ±1, first forbidden; ±2, second forbidden. The mean life is given by [15,19] I- j! T 27T3 ' \Q\2h where Q = matrix element (~ 1 for light elements; see Beta Decay, Sec. 3.11) g = constant For allowed transitions [15], A/ = 0, the function fk is approximately fk « 2x(aZ)3(£0 + l)2 The probabilities of the first forbidden to the allowed transition will have the ratio (aZ/2)2, and successive higher orders of forbiddenness will have probability ratios of (E0/R)2, where a is the fine structure constant, K37> and R is the nuclear radius. Sec. 3.13) BETA PARTICLES 69 Observation of K capture is possible only through the detection of the K x-radiation following absorption of a K electron. However, identification of K capture is sometimes hampered by a competing positron emission when this is followed by gamma radiation. If internal conversion of the gamma radiation is pronounced, the K x-radiation is then masked by similar radiation produced by the conversion of K electrons. When positron emission is absent or when present but not accompanied by gamma radiation, K capture can be detected unequivocally. In some radioisotopes the gamma radiation exhibits a much greater intensity than is expected from the observed positron activity. This, together with K x-radiation, readily establishes the existence of K capture. REFERENCES FOR CHAP. 3 1. Birge, R. T.: Phys. Rev., 13, 233 (1941). 2. "Handbuch der Physik," Vol. XXIV :1, p. 519, J. Springer, Berlin, 1933. 3. Bethe, H. and W. Heitler: Proc. Roy. Soc. {London), 146, 83 (1934). 4. "The Science and Engineering of Nuclear Power," Vol. I, Addison-Wesley Press, Inc., Cambridge, Mass., 1947. 5. Feather, N.: Proc. Cambridge Phil. Soc., 34, 599 (1938); E. Bleuler, and W. Zunti, Helv. Phys. Acta, 19, 137 (1946). 6. Rutherford, E.:Phil. Mag., 21, 669 (1911).. 7. Mott, N. F.-.Proc. Roy. Soc. (London), A135, 429 (1932). 8. Wentzel, G : Ann. Physik, 69, 335 (1922) 9. Mott, N. F.: Proc. Roy. Soc. {London), 125, 222, 259 (1929); N. F. Mott, and H. S. W. Massey, "Theory of Atomic Collisions," Oxford University Press, New York, 1935. 10. Fermi, E.: Z. Physik, 88, 161 (1934). 11. Slegbahn, K.: Proc. Roy. Soc. (London), 189, 527 (1947). 12. Pollard, E., and W. L. Davidson: "Applied Nuclear Physics," John Wiley & Sons, Inc., New York, 1942. 13. Kurds F. N. D., J. R. Richardson, and H. C. Paxton: Phys. Rev., 49, 368 (1936). 14. Nordheim, L. W., and F. L. Yost: Phys. Rev., 51, 942 (1937). 15. Konopinski, E.: Rev. Mod. Phys., 15, 209 (1943). 16. Wigner, E.: Phys. Rev., 51, 106 (1937). 17. Gamow, G., and E. Teller: Phys. Rev., 49, 895 (1936). 18. Alvarez, L.: Phys. Rev., 54, 486 (1938). 19. Bethe, H., and R. Bacher: Rev. Mod. Phys., 8, 55 (1936). 20. Cerenkov, P.: Compt. rend. acad. sci. U.R.S.S., 14, 101 (1937). 21. Frank, I., and I. Tomm: Compt. rend. acad. sci. U.R.S.S., 14, 109 (1937). 22. Gray, L. H.: Proc. Cambridge Phil. Soc, 40, 72 (1944). 23. Eisl, A.: Ann. Physik., 3, 277 (1929). 24. Gerbes, W.: Ann. Physik., 23, 648 (1935). 25. Glendenin,L. E., and C. D. Coryell: Atomic Energy Commission Report MDDC-19, 1946. 26. Libby, W. F.: Anal. Chcm., 19, 2 (1947). 27. Williams, E. J.: Proc. Roy. Soc. (London), 169, 531 (1939). 28 Fermi, E.: Phys. Rev., 57, 485 (1940). 70 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 Table 6. Average Energy of Beta Particles The data given below are taken from the computed and compiled values of average beta energies reported by Marinelli, Brinckerhoff, and Hine, Rev. Mod. Phys., 19, 25 (1947). To ensure the highest accuracy they computed average values only from magnetic spectrometer measurements reported after 1939. In the case of complex spectra, the average value of the components, determined from graphical analysis, is given as well as the average for the total spectrum. The average for simple spectra was computed from Fermi's theory for the energy distribution by the formula 'Eo / [Eo E= I EN dE I I N dE (see Beta Decay, Sec. 3.11) fEo / fEi -/, ENdE/ h The column giving percentage indicates either the per cent of beta particles with different E0 or the per cent of positrons to K capture. In the case of positron emission the average total energy is indi- cated by the product of the particle average energy and emission probability per disintegration printed in parentheses. The asterisk * indicates that the values given refer only to the highest energy component of the spectrum whereas the dagger t indicates the lowest energy component. Isotope Rad. Half-life, days % Eo kev + kev E, kev ± kev Et, kev ± kev Z El. A 1 H 3 0- 0+ 4,550. 100 17 5 .69 0 06 6 C 11 0.01415 970 10 380 40 14 0" 0+ 0+. K, 7 1.7 X 106 154 50 7 N 13 ?? 0.00703 1,170.0 ~ 100 1,240 575 20 30 475 45 11 Na 225 20 24 0", 7 0~ 0.61 1,390 5 540 20 IS P 3? 14.5 1,712 8 695 20 16 S 36 0- 88. 167 55 17 CI 38 0". 7 0.0259 53 4,940 60 2,230 90 11 2,790] 60 1,190 40 1,390 70 36 1,190 80 400 35 19 K 40 0'. 7 /S-, 7 0~, (?) 0+. 7 5 X 1011 1,350 50 490 60 42 0 515 3,500 1,395 20 Ca 45 180 260 100 21 Sc 44 0.167 * 1,470 20 645 35 46 0". 7 85. 1,117 23 V 48 0+. K, 7 0\ K, 7 0~. 7 16 58 715 15 (300 + 25) (0.58) (240 + 20) (0.35) 25 Mn 52 6.5 35 580 30 56 0.108 50 2,810 50 1,240 50 30 1,040 30 410 35 890 40 20 650 100 280 25 26 Fe 59 0". 7 47. 50 46 10 150 15 120 15 50 225 10 85 10 27 Co 55 /3+, K 0 75 1,500 50 (515 + 90)(?) 655 35 56 0+, 7 0 + , K, 7 0". 7 0 + . K, 7 0" 85 1,500 50 58 65 15 470 15 (195 + 20) (0.15) 60 1,940 310 99 29 Cu 61 0 142 78 1,230 20 (555 + 40) (0.78) 64 0.53 578 3 175 30 (205 ± 30) (0.58) 63 0\ K, 7 0+, K, 7 30 85 659 2,360 3 40 265 1,080 25 50 30 Zn 0.0271 9 1,400 40 615 30 (985 + 40) (0.98) 4 460 30 180 20 33 As 76 0", 7 B", 7 0+, K. 7 1 12 1.170 35 Br 82 1 5 465 10 150 15 48 Cd 107 0 28 0 31 320 10 (140 + 20) (0.003) +92 49 In 114 0". (7) 50. 1,980 30 765 30 940 30 Chap. 3] BETA PARTICLES Table 6. Average Energy of Beta Particles — {Continued) 71 Isotope Rad. Half-life, days % Eo kev + kev E, kev + kev Et, kev ± kev Z El. A 51 Sb 124 /»-. y 60. 55 2,450 70 980 40 660 35 45 740 30 260 25 53 I 128 0', y 0~, y 0 017 2,020 770 130 0.525 45 1,030 20 360 20 270 20 55 610 30 195 20 131 j8". y P-. y 8. 595 10 205 20 57 La 140 8. 12 2,120 80 835 60 60 1,400 40 510 40 495 40 28 900 30 320 30 77 Ir 194 79 Au 198 0-, y 0~, y 0- 0~. y 0-. y 0 81 * 218 40 835 50 2 7 970 320 83 RaE 210 4 85 1,170 5 330 10 91 UXj 234 0 00079 * 2,320 5 865 50 UZ 234 0.28 90| 450 30 150 20 72 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 Table 7. Ranges and Absorption Coefficients of Beta Particles from Radio- active Isotopes The data listed below are a compilation of values reported in recent literature. In order to avoid confusion in using the table, reference numbers for each value have been omitted but the principal literature from which data were obtained is listed at the end of the table. The maximum range, in mg/cm2, is given when known for aluminum and water as indicated by Al or W following its value. In most cases the range was deter- mined by Feather's method. The absorption coefficient a is defined by the usual expres- sion / = I0e~at where t is the thickness of aluminum absorber in milligrams per square centimeter. Values reported in the literature for the same isotope sometimes differ con- siderably in magnitude, but no effort was made to rectify these differences. Isotope Half-life Energy, mev Range, mg/cm2 a, cm2/mg Z El. A 1 H 3 12. 5y 0.017 0.23 Al 23 4 Be 10 1 . 3 X 106 y 0.560 180 Al 6 C 11 20.5 m 0.950 390 Al 415 W 14 4,700 y 0.140 20 Al 24 W 7 N 13 10.13 m 1.20 550 W 8 0 F 19 18 31 s 112 m 3.3 0.700 2.56 9 260 Al 20 12 s 5.0 0.93 11 Na 22 3.0y 0.580 215 Al 210 W 24 14. 8h 1.40 620 Al 640 W 8.1 12 Mg Al 27 10.2 m 1.8 2.56 13 28 2.4 m 3.3 2,700 W 8.7 14 Si 31 170 m 1.80 860 Al 8 15 P 32 14.3d 1.69 800 Al 810 W 5.3 16 S 35 87.1 d 0.107 13.5 Al 20 W 0.290 17 CI 38 37 m 5.0 2,700 W 8.7 19 K 40 4 X 108 y 0.40 610 W 42 12. 4h 1.52 ~ 660 Al J2.56 3.57 1,770 Al 3.57 1,900 W 20 Ca 45 180 d 0.2 80 W 128 Sc 49 44 30 m 3.92 h 7.5 21 1.5 680 W ~5.8 46 85 d 0.26 100 W 7.1 22 Ti V 51 51 48 6 m 72 d 16 d 1.6 0.36 1.0 5.4 65 23 270 W 52 3.9 m 2.05 3.9 Chap. 3] BETA PARTICLES 73 Table 7. Ranges and Absorption Coefficients of Beta Particles from Radio- active Isotopes — {Continued) Isotope Half-life Energy, mev Range, mg/cm2 a, cm2/mg Z El. .4 24 Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Rb Sr Sr Y Zr Cb Mo Rh Pd 55 52 56 59 56 60 60 65 61 64 66 63 65 69 69 70 72 71 75 77 76 81 80 82 86 88 89 90 90 93 95 97 94 95 99 101 104 104 109 111 1.3h 6.5d 2.59 h 47 d 85 d 10.7 m 5.3y 2.6h 3.4h 12. 8h 5 m 38 m 250 d 57 m 13.8 h 20 m 14.1 h 40 h 89 m 12 h 26. 8h 19 m 18 m 34 h 19. 5d 17.5 m 55 d 30 y 60 h 63 d 17 h 6 m 6.6 m 35 d 67 h 19 m 44s 4.2 m 13 h 26 m ~8 3 25 0.77 (1.05, 2.86) 0.26 1.50 1.35 0.30 1.9 0.9 0.58 Q9-) 2.9 7.3 0.4 1.0 770 YY 4 85 26 27 150 700 W W 43 147 78 80 Al 79 7.3 29 550 260 W W 33 3 2 30 1,700 w 107 17 1 10 3 31 1.68 1.71 1.2 11 1.9 7.7 1.5 7.0 0 . 465 1.6 4.6 1.50 0.65 7.6 10 3 9 6 37 75 7 13 3 7.8 33 34 1,570 W 4.3 7 9 35 6.4 37 160 W 35 6.7 7.6 38 39 40 860 700 770 1,100 Al W W w 8.8 4.7 60 1.0 7.0 1.4 0.15 1.5 1.8 7.3 9.4 ~5 41 9.5 42 75 570 Al Al 11.7 10 45 3.9 4.4 46 1.1 3.5 16.1 6.9 74 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 3 Table 7. Ranges and Absorption Coefficients of Beta Particles from Radio- active Isotopes — (Continued) Isotop B Half-life Energy, mev Range, mg/cm2 a, cm2/mg z El. A 47 Ag Cd Sn Sb Te I Ba La Pr Sm Eu Tb Dy Ho Tm Lu Ta W Re Os Ir Au 108 110 110 115 115 117 125 122 124 127 127 129 131 131 128 130 131 139 140 140 142 153 P 155 160 165 165 166 170 176 177 182 185 187 186 188 191 193 194 198 2.3 m 22 s 225 d 43 d 2.5d 3.75 h 9 m 2.8d 60 d 9.3h 90 d 72 m 25 m 30 h 25 m 0.525 d 8d 86 m 12. 5d 40 h 19. 3h 46 h 6.5y 15. 4d 3.9h 140 m 1.25 m 30 h 105 d 3.5h 6.6d 117 d 77 d 24.1 h 90 h 18 30 h 17 d 20.7 h 2.7 2.8 2.8 0.58 1.5 1.1 1.3-1.7 6.7 2.9 36.5 48 840 Al 7.0 10.7 8.5 50 5.2 51 (0.8, 1.64) 2.45 0.7 0.08 1.8 ~ 10 52 1,230 W 27.2 ~24 12.6 7 0.15 (2.02) 0.61 0.6 1. 1. 2.12 2.14 0.7 0.9 ~7.1 53 56 980 450 210 W w Al 5.33 7.9 57 59 390 1,050 w 9.6 5.4 62 27.5 63 26 1,180 Al 65 10 66 1.2 12.4 ~50 67 1.9 1.1 0.215 0.47 0.36 0.72 0.5 1.07 2.05 (1.5, 0.95) 0.64 2.2 1.0 7.1 69 17.3 71 48 Al 12. 50. 73 74 112 Al 46 70 20.7 75 16.9 5.5 76 14.5 77 184 Al 6.1 79 388 Al 19.3 Chap. 3] BETA PARTICLES 75 Table 7. Ranges and Absorption Coefficients of Beta Particles from Radio- active Isotopes — {Continued) Isotope Half-life Energy, mev Range, mg/cm2 a, cm2/mg z El. A 78 Pt 197 18 h 0.72 26 Hg 199 203 31 m 51.5 d 1.8 0.11 9.4 80 15.3 Al 0.44 77.5 Al 9.5 205 5.5 m 1.62 9.4 81 Tl 204 4.23 m 1.77 10 206 3.5 y 4.85 d 0.87 25.6 83 RaE 210 1.17 476 Al 520 W 16 91 UX2 234 1.14 m 2.32 1,105 Al 1,170 W UZ 234 6.7 h 0.45 250 W REFERENCES FOR TABLE 7 Seren, L., H. N. Friedlander, and S. H. Turkel: Phys. Rev., 72, 888 (1947). Marinelli, L. D., E. H. Quimby, and G. J. Hine: Am. J. Roentgenol. Radium Therapy, 59, 260 (1948). LrBBY, W. F.:Anal. Chem., 19, 2 (1947); Phys. Rev., 56, 21 (1939). Wdzdenbeck, M. L., and K. Y. Chu: Phys. Rev., 72, 1164 (1947). CHAPTER 4 PROTONS, DEUTERONS, AND ALPHA PARTICLES 4.1. Physical Properties. The proton, deuteron, and alpha particle occupy a position of special importance. Aside from their significance as forms of the simplest and most accessible nuclear structures, they are the only charged heavy particles produced in nuclear reactions (except for the few cases in which H3 and fission fragments are formed) and the only heavy particles normally obtained from high-energy accelerators. Consequently the interaction of these particles with matter is of fundamental importance. Table 8. Physical Properties of the Proton, Deuteron, and Alpha Particle Property Atomic weight (neutral) Packing fraction, 10 4 mu Charge, 10"20 abs emu Magnetic moment, nuclear magnetons Binding energy, mev Spin, units of h/2ir Statistics Proton 1.008123 81.2 1 . 60203 2 . 7896 Fermi-Dirac Deuteron 2.014708 73.6 1 . 60203 0.8565 2.17 1 Bose-Einstein Alpha particle 4 . 00390 '9.8 3 . 20406 28. 0 Bose-Einstein Qualitatively the interaction of protons, deuterons, and alpha particles with matter is very nearly the same for all three particles. Quantitatively the differences that exist are due almost entirely to the respective magnitudes of charge and mass of the particles. The following sections, with the exception of alpha decay, therefore, apply in principle equally well to all three particles. Physical theories of the structure of the particles and of their interaction with nuclei are rather involved and at the present time inconclusive because of the uncertainty of the nature of nuclear forces. Reviews of the various theories are to be found in the literature and will not be considered here. 4.2. Energy Loss of Fast Charged Particles. The mechanism chiefly responsible for the absorption or stopping of charged heavy particles (M ~ 1 mass unit) is the interaction of their electric fields with the electrons of the absorbing material. The electrons are regarded, according to the classical theory of the process formulated by Bohr, as harmonic oscillators that are set in motion by the passing particle from which they derive energy. On the basis of this model the rate of energy loss is adequately accounted for by 76 Sec. 4.2] PROTONS, DEUTERONS, AND ALPHA PARTICLES 77 the continual transfer of small fractions of the particle's kinetic energy to the excitation and ionization of atoms lying sufficiently near the path of the passing particle to be affected by its field. The greatest distance at which the field of the particle is effective in exciting atoms is of the order of 2v/v(\ — /32)1-, where v is the particle's velocity and v is the lowest vibra- tional frequency of the electrons. This corresponds to the radial distance beyond which the force on an electron due to the passing particle changes slowly compared to the electronic period in the atom. The interaction with distant atoms therefore may be treated by an adiabatic approximation which demonstrates that an electron, although temporarily perturbed, is left in its original state in an atom and does not absorb energy from the particle. A minimum radial distance from the path at which an atom can be excited is limited by the De Broglie wavelength X = //(l — /3'2)1/2/2ir mv, since an approach closer than this has no significance. The relativistic factor (1 — /32)^- is included to take into account the Lorentz contraction of the field at high velocities. In principle, the rate of energy loss is found by calcu- lating the amount of energy transferred to electrons of all those atoms of the absorber lying within the cylindrical volume surrounding the path of the particle and defined by the maximum and minimum radii indicated above. This calculation has been subject to numerous theoretical studies which, though differing somewhat in detail, have led to formulas that are now highly satisfactory for computing the rate of energy loss and the range of heavy charged particles. The first derivation of a stopping formula was given by Bohr [24] and was subsequently developed mainly by Bloch [25] Bethe [4,5,6], Miller [7], Fermi [15], and Halpern and Hall [26]. Assuming that the stopping of charged particles results wholly from excitation and ionization, calculations of the rate of energy loss —dE/dx in simple substances compare remarkably well with values derived from accu- rately measured ranges of alpha particles emitted by the natural radioactive elements. The most commonly used and accepted expression at the present time probably is that derived by Bethe [4,5,6]. It is applicable to mesons, protons, deuterons, and alpha particles over a wide range of energy. In its simple form, including the relativity correction but excluding certain correc- tions discussed below, it is given as dE lireWN dx mv- B B = Z 12] log ^j- - log (1 - /32) - 0« where B = a dimensionless quantity called the stopping number e = electronic charge m = electronic mass 78 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 N = number of atoms (not molecules) per cc 2 = charge number of particle Z = atomic number of absorbing atoms v = velocity of particle 0 = v/c 1 = average excitation potential of atom The range in energy over which the energy loss or stopping formula remains valid is determined (1) by the upper and lower limits inherent in its derivation and (2) by the appearance of effects at both low and very high energies which are not taken into account by the formula above. The lower limit arises from the assumption that the particle's velocity is greater than the highest orbital electron velocity in an absorbing atom, i.e., E ^>> MEk/wi, where EK is the K electron ionization potential and M and m are the masses of the particle and electron, respectively. This condition is necessary to ensure the constancy of the particle's charge ze. When the velocities of the incident particle and the electron are comparable, the prob- ability of electron capture is no longer negligible and the charge of the particle becomes indeterminate since it then fluctuates with successive collisions. The probability of electron capture and loss as the particle is slowed down and brought to rest has not been completely formulated as yet, and only empirical corrections for its effect on the stopping formula are possible. This uncertainty in the charge leads to considerable error in attempting to calculate the rate of energy loss for protons with energies less than ~ 0.2 mev and alpha particles with less than ~ 1.0 mev. The same difficulty makes the stopping formula generally inapplicable to very heavy and multiply charged particles such as fission fragments since the charge varies more rapidly and in some unknown way with the velocity even at very high energies (> 100 mev). The highest energies for which the simple stopping formula above can be applied are limited by the appearance at very great energies of the Fermi effect described in the next section. The average excitation potential I used in the stopping formula is usually considered to be a function only of the atomic number of the absorbing atoms and, in particular, to be independent of the kind of incident particle and its energy. As yet no completely satisfactory formula for its calculation has been provided. Its value can be determined empirically, however, with sufficient precision from accurately known range-energy data for protons or alpha particles in the absorber for which I is to be found. This is often done by adjusting the calculated range-energy curve to pass through the experi- mentally determined points by allowing / to be an arbitrary parameter [6,8,9,10]. The simplest and perhaps best theoretical value appears to be given by Bloch's conclusion [11] that / is directly proportional to the atomic number and by using Wilson's [30] empirical constant of proportionality, or Sec. 4.2] PROTONS, DEUTERONS, AND ALPHA PARTICLES 79 I = 11.5 Z ev. The values for 7 for various substances determined empiri- cally by Mano [12] and those calculated from the Bloch- Wilson formula are listed in Table 9. More recently Halpern and Hall [26] have introduced an analytical expression for I derived from a theory of ionization loss based on a multiple-dispersion-frequency model of the atom or molecule. In the energy range where the stopping formula above is accurate, the dispersion-frequency model gives the average excitation potential as the geometric mean of the dispersion frequencies Vi in the form n log Vm = \ fi log Vi i = 0 where /, is the fraction of electrons with a dispersion frequency vi and the sum is taken over all dispersion frequencies in the atom or molecule. The values of vi must be obtained from spectroscopic data and are expressed in units of (N ee2 firm)^ where Ne is the number of electrons per unit volume. The excitation potentials calculated by this method compare well with the values given in Table 9 only for light atoms; for heavy atoms they are as much as 20 per cent greater than the values given by Mano. Table 9. Average Excitation Potentials Absorber Z / ev [Mano] / ev (11.5 Z) Absorber Z / ev [Mano] / ev (11.5 Z) KH, 1 16.0 11.5 Cu 29 320 333.5 17.5 23.0 Zn 30 340 345 . 0 He 2 34.5 Kr 36 390 414.0 44 Mo 42 445 483.0 Li 3 38 34.5 Pd 46 490 529.0 ^N2 7 81 80.5 Ag 47 490 540.5 Air 7.23 87 83.15 Cd 48 495 552.0 80.5 [6] Sn 50 500 575.0 98.1 [13] Xe 54 530 621.0 MO, 8 99 92.0 P 78 790 897.0 Ne 10 132 115.0 Au 79 780 908.5 Al 13 155 149.5 Pb 82 800 943.0 A 18 195 207.0 Ni 28 325 322.0 It is seen from the stopping formula that the rate of energy loss for particles of different mass but with the same velocity is proportional to the square of the particle's charge. Protons and deuterons consequently lose energy at one-fourth the rate of alpha particles that have the same velocity. This property of the stopping formula provides a convenient means for computing 80 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 energy loss and range data for various kinds of particles when detailed calculations of the stopping number have been made for a wide range in velocity for any one particle. 4.3. Stopping-formula Corrections. When applied to protons, deuterons, and alpha particles, the stopping formula given in the last section is reliable over a wide range of energy without further modification, but at low energies (< 10 mev) and very high energies (> 1,000 mev) corrections for more complicated effects must be inserted. The largest error at very low energies is introduced by electron capture and loss, making the particles' time-averaged charge a function of velocity, The actual energy loss therefore is less than computed from the formula and for obvious physical reasons does not become infinite when v — > 0 as indicated by the stopping formula. As yet, however, no general theoretical formula- tion of a correction for this effect has been given. The error becomes appreciable for alpha particles below 1.0 mev and for protons below approxi- mately 0.2 mev. A second correction, formulated by Bethe [6], for low-energy particles arises from the reduced contribution of the K electrons, and in principle, also the L and M electrons, to the stopping power of medium and heavy atoms due to the screening effect of the outer orbital electrons. The correction for the reduced stopping power of the K electrons is contained in modifications of the stopping number B which, as given by Bethe [6], have the forms For E < — Z%JH, m B= (Z- 1.81) log ~+£* M For E > — Z\{iIH, m where E = energy of particle M = mass of particle m = electronic mass I h = ionization potential of hydrogen atom, 13.60 ev /' = average excitation potential of electrons outside K shell / = average excitation potential of entire atom Zeff = effective nuclear charge in K shell The numbers BK and CK are plotted in Fig. 15 as functions of r\ where mE 71 ~ MT^zJ(f Sec. 4.31 PROTONS, DEUTERONS, AND ALPHA PARTICLES 81 82 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 An approximate value of the effective nuclear charge at the K orbit may be obtained by using Slater's [28] screening constant of 0.3 for Is electrons; hence, Zeg = Z — 0.3 where Z is the actual atomic number. At very low energies the K electrons, except in very light elements, do not contribute to the stopping and BK — -> 0. At high energies where 17 ^>> 1, CK — » 0 and there- of (a) Ofl 07 Ofi OR 04 03 10 20 30 40 50 60 ATOMIC NUMBER 70 80 90 100 (b) ?.S El .EC rRO NS 2P 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0 10 20 30 40 50 60 70 80 90 100 ATOMIC NUMBER Fig. 16. Effective contribution of each K electron (a), and each L electron (b) to atomic number as a function of Z. [From H. Ilbnl, Z. Phys., 84, 1 (1933).] fore can be neglected. Consequently at high energies (> ~ 10 mev) the simple stopping formula is valid. It has also been pointed out by Bethe [6] that in medium and heavy elements all electrons in deep lying shells with ionization potentials greater than mE/M have little probability for excitation by a passing particle. These electrons (K, L, M, and possibly N) therefore contribute less than one charge unit per electron to the atomic number used in the stopping formula. The contributions, or oscillator strengths, of such electrons have been calculated by Honl [14] for the K and L electrons and are plotted in Fig. 16. The effective value of Z in the stopping formula is then Z0 =fKnK -^-JlUl + remainder of electrons, where /is the oscillator strength of an electron in the Sec. 4.4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 83 K or L shell and n is the number of K or L electrons. This correction is similar in its effect to the procedure followed by Duncanson [9] in treating both / and Z as empirical parameters in adjusting the simple stopping formula to the observed data. For very high energies, however, the correction is not important and the actual value of Z can be used. 4.4. Stopping Formula for High-energy Particles. An important correc- tion to the simple stopping formula was introduced by Fermi [15] for particles with very great energy traversing condensed materials. The effect that necessitates the correction arises from changes induced in the field of the passing particle due to local polarization of atoms in media that possess dielectric properties, or more specifically, media with a dielectric constant differing from unity. The rate of energy loss under these conditions is found to be smaller than that computed from the simple relativistic stopping formula which at very high energies increases as the logarithm of energy. The older stopping theories considered the field of the particle to be inde- pendent of the properties of the absorbing media. Thus, as a result of the Lorentz contraction of the particle's field, the collision radius, and conse- quently also the rate of energy loss, increases without limit as v — ■» c. This concept is no longer valid when polarization of the medium is taken into account. When the field of the particle is analyzed into its Fourier com- ponents, it is apparent that when v > «r!- each component of the field is propagated with a different velocity in the medium, or is subject to dispersion. Those frequency components with velocities less than v form wave fronts or bow waves at various angles with the direction of the particle. As v — > c the field is greatly altered as a result of dispersion but, most important, it approaches a limiting form in which all frequency components assume fixed phase relations. The distance at which atoms can be excited by the limiting form of the field remains finite and, correspondingly, the rate of energy loss approaches asymptotically a finite limiting value. In accordance with this description the reduction in rate of energy loss from the value indicated by the simple stopping formula becomes most important when the velocity of the particle exceeds ce~] '-. It is apparent that for electrons the effect of polarization should become appreciable for energies greater than several mev. The correction is of little use in this case, however, because energy loss by radiative collision also becomes significant and a stopping formula based only on ionization energy loss is no longer justified. This applies, fortunately, only to electrons, and the stopping formula can be validly used, so far as is known, for heavier charged particles for all prac- ticable energies. The Fermi corrections, therefore, must be adapted in the appropriate energy range. In general, the corrections become appreciable for protons and alpha particles with E <~ 104 mev and for mesons with E ~ 103 mev. 84 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 The model used by Fermi as the basis for calculating the reduction in energy loss clue to polarization is that in which electrons are regarded as classical oscillators and the influence of damping and conduction electrons is negligible. Further, it is assumed that each absorbing substance can be characterized by a single dispersion frequency v0, which can be obtained from spectroscopic and x-ray data. With these assumptions the dielectric constant of the absorbing medium may be expressed in the simple form . Airne2 e = 1 H »- When Fermi's corrections are combined with the simple stopping formula, the expressions applicable to particles with very high energies are [15] For v < ct -i.. dE = 2tt NZe'z1 dx mv2 For v > ce~Vl, dE 2ivNZeAz dx mv- log^jf- - log (1 - 02) + (1 - p) - loge log — n h 1 — log (e — lj 1 where / = average excitation potential e = dielectric constant The factor W is the maximum energy that can be transferred to an electron. According to Bhabha [13], W has the form 2m(E2 - M2cA) W = m2c2 + M2c2 + 2mE where m = mass of electron M = mass of particle E = energy of particle c = velocity of light The correction contained in the first formula is always negligible either when v c it approaches asymptotically the constant value given by the expression [15] dE __ 2xiV^422 dx mc2 where h = Planck's constant /, m2c2W , A V°gZAW2+V Sec. 4.6] PROTONS, DEUTERONS, AND ALPHA PARTICLES 85 Recently a more general treatment of stopping for charged particles with very high energies was formulated by Halpern and Hall [26]. Their theory, based on a multiple-dispersion-frequency model in which the effects of oscilla- tion damping and conduction electrons are also considered, is a generaliza- tion of Fermi's development. The correction in energy loss when these additional factors are taken into account is found to be somewhat less than in the Fermi theory, but the absolute increase in the rate of energy loss is not so fast as log E required by the simple stopping formulas. 4.5. Relative Stopping Power. Calculations of the stopping power of various substances relative to air are complicated by the dependence on the velocity of the particle as well as on the atomic number and average excitation potential of the absorber. Approximately, the ratio is given by N'Z' log (2mv2/r) NZ log (2mv2/Ie where the primed letters refer to the substance and the unprimed to air. Measurements of relative stopping powers of absorbers for alpha particles relative to air are given in Table 10 for two energies and in Fig. 17 for various energies. For heavy charged particles with energies greater than 1 mev the relative stopping power changes very slowly, while above 10 mev it remains essentially constant. Table 10. Atomic Stopping Power for Alpha Particles Relative to Air at Normal Temperature and Pressure Absorber RaC a [16] 6 mev a [10] Absorber RaC a [16] 6 mev a [10] H 0.200 0.20 Ni 1.89 He 0.308 0.35 Cu 2.00 2.57 Li 0.519 0.50 Zn 2.05 Be 0.750 Br 2.51 C 0.814 Kr 2.92 N 0.939 0.99 Mo 3.20 O 1.000 1.07 Ag 2.74 3.36 Ne 1.23 Cd 2.75 Mg 1.23 Sn 2.86 3.59 Al 1.27 1.5 I 3.55 Si 1.23 Ye 3.76 CI 1.76 Pt 3.64 A 1.80 1.94 Au 3.73 4.50 Ca 1.69 Tl 3.76 Fe 1.96 Pb 3.86 4.43 m 4.6. Atomic Stopping Power. The atomic stopping power a, frequently termed stopping cross section, is defined as the energy loss per centimeter 86 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 divided by the number of atoms per cubic centimeter. Using an approximate form of the energy-loss formula as an example, a is given by 4ireAz~Z . 2mv2 a ■- -r- log mv 1 ev/cm2 4.7. Mass Stopping Power. The mass stopping power is defined as the energy loss per centimeter divided by the density of the absorber or as the stopping power per unit density. From Bragg's empirical rule as well as 0 1 ENERGY OP ALPHA PARTICLES (MEV) 3 16 24 32 40 48 56 5 GOLD DC Ul §4 a. o z a. O 3 SILVER 1- m o 2 O 2 COPPER i- fc < 1 ALUMINUM CARBON HYDROGEN 0 'I 0 2 4 6 8 10 12 14 ENERGY OF PROTONS (MEV) Fig. 17. Atomic stopping power of various elements relative to air. from the stopping formula, it is found to vary approximately as the inverse square root of the atomic mass of the absorber. 4.8. Range of Heavy Charged Particles. The range of a charged particle in an absorber is the total path length traversed before the particle is brought to rest by complete loss of its kinetic energy. With an initial energy E0, in units of Mc2, the range is calculated with the aid of the energy-loss formula by the integral CEo R= / dE J0 —dE/dx where —dE/dx = energy loss per unit length of path cm Sec. 4.8] PROTONS, DEUTERONS, AND ALPHA PARTICLES 87 The evaluation of the integral must be carried out numerically, and when possible the integration is usually started at some well-established experi- mental value of the range and energy rather than that at zero kinetic energy, thus avoiding the error introduced by the poor fit of the stopping formula at very low energies where electron capture and loss become effective. Unlike the comparatively indeterminate range of beta particles and the exponential absorption of gamma rays, the ranges of heavy charged particles are well defined in that all particles of an initially monoenergetic beam are brought to rest after traversing the same distance through an absorber, with only a small statistical spread or straggling about the mean range. On the other hand, heavier particles with a higher charge number such as fission fragments do not exhibit well-defined ranges. Their charge varies rapidly with velocity due to electron capture, and elastic collisions with nuclei play a more important part; hence, the stopping formula cannot be applied even for a first approximation. It is probable, however, that at very great energies, in the order of 1,000 mev or more depending upon the mass of the particle, the stopping formula would also be applicable to these particles. At such energies the velocity would be great enough to satisfy the conditions required by the formula, and the charge would then remain constant. How- ever, even at such energies it is doubtful that the stopping formula will prove to be very useful since the range of a highly charged particle is small and the straggling large. At the present time the most accurately measured ranges are those of alpha particles from the natural radioactive isotopes. They have been measured repeatedly by numerous investigators over a period of many years and now stand as the final test of the accuracy of range calculations, at least for energies up to 10 mev. On the basis of early measurements of the range of alpha particles, three empirical relations were established for the variation of range in air as a function of energy: 1. Range between 0 to 3 cm, R r^ VH ~ E3/i cm 2. Range between 3 to 7 cm (Geiger formula), R = 9.67 X 10"2V cm 3. Range above 7 cm, R ^ y i r^ E2 cm These relations should be regarded only as qualitative, because in the variation of R with vn, the exponent n also depends on the velocity and increases from n = 1.4 for low velocities to n — 4.0 for very high velocities [6]. The relative range of a particle in a substance compared with its range in 88 I SOT OP I C TRACERS AND NUCLEAR RADIATIONS [Chap. 4 air cannot be calculated with accuracy by a simple expression because of the involved dependence on the stopping power of different atoms. Neverthe- less, when the range in air is known, a rough estimate of the range of alpha particles in substances other than air can be calculated from Geiger's formula in the energy interval for which it is valid. R = 3.2 X 10- RoVa cm where R„ = range in air in cm p — density of absorber A = average atomic weight of absorber Proton ranges have not been investigated so exhaustively as those of alpha particles but can be computed from the range formula with somewhat greater accuracy at lower energies because of the smaller straggling; the minimum velocity conditions for protons holds for energies as low as ~ 0.2 mev. However, if the alpha-particle range in a substance is known, the range of a proton with the same initial velocity can be obtained from the relation Ma \Zp/ Rv = rr + const cm Table 11. Ranges of RaC Alpha Particles in Various Substances [16] Substance Range X 10 3 cm Substance Range X 10 3 cm Li 12.91 Ag 1.92 Mg 5.78 Cd 2.42 Al 4.06 Sn 2.94 Ca 7.88 Pt 1.28 Fe 1.87 Au 1.40 Ni 1.84 Tl 2.33 Cu 1.83 Pb 2.41 Zn 2.28 where Mp, zp, Mu, za = mass and charge of proton and alpha particle, respectively The constant is included to adjust the range at very low energies since the straggling of alpha particles is greater than that of protons. Blackett and Lees [23] have evaluated the constants and give the range relation as Rp = 1.007222a - 0.20 cm In a similar way deuteron ranges can be obtained from the ranges of alpha particles with the same initial velocity from the relation Sec. 4.9] PROTONS, DEUTERONS, AND ALPHA PARTICLES 89 I« \zP/ Rd ~ inr I -- J -^a -- const ^ = 2.012i?c cm 4.9. Specific Ionization. The number of ion pairs formed by a charged particle per unit length of path is referred to as the specific ionization. Its value depends upon the absorbing medium and on the velocity and charge of the particle at any instant. The most intense ionization, as may be seen from the rate of energy loss indicated by the stopping formula, is produced near the end of the particle's range where the velocity is low. A maximum rV.X SOURCE THICK CCURCE Fig. 18. 3 RESIDUAL RANGE IN CENTIMETERS Bragg curve of specific ionization by alpha particles in air. value is reached and then drops rapidly to zero as the particle is brought to rest. At high energies the specific ionization remains relatively constant at one-third to one-tenth of its maximum value near the end of the particle's range. In air at normal temperature and pressure the specific ionization of alpha particles, for example, remains essentially constant with a value of roughly 2,000 ion pairs per centimeter for high energies. At low energies, it increases rapidly to a maximum of ~ 6,000 ion pairs for an energy correspond- ing to a residual range of approximately 0.4 cm, as shown in Fig. 18. Similar curves hold for protons and deuterons. The average energy W spent by charged particles in forming one ion pair has been subjected to extensive experimental and theoretical investigation. It is found that for energies greater than about 2.0 mev the value of W for protons and alpha particles remains essentially constant although there is a very weak dependence on velocity. In an exhaustive survey of the results obtained by various investigators, Gray [29] proposed the value of W = 36 ev per ion pair formed in air by protons and W = 31.5 ev per ion pair formed by alpha particles (measured with alpha particles from RaC')- For hydrogen 90 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 the values of W for protons and alpha particles are 35 + 1.5 ev per ion and 36 ev per ion, respectively (see also Table 12). Table 12. Average Ionization Energy Required to Form One Ion Pair by Alpha Particles (7 mev) [31] Absorber N2 0, Air Cl2 C02 BF3 CH CF4 W, ev '.. 33.7 28.5 32.1 25.0 31.2 33.3 27.4 31.1 4.10. Delta Rays. The recoil electrons produced by alpha particles, observed in a Wilson cloud chamber as short, faint straggling tracks branch- ing from the alpha track, are referred to as delta rays after J. J. Thomson [17]. The maximum energy imparted to a recoil electron, which occurs in a head-on collision, corresponds to twice the alpha-particle velocity or -Emax = 2mv2 = Am E IF Thus, for a 10-mev alpha particle the most energetic delta ray will have an energy of approximately 6,300 ev and a range in air of several millimeters. The average number of ion pairs liberated by a delta particle of energy Ed has been calculated to be [18] n (' + t) where / = ionization potential of absorber The number of delta rays produced and the distribution of their energy depends in a complicated way on the particle velocity and on the kind of absorber, and no satisfactory method for these calculations is available. 4.11. Straggling of Charged Particles. The observed ranges of initially monoenergetic particles of the same mass and charge exhibit a statistical fluctuation or "straggling" about an average value. Two factors are mainly responsible for straggling: (1) fluctuation in the number of ions produced per unit path length, particularly near the end of the range where the charge of the particle fluctuates; (2) statistical variation in the energy loss per ion pair. By plotting the number of particles in a beam against distance from the source, an integral range distribution or particle-range curve is obtained, as shown in Fig. 19. Differentiating this curve results in a differential number- range distribution curve which is the distribution of ranges about an average value R0. Because of the statistical nature of straggling this curve follows to a close approximation a Gaussian distribution given by the following Sec. 4.111 PROTONS, DEUTERONS, AND ALPHA PARTICLES 91 expression, provided that the beam of particles was monoenergetic initially [27]: PdR = -i- e-(R»-RWa* dR where P = probability that a particle has a range lying in the interval R to R + dR a = range straggling parameter R0 = mean range The 'parameter a is the half-width of the differential distribution curve at 1/e of its maximum height. It increases with energy, and its order of magni- tude may be illustrated by the observed value of approximately a = 0.13 cm for 10-mev alpha particles stopped in air. DIFFERENTIAL CURVE, THIN SOURCE EXTRAPOLATED RANGES DISTANCE FROM SOURCE R0 -.MEAN RANGE Fig. 19. Integral and differential number-range curves for heavy charged particles. The mean range Ru is the distance from the source to the maximum of the differential number-range (Gaussian) curve, or alternatively it may be defined as the distance at which the initial number of particles is reduced to one-half. In practice the extrapolated number-distance range is the most readily determined quantity. This is the range indicated by the intercept of a line extended along the straight portion of the slope of steepest descent of the integral range curve. The mean and the extrapolated ranges are then related by the expression i?es — R0 = ir -a These definitions are exact only for strictly monoenergetic particles such as those emitted from a source that is infinitesimal in thickness. In practice, sources and targets are often "thick" in that their thickness is comparable to or greater than the range of the particles. In this case the beam is not 92 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 strictly homogeneous because particles emitted by atoms at various depths are partially absorbed and scattered in different amounts before reaching the surface of the source. However, from thick, homogeneous samples and from thick targets in which the production of particles is uniform throughout the target, the extrapolated range obtained from the measured number-range curve gives a mean range that is representative of particles coming from the surface [6]. Corrections must be applied in all other cases such as "semi- thick" targets and sources where the thickness is comparable to the particle's range and thick targets when the radiation producing the particles does not penetrate the target with uniform intensity. 4.12. Scattering of Charged Particles. Elastic scattering of heavy charged particles is quantitatively accounted for on the basis of interaction between the coulomb fields of the incident particle of charge ze and the struck nucleus of charge Ze. It is assumed in such collisions that the particle does not approach the nucleus so closely as to be affected by the short-range nuclear forces since these fields result in a different kind of scattering. For alpha particles the minimum collision distance appears to be approximately 2.05 X 10~13ylw, where A is the atomic number of the struck nucleus. The simplest scattering occurs in collisions of particles with very heavy nuclei, for then the struck nucleus remains virtually stationary during the collision and the particle is deflected with little loss of energy and momentum. Rutherford's formula expressing the number of particles deflected into a unit solid angle at an angle 6 with the initial direction is then (ehZ V \2mv2J jsec4 - where n„ = initial number of particles per cm2 of the beam N — number of atoms per cc z = charge number of particle Z = atomic number of scatt.erer m = mass of particle Collisions of particles with nuclei of comparable or smaller mass must be corrected for the contribution of energy to the struck nucleus which recoils with an appreciable fraction of the initial kinetic energy of the incident particle. The general Rutherford formula for the number of particles, n, scattered into a unit solid angle at an angle 9 is (e2zZ\ , „ [cot 6 + Vcosec20 - (m/M)2]2 I J cosec d ■ \niv2/ Vcosec2 6 - (m/M)2 »(0) = n0N ( — 5-1 cosec3 6 where n0 = initial number of particles per cm2 of beam M = mass of nucleus m = mass of particle Sec. 4.13] PROTONS, DEUTERONS, AND ALPHA PARTICLES 93 The + sign is used if M > m, and — sign if M < m. This expression obviously reduces to the preceding formula when M y>> m. Although particles will be scattered in all directions, the intensity drops off very rapidly with increasing angle as measured from the forward direction, thus in the case of alpha particles on platinum, less than 1 particle in 8,000 will be scattered into an angle greater than 90 deg. Backscattering in light elements, consequently, is entirely negligible. In general, calculations of scattering of particles by heavy elements for energies up to about 10 mev are given to a high degree of accuracy by the Rutherford formulas. Deviations from Rutherford (coulomb field) scattering calculated from the formulas above will be found for certain energies of the incident particle depending upon the properties of the scattering nucleus. Anomalous scatter- ing will occur if the particle possesses sufficient energy to penetrate the electrostatic potential barrier and be affected by the nuclear forces or if the energy of the particle plus the internal energy of the scattering nucleus equals the energy of a quantum state of the compound nucleus. Anomalous scattering that increases slowly with increased particle energy can usually be identified with penetration of the potential barrier. Anomalous scattering that increases rapidly to a maximum intensity and then decreases as the energy is increased indicates resonance scattering. 4.13. Alpha Decay. The theory of alpha decay is based on the now familiar quantum mechanical problem of the penetration of charged particles through potential barriers. Some assumptions must be made about the shape of the potential field forming the barrier, but the theory can account for the main details of alpha emission and provide estimates of its probability. If it is assumed that the alpha particle already exists as a separate entity within the nucleus and that the only effect of the remaining particles on it is to provide a potential "well" in which the alpha particle exists in some energy state, the problem immediately reduces to the one-body model for alpha decay [19,20]. Within the nucleus it is assumed that alpha particles can move with relative freedom, but at the surface it is constrained from leaving by an effective surface tension maintained by the unsaturated, attractive nuclear forces of those particles lying at the surface. This force rises rapidly to a maximum value at a distance approximately equal to the nuclear radius. Beyond the radius, the nuclear potential field rapidly vanishes, and only the coulomb field due to the protons remains. The height of the potential barrier above the zero coulomb energy, i.e., the value approached asymptotically by the coulomb field at great distances, is approximately the magnitude of the coulomb field at the surface or I? e'zZ Eh~-R 94 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 Zero coulomb energy where z = alpha-particle charge Z = atomic number R = nuclear radius The field in the nucleus therefore may be represented by a cylindrical potential well, as shown in Fig. 20, extending an unknown distance E0 below the zero coulomb energy and a distance Eb above. Outside the potential well only the coulomb field is effective. In the nucleus, an alpha particle in an energy state above the zero cou- lomb energy has a finite probability of leaving by penetration through the barrier even though its energy is considerably smaller than the barrier height. If the alpha particle is raised to a level equal to the barrier, or into the continuum of states above the barrier by external excitation, it is emitted in a time of the order of 10-21 sec. When the alpha particle is excited to a quantum state lying below the top of the barrier, the probability of emission per unit time by penetration through the barrier is greatly reduced. The mean life r for alpha emission under this condition (alpha decay) is given by the expression r = T0ef where t0 ^ 10-21 sec and the function / depends on the charge and mass of the nucleus. If the observed kinetic energy of the alpha particle is small compared to 2e2Z/R, the function / is given approximately by Sir2e2Z STe(4ZmR)V> »- Radius -J Fig. 20. Diagram of potential fields of nucleus showing "square" potential well and coulomb barrier. / = hv h where Ea = energy of alpha particle above zero coulomb energy, or the observed kinetic energy of the alpha particle plus the recoil nucleus (Fig. 20) m = mass of alpha particle R = nuclear radius, « 1.47 X 10rl3A^ cm v = alpha-particle velocity h = Planck's constant The factor t0 is the mean life for emission in the absence of a barrier and may be thought of as the period of vibration of the alpha particle in the nucleus. The reciprocal of ef is the transmission coefficient, or penetrability, and Sec. 4.13] PROTONS, DEUTERONS, AND ALPHA PARTICLES 95 is the factor that determines the probability of emission through the barrier. It is a sensitive function of the barrier height and width as is readily apparent from the observed half-lives of the natural radioactive isotopes which range from 10~7 sec to 1010 years. Writing the expression for r in terms of logarithms, log r = - + B v where A = fv B = log T0 If it is assumed that the nuclear radius is nearly constant for all alpha emitters, A and B are then also nearly constant and the logarithm of the mean life is inversely proportional to the velocity of the alpha particle. A similar relation is found between the range R and the mean life. or log r = C - D log R log X = E log R + F where X = disintegration constant C, D, E, F = constants These important relations were first discovered empirically by Geiger and Nuttal [21] when they plotted the measured values of X and R for the alpha emitters of the natural radioactive series. The components of each series are found to fall remarkably close to straight lines as required by the expression above. REFERENCES FOR CHAP. 4 1. Crane, H. R., L. A. Delsasse, W.A. Fowler, and C. C. Lauritsen: Phys. Rev., 48, 484(1935). 2. Feenberg, E.: Phys. Rev., 49, 328 (1936). 3. Bethe, H., and R. F. Bacher: Rev. Mod. Phys., 8, 82 (1936). 4. Bethe, H.: Ann. Physik, 6, 325 (1930). 5. Bethe, H.: Z. Physik, 76, 293 (1932). 6. Livingston, S., and H. Bethe: Rev. Mod. Phys., 9, 263 (1937). 7. Miller, C: Ann. Physik, 14, 531 (1932). 8. Blackett, P. M. S.: Proc. Roy. Soc. (London), 136, 132 (1932). 9. Duncanson.W. E.: Proc. Cambridge Phil. Soc., 30, 102 (1934). 10. Mano, G.: Ann. Physik, 1, 407 (1934). 11. Bloch, F.: Z. Physik, 81, 363 (1933). 12. Mano, G.: Ann. Physik, 1, 446 (1934). 13. Bhabha, H. J. : Proc. Roy. Soc. (London), 164, 257 (1937). 14. Honl, H.: Z. Physik, 84, 1 (1933). 15. Fermi, E.: Phys. Rev., 57, 485 (1940). 16. von Taubenberg, H. R.: Z. Physik, 2, 268 (1920). 17. Thomson, J. J.: Proc. Cambridge Phil. Soc, 13, 49 (1900). 96 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 18. Fowler, R. H.: Proc. Cambridge Phil. Soc, 21, 531 (1923). 19. Gamow, G.: Z. Physik, 52, 510 (1929). 20. Gurney,R. W., and E. U. Condon: Phys. Rev., 33, 127 (1929). 21. Geiger and Nuttal: Cambridge Phil. Mag., 22, 613 (1911). 22. Bethe, H.: Phys. Rev., 50, 977 (1936). 23. Blackett, P. M. S., and D. S.Lees: Proc. Roy. Soc. (London), 134, 658 (1932). 24. Bohr, N.:Phil. Mag., 25, 10 (1913); 30, 581 (1915). 25. Bloch, F.: Ann. Physik, 16, 285 (1933). 26. Halpern, O., and H. Hall: Phys. Rev., 73, 477 (1948). 27. King, A., and W. M. Rayton: Phys. Rev., 51, 826 (1937). 28. Slater, J.: Phys. Rev., 36, 57 (1930). 29. Gray, L. H.: Proc. Cambridge Phil. Soc, 40, 72 (1944). 30. Wilson, R. R.: Phys. Rev., 60, 749 (1941). 31. Dick, L., P. Folk-Vairant, and J. Rossel: Helv. Phys. Ada, 20, 357 (1947). Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 97 Table 13. Range and Energy Loss of Protons in Hydrogen and Helium The following data were computed for hydrogen and helium at 0°C and 760 mm of mercury from the Bethe stopping theory. Corrections for noncontributing shells, the Fermi effect, and Brenisstrahlung are not included. Data calculated by W. Aron and B. G. Hoffman, Radiation Laboratory, University of California, for the Atomic Energy Commission. Energy, mev Hydrogen (/ = 17.5 ev) Helium (/ = 44 ev) Energy loss, mev /cm Range, cm Energy loss, mev/cm Range, cm 0 0 0 0 0 1 5.88476 X 10-2 1.0025 X 101 4.75985 X 10"2 1.3030 X 10l 2 3.36971 2.80637 3 2.41487 6.9061 2 00607 8.4160 4 1.90174 1.61918 5 1 . 57824 1.7410 X 102 1.35183 2 0778 X 102 6 1 . 35435 2.4270 1.16537 2 . 8769 7 1.18957 3.2169 1.02733 3 . 7930 8 1.06288 4.1076 9.20701 X 10"3 4.8229 9 9.62240 X 10~3 5 . 0979 8.35660 5.9645 10 8.80238 6.1855 7.66136 7.2155 11 8.12051 7.08158 12 7 . 54400 8 . 6480 6.59015 1.0039 X 103 13 7.04979 6.16793 14 6.62113 1 . 1485 X 103 5.80097 1 . 3281 15 6.24557 5.47889 16 5.91365 1.4687 5.19375 1.6931 17 5.61804 4.93944 18 5 . 35301 1.8246 4.71110 2 0980 19 5.11395 4 . 50487 20 4.89716 2.2157 4.31764 2.5419 25 4.05773 3 . 59050 30 3.48225 4.6776 3.08987 5.3241 35 3.06191 2.72299 40 2.74078 7.9416 2.44195 8 . 9943 45 2.48706 X lO"3 2.21941 X 10" ■' 50 2.28132 1.1961 X 104 2.03861 1 . 3498 X 104 55 2.11097 1 . 88867 60 1.96757 1 . 6697 1.76226 1.8791 65 1 . 84498 1 . 65406 70 1 . 73905 2.2115 1 . 56046 2 . 4736 75 1 . 64654 1.47862 80 1 . 56505 2.8188 1 . 40644 3.1597 85 1.49262 1 . 34229 90 1.42789 3 . 4886 1 . 28488 3.9046 95 1 . 36965 1.23320 100 1.31697 4.2186 1 . 18642 4.7154 98 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 Table 13. Range and Energy Loss of Protons it\ Hydrogen and Helium — (Continued) Energy, mev Hydrogen {I = 17.5 ev) Helium (/ = 44 ev) Energy loss, mev/cm Range, cm Energy loss, mev/cm Range, cm 125 1.11433 1.00617 150 9.76921 X 10~4 9.0290 8.83659 X 10-4 9.6737 175 8.77559 7.94951 200 8.02397 1.4386 X 106 7.27717 1 . 5955 X 105 225 7.43533 6.75029 250 6.96260 2.1104 6 . 32684 2.3356 275 6.57481 5.97928 300 6.25129 2.8704 5.68919 3.1712 325 5.97754 5.44364 350 5.74314 3 . 7065 5.23335 4.0893 375 5 . 54040 5.05144 400 5 . 36349 4 . 6086 4.89271 5.0787 425 5.20796 4.75315 450 5.02865 5 . 5697 4.62963 6.1303 475 4.94771 X 10~4 4.51967 X 10~4 500 4.83799 6.5814 X 105 4.42128 7.2363 X 105 550 4.65020 4.25293 600 4.49589 8.7302 4.11470 9.5859 650 4.36739 3.99967 700 4.25914 1.1022 X 106 3.90293 1 . 2085 X 106 750 4.16719 3 . 82084 800 4.08836 1.3418 3.75057 1.4701 850 4.02034 3.69004 900 3.96131 1.5904 3.63760 1.7410 950 3.90981 3.59196 1,000 3.86469 1.8461 3.55206 2.0194 1,500 3.61964 3 . 33866 2,000 3 . 54362 4.5895 3.27707 4.9940 2,500 3.52729 3 . 26866 3,000 3 . 53620 7.4212 3 . 28242 8.0499 3,500 3.55670 3.30613 4,000 3.58263 1.0232 X 107 3.33429 1 . 1074 X 107 4,500 3 . 61094 3.36423 5,000 3.64006 1 . 3001 3.39457 1.4046 5,500 3.68530 3.42457 6,000 3.69769 1.5719 3.45387 1 . 6967 6,500 3.72551 3.48228 7,000 3.75246 1 . 8403 3.50971 1 . 9839 7,500 3.77849 3.53614 8,000 3.80360 X 10~4 2.1050 X 107 3.56157 X 10-4 2 . 2666 X 107 8,500 3.82779 3.58604 9,000 3.85111 2 . 3663 3 . 60960 2 . 5456 9,500 3.87358 3.63227 10,000 3.89525 2 . 6244 3.65412 2 . 8209 Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 99 Table 14. Range and Energy Loss of Protons in Lithium and Beryllium The following data were computed for lithium and beryllium from the Bethe stopping theory. Corrections for noncontributing shells, the Fermi effect and Bremsstrahlung are not included. Data calculated by W. Aron and B. G. Hoffman, Radiation Laboratory, University of California, for the Atomic Energy Commission. Lithium (I = 34.5 ev) Beryllium (/ = 46 ev) Energy, mev Energy loss, mev/(mg/cm2) Range, mg/cm2 Energy loss, mev/ (mg/cm2) Range, mg/cm2 0 0 0 0 0 1 2.58707 X 10-1 2.8738 2.46973 X 10"1 2.9100 2 1.51183 8.1422 1.45866 8.4276 3 1 . 09382 1.60295 X 10 1 . 06050 1.65443 X 10 4 8.66545 X 10 '2 2 . 63834 8.42671 X 10~2 2.71890 5 7.22183 3.90797 7.03775 4.02471 6 6.21736 5.40540 6.06860 5.56018 7 5.47503 7.12294 5.35088 7.31884 8 4.90241 9.05655 4.79629 9 . 29626 9 4.44626 1.12012 X 102 4.35391 1 . 14873 X 102 10 4.07372 1.35535 3.99217 1 . 38884 11 3.76331 1.61096 3 . 69045 1 . 64959 12 3 . 50041 1 . 88670 3.43468 1.93067 13 3.27435 2.18225 3.21490 2.23179 14 3.07860 2.49751 3.02387 2 . 55269 15 2.90660 2.83183 2.85618 2.89312 16 2.75440 3.18540 2.70771 3.25285 17 2.61871 3.55788 2.57528 3.63168 18 2.49694 3.94910 2 . 45636 4.02940 19 2.38700 4.35880 2 . 34896 4.44583 20 2.28721 4.78701 2.25143 4.88079 25 1 . 90004 1.87264 30 1 . 63380 1.00445 X 103 1.61178 1.02152 X 103 35 1.43889 1.42058 40 1 . 28969 1 . 69902 1.27409 1 . 72503 45 1.17162 X 10~2 1 . 15808 X 10-2 50 1.07576 2.55219 X 103 1 . 06382 2.58817 X 103 55 9.96287 X lO-3 9.85637 X 10~3 60 9.29321 3.55561 9.19723 3.60244 65 8.72019 8 . 63296 70 8 . 22467 4.70211 8.14481 4.76052 75 7.79157 7.71801 80 7.40969 5.98531 7.34156 6.05595 85 7.07034 7.00694 90 6.76674 7.39944 6.70749 7.48288 95 6.49347 6.43788 100 6.24616 8.93925 6.19383 9.03599 100 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 Table 14. Range and Energy Loss of Protons in Lithium and Beryllium — (Continued) Energy, mev Lithium (/ = 34.5 ev) Beryllium (/ = 46 ev) Energy loss, mev/(mg/cm2) Range, mg/cm2 Energy loss, mev/ (mg/cm2) Range, mg/cm2 125 5.29376 5.25348 150 4.64686 1.83635 X 104 4.61426 1.85324 X 104 175 4.17853 4.15124 200 3.82395 3.03134 3.80050 3.05609 225 3.54605 3.52554 250 3.32275 4.44008 3.30454 4.47303 275 3.13950 3.12314 300 2.98657 6.03164 2.97173 6.07293 325 2.85714 2.84357 350 2 . 74630 7.78077 2.73381 7.83041 375 2.65042 2.63886 400 2.56675 9.66654 2.55601 9.72443 425 2.49320 2.48317 450 2.42807 1.16714 X 106 2.41870 1.17374 X 106 475 2.37013 X 10-3 2.36131 X 10~3 500 2.31826 1.37804 X 105 2.30995 1 . 38542 X 105 550 2.22951 2 . 22209 600 2.15662 1.82624 2 . 14995 1.83512 650 2.09596 2.08993 700 2.04490 2.30310 2.03943 2.31336 750 2.00157 1 . 99659 800 1.96446 2.80251 1 . 95993 2 . 81402 850 1 . 93249 1.92835 900 1.90476 3.31983 1 . 90099 3.33245 950 1.88062 1.87719 1,000 1 . 85950 3.85146 1.85638 3.86504 1,500 1 . 74605 1.74518 2,000 1.71259 9 . 53948 1.71322 9.55613 2,500 1.70722 1 . 70900 3,000 1.71361 1.53906 X 106 1.71635 1.54013 X 106 3,500 1.72531 1.72887 4,000 1 . 73941 2.11859 1.74371 2.11847 4,500 1.75451 1 . 75947 5,000 1 . 76986 2 . 68852 1.77542 2 . 68683 5,500 1 . 78645 1.79119 6,000 1 . 79998 3 . 24846 1.80659 3.24515 6,500 1.81444 1.82151 7,000 1 . 82840 3 . 79956 1.83592 3.79418 7,500 1.84187 X 10~3 1 . 84980 X IO-3 8,000 1.85484 4.34252 X 10fi 1.86316 4.33482 X 106 8,500 1.86732 1.87601 9,000 1.87934 4.87808 1.88837 4.86790 9,500 1.89091 1.90028 10,000 1 . 90207 5 . 40695 1.91175 5.39416 Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 101 Table 15. Range and Energy Loss of Protons in Boron and Carbon The following data were computed for boron and carbon from the Bethe stopping theory. Corrections for noncontributing shells, the Fermi effect and Brcmsstrahlung are not included. Data calculated by W. Aron and B. G. Hoffman, Radiation Laboratory, University of California, for the Atomic Energy Commission. Energy, Boron (/ = = 57.5 ev) Carbon (/ = 69 ev) mev Energy loss, mev/(mg/cm2) Range, rag/cm2 Energy loss, mev/(mg/cm2) Range, mg/cm2 0 0 0 0 0 1 2.42467 X 10-1 2.890 2.41758 X 10-l 2.760 2 1 . 44542 8.4650 1.49676 8.1130 3 1.05529 1.66485 X 10 1.09761 1 . 59838 X 10 4 8.40700 X 10"2 2.73305 8.75831 X 10-2 2 . 62925 5 7.03397 4.04064 7.33961 3 . 88859 6 6.07363 5.57469 6.34518 5.35789 7 5.36113 7.33162 5.60616 7.03867 8 4.80635 9 . 30499 5.03354 8.92378 9 4.36942 1 . 14905 X 102 4.57573 1 10106 X 102 10 4.00899 1 . 38826 4 . 20066 1.32935 11 3.70811 X 10"2 1 . 64782 3 . 88732 12 3.45285 1.92749 3.62130 1 . 84374 13 3 . 23335 2.22697 3 . 39243 14 3.04245 2 . 54597 3.19326 2.43321 15 2.87479 2.88425 3.01826 16 2.72627 3.24160 2.86317 3.09577 17 2.59374 3.61779 2.72471 18 2 . 47468 4.01262 2 . 60039 3 . 82973 19 2.36710 4.42591 2 . 48783 20 2 . 26939 4.85748 2 . 38565 4 . 63358 25 1 . 88953 1.98812 30 1.62761 1.01441 X 103 1.71372 9.65798 35 1 . 43545 1.51222 40 1.28811 X 10~2 1.71063 X 103 1.35762 X 10"2 1 . 62667 X 103 45 1.17135 1.23504 50 1.07642 2 . 56400 1.13533 2 . 43603 55 9.97656 X 10--3 1.05256 60 9.31220 3 . 56604 9.82726 X 10"3 3 38580 65 8.74326 9.22900 70 8.25089 4 70951 8.71124 4 . 46008 75 7.82082 8.25809 80 7 . 44035 5.98793 7.85829 5 . 67979 85 7.10259 7.50276 90 6.80024 7 . 39565 7.18446 7 01242 95 6.52797 6.89777 100 6.28146 8.92731 6.63817 8.46197 102 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 Table 15. ] R.ANGE AND ENERGY LOSS OF PROTONS in Boron and Carbon — (Continued) Energy, mev Boron (/ = : 57.5 ev) Carbon (/ = 69 ev) Energy loss, mev/(mg/cm2) Range, mg/cm2 Energy loss, mev/(mg/cm2) Range, mg/cm2 125 5.33120 5.63703 150 4.68484 1.82853 X 104 4.95568 1.73119 X 104 175 4.21641 4.46169 200 3.86146 3.01278 4.08726 2 . 85450 225 3.58311 3.79356 250 3.35934 4.40695 3.55741 4.16715 275 3.17563 3.35463 300 3.02229 5.98040 3.20164 5 . 65534 325 2.89247 3.06459 350 2.78129 7.70817 2.94721 7 . 28607 375 2.68510 2.85566 400 2.60117 9.56958 2.75705 9.03835 425 2.52738 2.67915 450 2.46208 X IO-3 1.15473 X 105 2.61020 X 10-3 1 . 09040 X 105 475 2.40394 2 . 54883 500 2.35192 1.36267 2.49391 1 . 28652 550 2 . 26294 2 . 39999 600 2.18989 1 . 80424 2.32290 1 . 70288 650 2.12914 2.25880 700 2.07803 2.2737 2 . 20489 2 . 14536 750 2.03470 2.15920 800 1.99763 2 . 76500 2.12012 2 . 60832 850 1.96571 2.08649 900 1.93808 3.27353 2.05739 3.08746 950 1.91405 2.03209 1,000 1.89306 3.79587 2.01001 3.57945 1,500 1.781369 1.89296 2,000 1 . 74998 9.37126 1.86071 8.82617 2,500 1 . 74663 1.85803 3,000 1 . 75493 1 . 50904 X 106 1.86757 1.42023 X 106 3,500 1 . 76841 1.88251 4,000 1.78417 2.07442 1.89981 1.95134 4,500 1 . 80080 1.91798 5,000 1.81758 2.62974 1.93626 2.47274 5,500 1.83414 1.95427 6,000 1 . 85028 3.17499 1.97432 2.98436 6,500 1 . 86591 1.98878 7,000 1 . 88099 X 10~3 3.71096 X 106 2.00513 X 10-3 3.48711 X 106 7,500 1.89550 2.02087 8,000 1.90947 4.23856 2.03601 3.98199 8,500 1.92290 2.05041 9,000 1.93577 4.75864 2.06455 4.46971 9,500 1.94825 2.07802 10,000 1.96023 5.27195 2 . 09099 4.95096 Chap. 4.] PROTONS, DEUTERONS, AND ALPHA PARTICLES 103 Table 16. Range and Energy Loss of Protons in Nitrogen and Oxygen The following data were computed for nitrogen and oxygen at 0°C and 760 mm of mercury from the Bethe stopping theory. Corrections for noncontributing shells, the Fermi effect and Brcmsstrahlung are not included. Data calculated by W. Aron and B. G. Hoffman, Radiation Laboratory, University of California, for the Atomic Energy Commission. Energy, mev Nitrogen (/ = 80.5 ev) Oxygen (/ = 92 ev) Energy loss, mev /cm Range, cm Energy loss, mev/cm Range, cm 0 0 0 1 2.81579 X lO"1 2.220 3.08769 X 10-1 1.990 2 1 . 70599 7.4883 1 . 88442 3 1 . 25422 1.3877 X 10 1.39013 1 . 25434 X 10 4 1.00377 2 . 2841 1.11442 2.06241 5 8 . 42394 X lO-2 3.3775 9.36501 X 10-2 3 . 04653 6 7 . 29050 4.6577 8.11301 4.19685 7 6.44692 6.1192 7.17990 5.51021 8 5.79250 7 . 7584 6.45524 6.98123 9 5.26878 9.5707 5.87478 8 . 60730 10 4.83937 1.15531 X 102 5 . 39848 1.03847 X 102 11 4.48037 1.37025 5.00002 1.23112 12 4.17540 1.60162 4.66135 1.43840 13 3.91288 1.84917 4.36967 1.66012 14 3 . 68432 2.11268 4.11561 1 . 89604 15 3 . 48340 2.39194 3.89218 2 . 14601 16 3.30528 2.68676 3.69403 2 40982 17 3 . 14674 2.99697 3.51701 2 . 68733 18 3.00320 3.32232 3.35784 2 . 97843 19 2.87391 3 . 66287 3.21389 3 . 28295 20 2.75641 4.01819 3.08302 3 . 60069 25 2 . 29893 2.57320 30 1.98284 8.36328 2 . 22063 7 . 48263 35 1.75056 1.96136 40 1.57223 X 10-2 1.40722 X 103 1.76220 X 10-2 1.25780 X 103 45 1.43076 1 . 60414 50 1.31565 2.10586 1.47547 1 . 88092 55 1 . 22005 1 . 36858 60 1 . 13936 2.92525 1.27833 2.61139 65 1.07022 1 . 20098 70 1.01036 3.85941 1 . 13399 3.44384 75 9.57973 X 10-3 1.07537 80 9.11738 4.90309 1.02361 4.37358 85 8.70613 9.77534 X IO-3 90 8.33789 6.05152 9.36328 5.39637 95 8.00616 8.99176 100 7 . 70574 7 . 30039 8.65525 6 . 50835 125 6.54676 7.35665 104 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 Table 16. Iange and Energy Loss of Protons in Nitrogen and Oxygen — {Continued) Energy, mev Nitrogen (/ = 80.5 ev) Oxygen (/ = 92 ev) Energy loss, mev/cm Range, cm Energy loss, mev/cm Range, cm 150 5.75759 1.49208 X 104 6.47202 1.32898 X 104 175 5.18522 5.83020 200 4.75126 . 2.45506 5 . 34346 2.18543 225 4.41080 4.96152 250 4.13700 3.58761 4.65432 3.19226 275 3.91216 4.40202 300 3.72444 4 . 86483 4.19136 4.32736 325 3.56551 4.01299 350 3.42937 6.26646 3.86019 5.57270 375 3.31159 3 . 72800 400 3.20881 7.77573 3.61265 6.95639 425 3.11845 3.50910 450 3.03849 X 10~3 9.37860 X 104 3.42149 X 10-3 8.38053 X 104 475 2.96731 3.34160 500 2.90363 1.10632 X 105 3.27013 9.87644 550 2.79471 3.14791 600 2.70533 1.46387 3 . 04763 1.30508 X 10s 650 2.63102 2.96427 700 2.56855 1.84375 2 . 89420 1 . 64225 750 2.51561 2 . 83485 800 2.47035 2.24112 2.78411 1 . 99487 850 2.43142 2 . 74048 900 2.39774 2.65229 2.70276 2 . 35970 950 2 . 36848 2 . 66999 1,000 2.34294 3.07441 2.64141 2.73416 1,500 2 . 20809 2.49096 2,000 2.17159 7.57273 2 . 45093 6.72149 2,500 2.16934 2.44927 3,000 2.18120 1.21778 X 106 2 . 76339 1 . 08000 X 106 3,500 2.19927 2.48441 4,000 2.22001 1.67243 2 . 50837 1 . 48244 4,500 2.24171 2.53335 5,000 2 . 26350 2.11853 2 . 55840 1.87720 5,500 2 . 28493 2 . 58300 6,000 2.30578 2.55621 2.60691 2 . 26434 6,500 2.32593 2.63001 7,000 2.34534 2.98618 2.65226 2 . 64462 7,500 2.36403 X 10-3 2 . 67366 X 10"3 8,000 2.38198 3.40922 X 106 2.69421 3.01867 X 10" 8,500 2.39924 2.71325 9,000 2.41584 3 . 82604 2.73296 3.38722 9,500 2.43180 2.75123 10,000 2.44718 4.23728 2 . 76882 3.75071 Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 105 Table 17. Range of Protons in Aluminum Range data for energies 0.117 to 1.842 mev reported by D. B. Parkinson, R. G. Herb, J. C. Bellamy, and C. M. Hudson, Phys. Rev., 52, 75 (1937). Range is given in centimeters and distinguished by an asterisk *. Range data for energies from 1 to 13 mev are taken from M. S. Livingston, and H. Bethe, Rev. Mod. Phys., 9, 263 (1937). Data for energies 13 to 10,000 mev are calculated from Bethe theory by J. H. Smith, Phys. Rev., 71, 32 (1947). Bethe correction Ck is included, but Fermi effect is not taken into account. Average excitation potential, / = 150 ev. Energy, mev Energy loss, mev/fmg/cra1) Range, mg/cm2 Energy, mev Energy loss, mev/ (mg/cm2) Range, mg/cm2 0.117* 0.979 X 10"< 1.44 2.51 3.46 4.67 5.39 5.93 25 30 35 40 45 50 60 1.682 1.456 1.289 1 160 1 . 058 0.9743 0.8458 X 10-2 8.369 0.166* 11 .57 0.267* 15.23 0.342* 19.33 0.433* 23.85 0.486* 28. 78 0.520* 39.83 X 10= 0 630* 7.69 9.65 15.6 23.8 37.6 3.45 6.69 10.8 70 80 90 100 120 140 160 180 0.7516 0 6794 0.6222 0 5757 '0 5047 0.4530 0.4136 0.3826 52 .40 0.745* 66.42 1 .055* 81 .82 1.393* 98.54 1.842* 135.8 1 177.7 1.5 224.0 2 11.5 X 10"2 274.3 2.5 9.85 15.6 200 0.3576 328.4 3 8.62 21.0 250 0 3120 478.7 3.5 7.69 27.3 300 0.2813 648.0 4 6.96 34.5 350 0.2593 833.4 4.5 6.37 42.1 400 0.2428 1033 5 5.88 50.3 500 2.201 X 10"3 1.467 X 105 5.5 5.47 59.0 600 2.054 1.938 6 5.12 69.1 700 1.952 2.438 6.5 4.82 79.2 800 1.879 2.961 7 4.55 90.0 850 1.851 3.229 7.5 4.31 101.3 900 1.826 3.501 8 4.10 113.2 950 1 802 3.777 8.5 3.92 125.6 1,000 1 785 4.055 9 3.75 138.8 1,250 1 721 5.484 9.5 3.59 152.4 1,500 1.688 6.952 10 3.45 166.7 1,750 1 .671 8.441 10.5 3.32 181.4 2,000 1.664 9.941 11 3.21 196.6 2,250 1.663 11.44 115 3.10 212.5 2,500 1.665 12.95 12 2.99 229.0 2,750 1.670 14.45 12.5 2.90 246.1 3,000 1.677 15.94 13 2.816 263.7 4,000 1.710 21.85 13 5 2.734 281.8 5,000 1.747 27.63 14 2.659 300.6 6,000 1.782 33.30 15 2.518 3.393 X 102 7,000 1.815 38.86 17 2.281 4.228 8,000 1.845 44.32 19 2.089 5.146 9,000 1.873 49.70 21 1.930 6.143 10,000 1.898 55.01 23 1.796 7.218 106 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 Table 18. Range of Protons in Paraffin (CH2)„ Range-energy data calculated from the Bethe theory by J. O. Hirschfelder, and J. L. Magee, Phys. Rev., 73, 207 (1948). Energy, mev Range, mg/cm2 Energy, mev Range, mg/cm2 0.005 0.02322 1.8 5 . 23363 0.010 0.03197 1.9 5 . 74061 0.015 . 0.03732 2.0 6.26829 0.02 0.04143 2.1 6.81661 0.03 0.04824 2.2 7.38533 0.04 0.05462 2.3 7.97427 0.05 0.06096 2.4 8.58326 0.10 0.09613 2.5 9.21214 0.15 0.13860 2.6 9.86087 0.20 0.18908 2.7 10.52932 0.3 0.31370 2.8 11.21735 0.4 0.46833 2.9 11.92483 0.5 0.65115 3.0 12.65163 0.6 0.86101 3.5 16.57086 0.7 1.09677 4.0 20.95967 0.8 1.35759 4.5 25.81139 0.9 1.64291 5.0 31.11793 1.0 1.95202 5.5 36.87259 1.1 2 . 28446 6.0 43.06963 1.2 2 . 63976 6.5 49.70417 1.3 3.01756 7.0 56.77056 1.4 3.41751 7.5 64.26439 1.5 3 . 83930 8.0 72.18204 1.6 4.28273 8.5 80.52013 1.7 4.74757 9.0 89.27502 10.0 108.0222 11.0 128.4035 12.0 150.4002 13.0 173.9955 14.0 199.1717 Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 107 3 o > UJ 1000 cr 10" 10' VELOCITY ( cm per sec ) Fig. 21. Energy-velocity curves for alpha particles, protons, and mesons. {Calculated by B. G. Hoffman, University of California, Radiation Laboratory.) 108 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 swM-g-ua ( fi|oi * * ) Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 109 ENERGY IN MEV Fig. 23 110 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 ENERGY IN MEV 7 8 9 50 40 30 RANGE OF PROTONS IN AIR 5 to 18 mev 15° C, 760 mm. Hg, 1 = 80.5 ev Redrawn from M.S.Livingston and H.Bethe, Rev. Mod. Phys. 9,269(1937) 12 13 14 15 ENERGY IN MEV Fig. 24 b 1 1 ' ' 1 i I 170 150 16 17 18 130 Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 111 2500 ENERGY IN MEV 5000 7500 10 000 o UJ © < T — — t — — i" •— +" mmm mm o « o UJ © z < cr RANGE OF PROTONS IN AIR 0 to 10,000 mev I5°C. 760 mm Hg, 1 = 80.5 ev Plotted from data calculated from the Bethe theory by J.H.Smith, Phys.Rev. 71, 32 (1947 ). ■ i m ■ \ ' I : -;t=mtmi 100 200 ENERGY IN MEV Fig. 25 300 400 112 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 (3 aAjno) A3W Nl A9U3N3 (I 8Ajno) A3IAI Nl A9U3N3 Chap. 4] PROTONS, DEUTERONS, AND ALPHA PARTICLES 113 o (3 3AJno) A3W Nl A9H3N3 .O 0. E u o E UJ CO < ID o o 1 - ... . ,,,,, ,.,. , , , \ 1 '.'I'" , .„. J ^ ' st«y — W~i — h- : 1 - i : — ! — — r~- — \ ■ i _ " '' : ' ! i HK-T-+ =:f=i--qpri : ...: '-! !■ ! -IV! 1 : V : ' ~^PW - 1 ;■ ■; ' ; . j .. j': ijjtl o S-. * w S * — b — 1 % 3 — 2 * § CO io * 2 >. O _ -° |— II T> O 2 tt: < 3 ^^^ Q. ij u II -J o H- ■ ° " o fe UJ > . •• ■• i z < or y » — +— 4- 7^flii illlirlJ wmi 8 22 20 2 O UJ o z < HI6 or OiMp? [ ■r- -r nillSpfi '-.'-'. ?*4r?::{'4> 1/ . 4— l-i -4-4-4- — 4-4- fr r-r .Itnin.l'-M.I'-it, J-,;,., iil^r H^u 14 ENERGY IN MEV Fig. 32 10 II 12 Chap. 4] PROTOXS, DEUTEROXS, AXD ALPHA PARTICLES 119 (Z 9Ajn0) A3W Nl 39NVy CM o 2 2 (1 *AjnQ) A3W Nl 39NVU 120 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 (3 aAjno) A3W Nl A9H3N3 (I 8AjnQ) A3W Nl A9H3N3 CHAPTER 5 NEUTRONS 5.1. General Properties Atomic weight [1]: = 1.008937 + 0.0000075 Magnetic moment [2]: = —1.91307 + 0.0006 nuclear magnetons Half-life: - — ' 20 min Statistics: Fermi-Dirac The absence of charge makes the interaction of neutrons with matter strikingly different from that of charged particles. Interaction with electrons is entirely negligible, and interaction with coulomb fields of nuclei does not occur; hence, neutrons do not lose energy by ionization or radiation. Con- sequently there does not exist a range-energy relation such as that which describes the behavior of charged particles traversing absorbing media. But by virtue of their electrical neutrality, neutrons of all energies, down to those with nearly zero kinetic energy, have free access to nuclei, with which they readily combine to form unstable compound nuclei. The effects of neutrons on matter, therefore, must be described in terms of the nuclear reactions they produce. More specifically, the essential properties that must be known are the probabilities or cross sections for the various nuclear interactions that may be induced as a function of neutron energy and the kind of nuclei that constitute the matter. The very marked dependence of neutron processes on energy has led to the universal use of the terms fast, slow, and thermal to indicate broad and rather indefinite ranges of neutron kinetic energy. Fast neutrons are those with energies greater than tens of kev; slow neutrons are those with energies less than this. Included in the latter group are thermal neutrons that possess energies of the order of kT, ~ 0.02 ev, where k is Boltzman's constant and T is the absolute temperature. Neutrons from nearly all sources are fast since they are emitted in nuclear reactions with kinetic energies of the order of 1 mev. Consequently slow neutrons can be obtained only by slowing down fast neutrons through elastic collisions, usually with light nuclei. This may be accomplished with exten- sive volumes of substances such as graphite or water surrounding the fast neutron source. After losing their kinetic energy the neutrons tend to diffuse through matter in much the same way as gases. Under such condi- 121 122 JSOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 tions, when equilibrium is established between the rates of formation and loss of thermal neutrons, the properties of the neutron gas may be described in terms of the spatial density and distribution of kinetic energies, together with associated quantities such as neutron flux, mean free path, and diffusion length. Associated with each neutron as with all particles is a De Broglie wave for which the wavelength in angstrom units is X = h/mv = 0.2S6E~1/2 where E is the kinetic energy in electron volts. Thermal neutrons have wavelengths comparable to interatomic distances, and because of the absence of charge they are diffracted and reflected by crystals in much the same way as x-rays of the same wavelength. 5.2. Neutron Processes. In accordance with Heisenberg's uncertainty principle the probability per unit time that an excited nucleus, formed by capture of a neutron, undergoes a transition to a lower excited state is related to the uncertainty in the energy, AE, of the initial quantum level of the compound nucleus. This is expressed as the probability of a transition per unit time or l/At = AE/h, where h = Planck's constant/27r and At is the uncertainty in time which is taken as the mean life of the state. Each quantum state has a most probable energy, its exact resonance energy, but because of the uncertainty principle the energy of the corresponding level in individual nuclei of the same species falls on a distribution curve forming a peak for which the maximum is the most probable value of the level energy. The uncertainty in energy of a particular level, designated by T and expressed in electron volts, is taken as the width of the associated resonance peak at one-half its maximum value. It is referred to as the total width of the level. When the width of a level is small, the mean life of the excited state is large. The lowest excited levels of nuclei are, in general, widely spaced, usually at intervals of the order of several kev. The resonance peaks representing the energies of the levels consequently are well-defined and widely spaced compared with their widths. At higher excitation energies, however, the density of levels increases until, for energies between 5 to 8 mev, the spacing between levels is reduced to only 10 to 20 ev. Discrete resonances then no longer exist; the levels are broad and tend to overlap because of their small separation. Consequently, when nuclei are raised to excited states of high energy, for example by capture of fast neutrons, many levels may be affected which then contribute to the nuclear processes by which the nucleus returns to lower lying levels or to the ground state. In general the total width T is the sum of the partial widths of various proc- esses that may occur in the transition. This includes the emission of gamma rays, neutrons, charged particles and, in the special case of elements beyond actinium, also fission. The total width therefore is V = Ty + r„ + Tg + T/. Sec. 5.3] NEUTRO.XS 1 23 Normally when a slow neutron is captured by a light or medium nucleus, only one such process is highly probable. At high excitation energies, how- ever, several processes may compete with probabilities of roughly the same magnitude. The kinds of interactions that occur when nuclei are bombarded with neutrons depends, superficially at least, on the kinetic energy of the incident neutrons and on the particular kind of nucleus. In all cases neutron inter- action leads to one of the following processes: 1. Elastic scattering. The kinetic energy and momentum of the incident neutron are shared by the recoil neutron and nucleus according to the laws of conservation of energy and momentum; otherwise the struck nucleus is left in its initial state. 2. Radiative capture (n, 7). The struck nucleus retains the neutron and emits a gamma ray. 3. Neutron emission (n, n), (n, 2n), etc. After capture of a neutron, one or more neutrons are boiled off. 4. Charged-particle emission (n, p), (n, d), (n, a), etc. After capture of a neutron one or more charged particles, or a combination of particles, are emitted. 5. Fission (n, f). A neutron is captured and the compound nucleus splits into two large fragments (see Fission, Chap. 6). 6. Other processes are reported in which very high-energy neutrons (~ 100 mev) totally disintegrate the nucleus or lead to the emission of a large number of particles (spallation). All but elastic scattering are capture processes. The incident neutron plus the struck nucleus (Z, A) form a compound nucleus (Z, A + 1) which instantly (~ 10~10 to 10-20 sec) disintegrates by one of the processes indicated above. The residual nucleus is, except when elastic re-emission of the neu- tron occurs, radioactive and subsequently decays at a relatively slow rate by emission of those radiations characteristic of radioactive decay. 5.3. Elastic Scattering of Neutrons. The precise manner in which neutrons are scattered by nuclei depends in a complicated way on the nuclear forces. Scattering into certain angles may be favored over others (anisotropic scattering), and the cross section usually exhibits strong dependence on neutron energy. At the present time evaluation of such effects of nuclear interaction is possible only from experiment. For many purposes, however, scattering may be considered isotropic in that all angles as measured from the center of mass coordinate system are equally probable. If scattering is both isotropic and elastic, neutrons are then scattered by nuclei in essentially the same manner as ideal gas molecules. The kinetic energy and momentum of the incident neutron are shared by the recoil neutron and nucleus as required by the conservation laws of energy and 124 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 momentum. The struck nucleus remains in other respects unchanged as a result of the collision, and hence no energy is lost to excitation. The kinetic energy transferred to the recoil nucleus is 4wM sin2 0/2 _ _, Em = —i 1 m2 E» = otEo mev [m + my where m = mass number of neutron M = mass number of nucleus E0 = initial energy of neutron, mev 0 = deflection angle of neutron from its initial direction with respect to the center of mass Similarly, the energy lost by the neutron is En = E0{\ — a). The greatest amount of energy is lost in a head-on collision where 0 = 2r. If the nucleus is massive, the neutron will reverse its direction but sustain little loss of energy; however, if the struck nucleus is a free proton, ra ~ Af and the neutron may in a head-on collision be brought practically to rest in a single collision. In traversing a scattering medium a fast neutron will make many collisions before it is reduced to thermal velocities. The ratio of the neutron energy after a collision to its initial energy is, on the average, a constant whose magnitude depends on the mass of the scattering nuclei as given by the expression E, _, E, where £ = 1 - ^-— - — log 2M 6 M - 1 M+ 1 Ei = initial neutron energy E2 = final neutron energy (for heavy nuclei) The average number of collisions required to reduce the neutron from energy E0 to energy E is then N = \ log | If the scatterer is a hydrogenous substance, the average residual kinetic energy of the neutron after a collision with a hydrogen atom is 1/e of its initial value; hence, after n collisions the residual neutron energy is just E = E0/en. The elastic scattering cross section for nuclei must be determined from experiment because of the absence of sufficiently detailed knowledge of nuclear forces. The functional relation of the cross section has, however. Sec. 5.3] NEUTRONS 125 been established [4]. For isotropic scattering, it may be expressed as the sum of two distinct processes. The first arises from potential scattering for which the cross section is identical to that obtained for the collision of two hard spheres and is just equal to the total effective surface area of the nucleus. The second or resonance term becomes important when the energy of the incident neutron is nearly equal to that of a quantum state of the nucleus. Resonance scattering may then make a large contribution to the cross section. Breit and Wigner [3] have shown that when the De Broglie wave- length of the neutron is large compared to the nuclear radius and the levels are widely spaced so that only one level is affected, the cross section near resonance can be represented by an expression similar to that for the dis- persion of light. The total cross section, therefore, may be written as the sum of potential scattering and the Breit- Wigner "one-level" formula [3,4]. = ^ + l(1±2iTl)^ 4R(E - Er) + XrTn — p— cm- (E - Ery + Z- where R = effective nuclear radius E = neutron energy Er = resonance energy Xr = neutron wavelength at resonance ( = h2/ Sir2 /jlE)^ n = reduced mass = mM /(m + M) Yn = neutron width of level T = total level width i = angular momentum of nucleus before collision, + sign if spin of resonance level is i + } £; — sign if i — 1 •_>• If i = 0 (even-even nuclei) + sign is used The shape of the curve for the second term near resonance is similar to the dis- persion curve for light. A maximum occurs near exact resonance where o-max = 47r7t2 + lirXlTn/T, and a minimum value is found at Er — -Emin = hrTn/2R where crmin = 2tR2. The relative magnitude of resonance and potential scattering is made apparent by the ratio of their cross sections at exact resonance .,2n) — 7riv-£ (, + «-&) .*?*] 1-11 + ^-^— " e l cm2 where T = temperature correlated to observed energy distribution, T = 2(5En/A)K mev £ = sticking probability for neutrons of high energy (> 1.0 mev) At high energies En — Eb » T, and the (n, 2n) process becomes more prob- able than (n, n). The process involving the emission of more than two neu- trons becomes increasingly more important at very high energies, i.e., when Ei » Eh. d. Char ged-par tide Emission (n, p), (n, d), (n, a), . . . . Reactions leading to the emission of charged particles are probable only when the incident neutron energy is sufficiently high so that the available energy is great enough to allow a charged particle to pass over the electrostatic poten- tial barrier. Assuming the average cross section for high energies to be of the form aq = TR^ cm2 the charged particle width is the product of the emission width without the barrier r'9 and the penetrability factor P = e~f. Because of the large num- bers of levels excited by neutrons with energies high enough to result in charged-particle emission, the energy distribution of the emitted particles is continuous and probably roughly Maxwellian. Ordinarily, the cross section for charged-particle emission is small because of the strong competition from the more favorable (n, n) process or at very high energies, from (n, 2n), (n, 3n), etc. e. Fission (see Fission, Chap. 6). /. Other Processes. At energies of the order of 100 mev and greater, neutron bombardment frequently leads to the emission of great numbers of particles and probably complete disintegration of certain nuclei. Such processes are still under investigation at the present time (184-in. synchro- cyclotron at the Radiation Laboratory of the University of California). 5.6. Neutron Diffusion. For practical purposes neutrons are obtained either by the reactions (a, n) and (7, n) from mixtures of a radioactive isotope such as radium, and a "target" material such as beryllium, or from appro- priate targets bombarded with heavy particles in high-energy accelerators. However, all such sources provide only fast neutrons, and when slow neutrons are required it is necessary to slow down the fast neutrons with appropriate Sec. 5.6] NEUTRONS 131 forms of moderators. If the source (or the fast neutron beam from a cyclo- tron) is enclosed with materials such as water or paraffin for which the ratio of the scattering to capture cross section is large, the fast neutrons are rapidly reduced to thermal energies by elastic collisions. Once neutrons have been reduced to thermal velocities they continue for the remainder of their lives to diffuse through the medium. On the average they gain in subsequent collisions as much energy as they lose, and their average velocity depends only on the temperature of the medium. Ulti- mately each neutron is lost by capture, by decay into a proton and an elec- tron, or by diffusion out of the medium. When equilibrium is reached, the rate of formation of thermal neutrons just equals the rate of loss by all three processes, and the neutron density throughout the medium remains constant with time although not in space. If the diffusing medium is a hydrogenous substance such as paraffin, most of the scattering nuclei have the same mass number as the neutron and diffusion resembles in some respects the self- diffusion of gases. Substances containing heavy nuclei, on the other hand, allow very small momentum transfer per collision, and the neutrons scatter elastically as from a solid, immovable object. The conditions here are more like the diffusion of an electron gas in a conductor. In the stationary state, characterized by equal rates of thermal neutron loss and gain, the energy distribution of neutrons is Maxwellian except for a high-energy tail which varies as E~?'-. For the Maxwellian region the num- ber of neutrons with energies lying in the interval E to E -f- dE is N dE = WW^'" dE where k = Boltzman constant T = absolute temperature Q = number of neutrons produced per sec t = mean life time for capture The factor Qr is just the total number of neutrons with all energies. The average velocity is v = (SkT/tmr)1^, where m is the mass of the neutron. At room temperature, 20°C, v is about 2.5 km per sec. Assuming that all neutrons within a diffusing medium possess thermal velocities, or more exactly, have a Maxwellian distribution for a given temperature, the neutron density in neutrons per cubic centimeter may then be described by a diffusion equation in much the same way as for gases. It is essentially an expression of the law of conservation of neutrons stating that the rate of change in the number of neutrons per cubic centimeter in an element of volume dV at the point (x,y,z) and time / equals the number of neutrons produced per second plus the divergence of the neutron flux through dV minus the number absorbed per cubic centimeter per second. 132 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 — = div (D grad n) + q dt t where D = diffusion constant q = source strength; number of thermal neutrons produced per unit time as a function of position t = mean life of neutron before capture In the steady state dn/dt = 0; the density distribution does not change with time. Furthermore, if the medium is homogeneous and isotropic, the diffusion equation then reduces to fl Dy2n + q - - = 0 r or The diffusion constant D is found from ordinary kinetic theory to be given by D = Xtrf/3, where Xtr is the transport mean free path and v is the neutron velocity. This relation is found to hold for neutron diffusion provided that the scattering is isotropic, scattering and absorption cross sections are con- stant, and the rate of change of n is small within a distance of one Xtr. The quantity Xtr is the mean distance a neutron travels through the medium in the direction of its initial motion after a great number of collisions. This is related to the transport cross section by Xtr = 1/Natr, where N is the number of nuclei per cubic centimeter. The quantity o-tr is, in turn, defined by o\r = as (I — cos 6), where as is the scattering cross section and cos 6 is the average value of the cosine of the angle of deflection from the initial direction in each collision. If the scattering is strictly isotropic, i.e., all angles are equally probable, then cos 0 = 0, crtr = as and Xtr = X, where X is the mean free path or X = l/Na. The value of cos 6 for anisotropic scattering depends on both the mechanism of scattering and the mass number of the scattering nuclei. The first effect must be determined empirically, but the latter effect leads to au = as(l — 2/3M), where M is the mass number of the scattering nucleus. In the case of hydrogen, for example, scattering is pre- dominantly forward since a neutron cannot be scattered more than 90 deg in a single collision. The effect in hydrogen is large, whereas in heavy elements it is entirely negligible. In some media the absorption cross section co becomes the albedo for a plane boundary 1 - (2X/3L) 7 1 + (2X/3L) Material such as concrete is particularly useful for reflectors and also serves as a barrier around moderators to reduce the health hazard to person- nel working in the vicinity. REFERENCES FOR CHAP. 5 1. Hughes, D.: Phys. Rev., 70, 219 (1946). 2. Bloch, F., D. Nicodemus, and H. H. Staub: Phys. Rev., 74, 1025 (1948). 3. Breit, G., and E. Wigner: Phys. Rev., 49, 519 (1936). 4. Bethe, H: Rev. Mod. Phys., 9, 151 (1937). 5. Bethe, H, and G. Placzek: Phys. Rev., 51, 450 (1937). 6. Kapur, P. L., and R. Peirels: Proc. Roy. Soc. (London), 166, 277 (1939). 7. Siegert, A. J. Y.-.Phys. Rev., 56, 750 (1939). 8. Weisskopf, V. F., and D. H. Ewing: Phys. Rev., 57, 472 (1940). 9. Feshback, H, D. C. Peaslee, and V. F. Weisskopf: Phys. Rev., 71, 145 (1947). 136 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 Table 20. Thermal Neutron Activation Cross Sections The following table is a list of thermal neutron activation cross sections measured and reported by L. Sercn, II. N. Friedlander, and S. H. Turkel, Phys. Rev., 72, 888 (1947). Cross sections were determined by measuring the absolute beta emission (or positron and K capture) from thin foils irradiated with thermal neutrons. Assuming that one beta particle is emitted per neutron captured, the thermal neutron cross section a was calculated from u = nva-N, where u = number of neutrons captured per unit time, nv = thermal neu- tron flux, and N = number of atoms of detector. The probable error of most values is 20 per cent; those with a probable error of 10 per cent are indicated by * and those with a probable error of 40 per cent by ]. Isotope Half-life Isotopic cross section, barns Natural atom cross section, barns Z El. A 8 O 18 31 s 2.2 X 10-4 4. X 10 7 9 F 19 12 s 0.0094 0.0094 11 Na 23 14.8 h 0.63 0.63 12 Mg 26 10.2 m 0.048 0.0054 13 Al 27 2.4 m 0.21 0.21 14 Si 30 170 m 0.116 0.00485 15 P 31 14.3 d 0.23 0.23 16 S 34 87.1 d 0.26 0.011 17 CI 35 2X106y 0.169 0.13 37 37 m 0.56 0.137 19 K 41 12. 4h 1.0 0.067 20 Ca 40 8.5d < 0.000125f < 0.00012f 44 180 d 0.63 0.013 48 30 m 0.55 0.00105 48 150 m 0.025 0.00039 21 Sc 45 85 d 22. 22. 22 Ti 50 6 m 0.141 0.0075 50 72 d 0.039 0.0021 23 V 51 3.9 m 4.50 4.50 24 Cr 50 26.5 d 11. t 0.50f 54 1.3h ~ 0.0061 ~ 0.00014 25 Mn 55 2.59 h 10.7 10.7 26 Fe 58 47 d 0.36 0.0010 27 Co 59 10.7 m 0.66 0.66 59 5.3y 21.7 21.7 28 Ni 64 2.6h 1.96 0.0173 29 Cu 63 12. 8h 2.82 2.0 65 5 m 1.82 0.56 30 Zn 64 250 d 0.51 0.26 68 57 m 1.09 0.19 68 13. 8h 0.31 0.054 31 Ga 69 20 m 1.40 0.855 71 14.1 h 3.36 1.30 Chap. 5] NEUTRONS 137 Table 20. Thermal Neutron Activation Cross Sections — {Continued) Isotope Half-life Isotopic cross section, barns Natural atom cross Z El. A section, barns 32 Ge 70 40 h 0.073 0 0155 70 11 d ~ 0.45| ~0.095f 74 89 m 0.38 0.14 76 12 h 0 . 085 0 . 0055 33 As 75 26.8 h 4.2 4.2 34 Se 74 115 d 22. | 0.2f 78, 80 78, 80 82 19 m 57 m 30 m 0.23 0.017 0.060 0.0056 35 Br 79 18 m 8.1 4.1 79 4.4h 2.76 1.39 81 34 h 2.25 111 37 Rb 85 19.5 d 0.72 0.52 87 17.5m p. 122 0 . 033 38 Sr 86 2.7h 1.29 0.127 88 55 d 0.0050 0.00415 39 Y 89 60 h 1.24 1.24 40 Zr 92 63 d 0.33 0.073 94 17. Oh 0.053 0.009 96 6 m - 1.07t ~0.016| 41 Cb 93 6.6 m ~1.0f -l.Ot 42 Mo 100 19 m 0.475 0.044 98 67 h 0.415 0.10 92? 7 h O.OOlf 44 Ru 102 104 4 h 0.122 ? 37 h 0.15 ? Rh 103 40 d 44s 0.37 45 137.* 137.* 103 4.2 m 11.6* 11.6* 46 Pd 108 13 h 11.2 3.0 110 26 m 0.39 0.0525 47 Ag 107 2.3m 44.3 23. 109 22 s 97. 46.6 109 225 d 2.3 1.1 48 Cd 114 2.5d 1.1 0.30 114 43 d 0.14 0.040 116 3 . 75 h 1.4 0.10 p 2 m 0.05 49 In 113 48 d 56.* 2.52* 115 13 s 51.8* 49.5* 115 54 m 144.6* 138.* 50 Sn 112 105 d ~ 1.1* - 0.012f 124 9 m 0.574 0.039 < 125 40 m 0.0142 138 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 Table 20. Thermal Neutron Activation Cross Sections — {Continued) Isotope Half-life Isotopic cross section, barns Natural atom cross section, barns Z El. A 50 Sn < 125 26 h 0.072 < 125 < 125 Sb 121 10 d 400 d 2.8d 0.009 0.018 51 6.8 3.8 123 60 d 2.5 1.1 52 Te 126 9.3h 0.78 0.15 126 90 d 0.073 0.014 128 72 m 0.133 0.0436 128 32 d 0.0154 0.00504 130 25 m 0.222 0.0735 130 30 h . < 0.008f < 0.003f 53 I 127 25 m 6.25 6.25 55 Cs 133 3h 0.016 1.016 133 1.7y 25.6 25.6 56 Ba 138 86 m 0.511 0.367 57 La 139 40 h 8.4 8.4 59 Pr 141 19. 3h 10.1 10.1 62 Sm ? 152 21 m 46 h 1.10 138. 35.8 ? 60 d < 0.008f 681. 63 Eu 151 9.2b. 1,380. 151, 152 Gd ? ? 5-8 y 9.5h 20 h 390. 64 2.3 ~0.9f — 0.6f < 0.25f 10.7 ? 8.6d ? 160 d 65 Tb 159 3.9h 10.7 66 Dy 164 140 m 2,620. 725. 164 1.25 m 120. 33. 67 Ho 165 30 h 59.6 59.6 69 Tm 169 105 d 106. 106. 71 Lu 175, 176 176 3.4h 6.6d 15.9 3,640. 91.0 72 Hf 180 46 d 10.0 3.5 73 Ta ? 181 16.2 m 117 d 0.034 20.6 20.6 74 W 184 77 d 2.12 0.64 186 24.1 h 34.2 10.2 75 Re 185 90 h 101. 38.5 187 18 h 75.3 46.5 76 Os 190 30 h 2.50 0.66 192 17 d 5.34 2.19 77 Ir 191 1.5 m 260. 100. 191 70 d 1,000. 388. Chap. 5] NEUTRONS 139 Table 20. Thermal Neutron Activation Cross Sections — {Continued) Isotope Half-life Isotopic cross section, barns Natural atom cross Z El. A section, barns 77 Ir 193 20. 7h 128. 79.0 78 Pt 196 18 h 1.1 0.30 78 Pt 196 3.3 d 4.5 1.20 198 31 m 3.92 0.292 79 Au 197 2.7 d 96.4 96.4 80 Hg 204 5.5 m 0.34 0 . 0428 202, 204 Tl 203 51.5 d 4.23 m 0 725 81 0.273 0.079 205 3.5 y 3.1 2.2 83 Bi 209 5.0 d 0.015 0.015 140 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 i!i!' , | ! ! i TTT ' ' TTTT i i i ' ■ 1 ! r! - ■ r ! ; . rr |3p. 1 ■ : : •- ■ : ■ : i i i i I i : : • ;:;r j . : 1 : • : : j i 7 J3 "ft : ; : : : j i i ■ ■' f - - : ; • : : !-i ■-:-! r ! ■ I z ° ■!"M 1 1 h i h-4- tr § :- : • - : :-• i c 2 o 11 . .. ™ - ^^ E ~H~" 4z: - - V~I * 4~ D tN Dy pe - — f w 1 - S= - :■ En - z <" ■ y «» d " i±h" ; : , , ^ -2 ■ Tl i ° ° : * ! r f ''• '. • M } i ■■- ! i f o i : Q 1-1 H \i\i\':' ! - • ! I I - i ; X T * > ^^ — ! u ■ ; 4 I I .X-i jj — - •c 1-5"- 0- >. ■ i i ; \ 4 ; I ■ 1 . r : ; i r fc » i | o a: m — UJ? ===£ ■o -1 1 ^g j [ - E = " : ": eWee^ -f-4- |.| 4 cc o< <" 1 11 J :~ «t 5 "tf \<^ - : 1-* : ' - - 4 [■j- |~j- j XI irj-ErJ}- f \ -\ j rlrjz: i ; : : • ': i : ■ . : _-. ->- ■J^ ^:- ~ ■ r : ] T- j ; : 1 r yP^ _ . ■ i : ? ■ : " *~ i " \ 4 : 4 L1 : 1- £=- j= -r-J-|-4^ ~ =f : | |"-^£: -: - : 1 ., -\^-^-^^r t : ; '. : — 4 t-14- ~[~]~ — I j ' ■ — =e ' — — - j - i . 1 4 t r ~ : . : '. i i j : T : - - * ; i i : : : : ■ ! T • '} : : ' : 1 1 j 1 1 j i 1 l '- : : i " ■ ; J _;:;;::::. : --- ■_ : ■ i : : , ~]f~~ . j . •- - ]~ m "rrr~n : 1 | - - | 1 — Lz_ \ ~~ ------ - 44- 41; - | : "rut 4 — " 4 1 __-._. ; . : : : : ^r~^_ 1=11111111= - - T~ -t: > UJ 5 E _ uj io W UJ O Ph § o 00 o o SNdVa ? o o Chap. 5] NEUTROM! 141 SNHVa 142 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 SNdV8 Chap. 5] NEUTROXS 143 I'!1 I !■'■" ■ ; i • j ri-nffHI'jHM :■ i • : 1 ■ ' | ' !'T — — , ' ! ,' ^ o _L^_ • ; : — i_ \ .___^ - ~\ '■ ■ \ ■ ' ■ 8| =M= : ; : : • ; : . • ." : : _ — -1 LJ i. ! ' 1 : j i" j \ Y1 tt"H"" * \ E LlJ to ^m^ =^fc:„:__ . iL^. r -p . EjE- — — 1 ■ 1 ;- — RBON ss Sectior SCIENCE Ar , Volume 1, Inc. ; i — — 1 i _ ■ -i" - ~ ; ; ;'" 3 — — — ! — | :-: ~~ — _ | _ .•.;.. -T- CA 1 Cro THE S OWER Press. __ ^rjfSrT^T- - : - ...... 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T -- = ^^~ — — . ■ ■ _ - -►— -: - -j j | j~^^ =pp ~t- — 1 — 1 R o >- UJ z fe «0 m ro CM sNava 144 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 5 <£ 5j- rO SNdva O or ill ELECTROSTATIC FIELD Fig. 43. DISTANCE FROM CENTER OF NUCLEUS Diagrammatic representation of potential fields of nucleus. energy, gamma-ray and neutron emission are more probable than fission, but if it is greater, fission of the compound nucleus is most probable. Thus, neutrons with only thermal kinetic energies induce fission in the nuclei U23" and Pu239 with greater probability than for radiative capture since the neutron binding energies of 5.4 and 6.4 mev are greater than the respective critical energies of 5.2 and 5 mev. On the other hand, the probability of fission in U23S and Th232 becomes important only for fast neutrons since the critical energies are of the order of 1 mev greater than the neutron binding energy. In general, the fission barrier height in the heaviest nuclei with odd atomic weight is lower than the neutron binding energy, thus allowing fission to be induced by thermal neutrons. The absolute fission cross section depends, as in all other nuclear reactions, on the neutron energy. When fission can be induced by thermal neutrons, well-defined resonance peaks may be involved at certain energies. The fission cross section at exact resonance is then many times greater than its off-resonance value. The cross section in the thermal-energy region when 150 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 resonances are absent varies as E~VK When, because of a high fission barrier, fission can be induced only by fast neutrons, the resonance levels of the nucleus are broad and closely spaced and thus lose their identity. The cross section in this case decreases almost uniformly with increasing energy approximately as E"1. The reaction time of nuclear processes or, more correctly, the mean life of a highly excited nucleus is in general exceedingly small, < 10-10 sec. It is to be expected therefore that under conditions which make fission a highly probable process compared to radiation and neutron emission the mean time for fission following neutron capture should be of this order of magnitude. This was demonstrated in experiments by Feather [13], indicating that fission may occur in an interval at least as short as 5 X 10-13 sec, and by > ■ E x ^ /T+- +^ (k :). +) Fig. 44. Simplified concept of deformation of liquid-drop nucleus undergoing fission. The unexcited nucleus is represented as a sphere with uniform distribution of charge (protons). The relative strengths of the surface tension r and electrostatic forces E are indicated by lengths of vectors. Deformation of the drop induced by external forces causes a reduction in r at the point of least curvature and an increase in the repulsive force E due to the redistribution of charge to regions of large curvature. Wilson [14] who showed that less than 5 X 10-5 of the fissions are delayed as long as 10~8 sec. 6.3. Stability of Heavy Nuclei. The stability of heavy nuclei against fission depends on the relative magnitudes of the short-range nuclear forces responsible for an effective surface tension and the repulsive electrostatic field of the protons. Since the volume of the nucleus is directly proportional to the number of particles, A, it contains [7], the energy associated with the short-range forces maintaining a stable spherical nucleus is proportional to the nuclear surface, A-kR2 ~ A ^. Counteracting this, the uniform distribution of charge eZ gives rise to an electrostatic energy proportional to Z2A ^ which increases more rapidly with nuclear size than does the surface tension. A critical value of the ratio of the two fields, expressed by Z2{A^/A^) = Z2/A, is attained for increasing nuclear size when the electrostatic field exceeds the nuclear binding forces and the nucleus is no longer stable against spontaneous fission. A semiempirical calculation by Bohr and Wheeler [4] leads to a critical value of Z2/A = 47.8. Nuclei with Z2/A only slightly smaller (~ 15 per cent) than the critical value exhibit a marked stability against spontaneous fission when unexcited, Sec. 6.4] FISSION 151 but division becomes highly probable for small deformations in the spherical form induced by external excitation. Classically, the minimum or critical excitation energy required to induce fission is equivalent to the height of the potential or fission barrier formed by the difference of the attractive nuclear field and repulsive electrostatic field. Alternatively, it is the energy neces- sary to induce a deformation of a liquid drop for which the cohesive forces become smaller than the repulsive forces within the drop. The height of the barrier decreases with increasing value of Z2/A, and when Z2/A = 47.8, the fission barrier vanishes entirely. For nuclei with Z2/A near the limiting value, the critical excitation energy for fission was calculated by Bohr and Wheeler [4] who gave the expression E = AttItA^ where x = Z2/47.$A 98 11,368,, u 135 (1 ~ x) 34^25 (1 - X) + ••• J mev Airr20T =14 mev r0 = 1.47 X 10- w cm [4,8] When the critical energy of a nucleus is smaller than the neutron binding energy, as it is for U234, fission can follow from the capture of thermal neu- trons. When on the other hand it is greater than the binding energy, fission becomes probable only when the kinetic energy of the incident neutron is great enough to make up the deficit. An estimate of the neutron binding energy in heavy nuclei, therefore, is important to determine the neutron kinetic energy necessary to induce fission. For nuclei with masses greater than A = 230, the neutron binding energy has a value between 5 and 7 mev. On capture of a neutron this energy plus the neutron kinetic energy is con- tributed to excitation of the compound nucleus. From the relation Mc2 = E, the binding energy Ei can be calculated from the mass difference of the initial and compound nuclei Eb = 931 (If .4 - MA+l + n) for which the masses M A and MA+\ may be estimated from the semiempirical relation given in Sec. 1.4. Spontaneous fission is possible but relatively improbable in unexcited nuclei and in nuclei with less than the critical excitation energy. The half- life for spontaneous fission from the ground state appears to be 1017 to 1022 years for fissionable nuclei such as thorium, uranium, and plutonium. 8.4. Fission Fragments. The mass distribution of fission fragments exhibits a marked asymmetry about a value of one-half the mass of the initial compound nucleus. Division into two fragments of nearly equal mass occurs with little probability, ~ 0.01 per cent; instead, as shown in 152 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 Fig. 45, the masses tend to group into symmetrical distributions about a light and heavy component. The most probable fragments from U236, for example, are those with masses 95 and 140, corresponding to the maxima of the empirical yield curve. These values appear to be nearly the same also for U239 and Th233. The total variation in mass ranges from approximately ^—^ i_ y^^ \ / \ / \ f , \ -10" z i ' / — g ui Z o I0'e u p- z o CO J° -3 u- 10 io-4 in"8 70 80 90 130 140 150 160 100 110 120 MASS NUMBER Fig. 45. Yield of fission products from U235 as a function of mass number. [From J. Am. Cliem. Soc. 68, 2435 (1946-).] 70 to 160 although a very high percentage of the yield is confined to the two mass groups 80 to 110 and 128 to 154. In all instances the sum of the atomic weights of the two fragments is somewhat smaller than the initial nucleus owing to the loss of two to three prompt neutrons. No satisfactory theory has as yet been provided which accounts for the asymmetry in fission yield. Sec. 6.5] FISSION 153 The distribution in charge of primary fission fragments is less easy to establish, and conclusive experimental or theoretical results have not yet been reported. It is likely however that there is no unique charge associated with each mass but rather a number of possible values of charge distributed about a mean value for each mass. The greatest portion of the total energy released in fission appears as kinetic energy of the fragments. A rough estimate of the recoil energy may be calculated from the electrostatic analogy of two charged particles. Assum- ing the fission fragments to be two spheres with charges Zx and Z2 and initially in contact, the potential energy is then P eZiZo = = 1.47 X lO-13^ + A2*) ergS where A\, Ao = atomic weights of fragments The recoil energy computed by this method is approximately 200 mev, about 25 per cent greater than the best experimental value. Measurements of the average recoil energy have been made by many investigators [10,15,21,22, and others] who have reported values varying from 120 to nearly 200 mev. The total kinetic energy imparted to the fragments does not have a unique value but exhibits a statistical variation about a mean value of about 160 mev [21,23,24,25,26]. The distribution appears to be symmetrical about this value and has a spread from 120 to nearly 200 mev. Each of the two fragments from a single fission share the total kinetic energy inversely as their respective masses, E\/E2 = M2/M1. When the observed energies of the fragments are plotted separately, two symmetrical distributions are obtained with mean values of approximately 60 and 92 mev, corresponding to the heavy and light components, respectively. The width of the low- energy peak at one-half its maximum value is approximately 25 mev, and for the high-energy component it is about 16 mev. The characteristics of the energy-distribution curve appear to be nearly the same for Th232, U235, U238, and Pu239. Although small differences for these isotopes have been found, the variation in values reported for any one fissionable isotope appears to be greater than the differences between the energy distributions for the four isotopes above. 6.5. Absorption and Range of Fission Fragments. The interaction of fission fragments with matter involves the same processes as in the stopping of lighter charged particles such as alpha particles, namely, ionization and elastic nuclear collisions. Nevertheless, the characteristics of the rate of energy loss and the range of fission fragments as functions of velocity are strikingly different than for alpha particles owing to their great mass, high charge number, and relatively low velocity. The range is small, the ioniza- tion is many times more intense than that produced by alpha particles, and 154 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 elastic collisions with nuclei take a relatively more important part in the stopping of fission fragments than in the stopping of lighter charged particles. Despite the great kinetic energy (160 mev total) with which the fragments recoil at the moment of separation in the fission process their velocities are relatively low. The most probable initial velocities of the light and heavy groups are found to be about 13.3 X 108 cm per sec and 9.0 X 108 cm per sec, respectively [33]. These velocities are lower than the orbital velocities of electrons in the innermost shells of the fragments. Such electrons with velocities greater than that of the fragment are most likely to be retained as a permanent core from the instant the two fragments separate. Although the fragments are never completely stripped of electrons, the initial deficiency at the moment of separation has been found on the average to be about 20 electrons for the light group and about 22 for the heavy group of fragments. As a fragment is slowed down by an absorbing medium, additional electrons are captured and the charge of the particle rapidly decreases until the full complement of electrons is attained when the fragment is brought to rest. The specific ionization along the path of the fragment does not follow the Bragg curve which describes the ionization produced by protons and alpha particles. Instead, the ionization is most intense at the beginning of the path where the fragment has its greatest charge and then diminishes rapidly along the path owing to the decrease in charge resulting from electron capture as the particle loses momentum. The fragment continues to ionize until brought to rest, but below a velocity of about 2.5 X 108 cm per sec the electron shells remain nearly filled and energy loss by ionization is negligible. Energy loss at low velocities, < 2.5 X 10s cm per sec, is due almost entirely to elastic collisions with nuclei. Large fractions of the fragments' residual kinetic energy and momentum may be lost in single collisions, and relatively few collisions are necessary to stop the fragment. The average number of collisions depends on the atomic weight of the absorbing medium, but even in light elements it is probably less than ten. The recoil nuclei are observed in cloud chambers as short branches of varying length extending from the track of the fission fragment. In light gases such as hydrogen the fragment track remains relatively straight and shows many branches, whereas in gases of medium atomic weight such as zenon, collisions are fewer and the fragment track is more strongly deflected. The stopping of fission fragments in the first part of the range where ionization is most important results in a nearly linear relation between velocity and range, as shown in Fig. 46. In the second part, below a velocity of 2.5 X 108 cm per sec, the range is influenced solely by elastic collisions and decreases rapidly to zero. The great variation in the number of collisions that fragments undergo strongly influences the shape of the second part of the velocity-range curve and makes straggling large. The straggling is Sec. 6.6] FISSION 155 further enhanced by the variation in initial energy, charge, and mass of the fragments. Efforts to calculate a stopping formula and range-energy rela- tion have been unsuccessful, mainly because the charge of the fragment is a rapidly changing and, as yet, unknown function of velocity. The stopping theory proposed by Bohr [25] is, however, confirmed in principle by results of range and stopping-power measurements [33,34,35]. As is to be expected from the mass and energy division of fission fragments, short- and long-range groups are found which have been shown to correspond to the light and heavy fragments, respectively. Ranges of the two groups in various gases are given 14 Si? Heavy fragment . / E u 10 - o r 8 // / s >s / / 5 b / / \ /, Light frogmen! > m //■ 4 J? 2 // Y ''''■' 1.2 1.6 2 0 2 4 Range in cm air 3.2 Fig. 46. Velocity-range curves of light and heavy fission fragments in air [34]. in Table 21. Table 22 gives the stopping power of various solid absorbers determined by Segre and Wiegand (37) from absorption measurements with thin foils. More detailed ranges are given in Table 23. Table 21. Ranges of Fission Fragments in Gases [35] Gas Short-range group, mm Long-range group mm Hydrogen Deuterium Helium. . 17.7 18.9 23 19.4 18 21.1 22.5 28 Argon Xenon 23.9 23 6.6. Radioactive Chains. The excitation energy of fission fragments which still remains after evaporation of prompt neutrons is subsequently lost by emission of delayed neutrons, beta particles, neutrinos, and gamma rays. The remaining excess of neutrons is transformed to protons by successive beta decay or, less frequently, lost by delayed neutron emission, until the 156 TSOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 Table 22. Transmission and Stopping Power of Various Substances for Fission Fragments [37] The upper number of each pair is the foil thickness in milligrams per square centimeter necessary to stop a given fraction of fragments. The lower number is the stopping power relative to aluminum. Some error was introduced by the method of detection, and the second set of absorber thickness for the end point, in parentheses, is corrected for 0.8 mg per cm2 of aluminum to give what is estimated to be the true end point. Fraction of frag- ments absorbed Collodion Aluminum Copper Silver Gold 0.1 0.11 0.18 0.28 0.33 0.60 1.6 0.64 0.55 0.30 0.2 0.22 0.36 0.54 0.68 1.16 1.64 0.64 0.53 0.31 0.3 0.32 0.54 0.82 0.98 1.68 1.69 0.66 0.55 0.32 0.4 0.42 0.72 1.10 1.30 2.20 1.72 0.66 0.55 0.33 0.5 0.54 0.90 1.36 1.62 2.78 1.67 0.66 0.55 0.34 0.6 0.64 1.10 1.66 1.96 3.34 1.72 0.66 0.54 0.33 0.7 0.74 1.36 2.0 2.33 3.95 1.84 0.68 0.58 0.35 0.8 0.91 1.63 2.34 2.75 4.65 1.78 0.69 0.59 0.35 0.9 1.23 2.06 2.85 3.39 5.7 1.67 0.72 0.61 0.36 1.0 2.10 2.9 4.10 4.80 9.0 1.37 0.71 0.60 0.42 (2.6) (3.7) (5.2) (6.1) (11.14) fragments are enabled by these radioactive chains to terminate in known stable isotopic species. An example of a typical chain is that following from the initial fission fragment 52Te135 [12]: 54Xe135— 3m / \ 52Tet35— 2w -> 53I135— 6.7 55Cs135— 2.5 X 104y -> 56Ba135 \ / 54Xe135— 9.2h (stable) A few of the many possible initial fission fragments are known to be stable, whereas others decay by the emission of as many as six successive beta particles. On the average each fragment undergoes three beta transforma- tions accompanied by its characteristic isomeric transitions. Many of the Sec. 6.6] FISSION 157 Table 23. Ranges of Fission Fragments [36] Extrapolated and mean ranges of plutonium fission fragments in normal air, and the straggling as indicated by the widths at half-height of the differential range curves. Normalized Normalized Average width at Mass number Isotope extrapolated mean half-maximum, range, cm range, cm per cent 83 2.4-h Br 2.895 2.65 13.4 91 9 . 7-h Sr 2 . 738 2.55 11.4 92 3.5-h Y 2.717 2.55 10.5 93 10 h Y 2.697 2.53 10.1 (94) 20-m Y 2.687 2.52 10.5 97 17-h Zr 2.661 2.50 10.7 99 67-h Mo 2 . 635 2.48 10.8 105 36.5-h Rh 2 . 587 2.42 11.4 109 13.4-h Pd 2 . 508 2 . 35 10.7 112 21-h Pd 2.416 2.24 13.4 117 1.95-h In 2.246 2.08 10.1 127 93-h Sb 2.248 2.09 11.9 129 4.2-h Sb 2 . 243 2.09 12.5 132 7 7-h Te 2.198 2.05 11.5 133 60- m Te 2.180 2.04 11.8 (134) 43-m Te 2.180 2.04 11.4 140 12.8-d Ba 2 080 1.92 12.6 143 33-h Ce 2.040 1.89 11.8 149 47-h 61 1.977 1.82 13.1 (157) 15.4-h Eu 1.949 1.79 15.1 end activities of the observed chains correspond to earlier known activities produced by other processes. The total decay energy associated with the chain activities of the two fragments has been measured by several investigators but with conflicting results because of the difficulties encountered in evaluating with accuracy the energy associated with the very short half-lives and penetrating gamma rays. The average total decay energy is probably between 20 and 30 mev per fission. The fraction of the total energy contributed separately to beta particles and gamma rays is not certain, but Way and Wigner [16] have given an empirical formula for the rate of energy loss by gamma rays in the interval 10 < / < 107 sec as Er = 1.26rK2 mev (fiss)/sec and for the average total energy Et = 2.66/-1-2 mev (fissVsec Experiments by Bernstein et al. [17] on the yield of gamma rays with 158 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 Table 24. Yield of Hard Gamma Rays from Fission Products [17] Half-life Energy, mev Gamma rays per fission 2.5s 3.4 0.00015 41 s 2.25 0.0042 2.4 m 2.65 0.045 7.7 m 3.0 0.038 27 m 2.6 0.046 1 . 65 h 2 62 0.132 4.4h (3) 1.58 53 h (3) 0.675 Total 2.5 energies greater than 2.17 mev from fission products indicate about eight gamma-ray components, as shown in Table 24. 6.7. Prompt Neutrons. On the basis of the existence rules for stable isotopes (Sec. 1.1) it is apparent that the two fragments of medium atomic weight formed in the fission of a heavy element must contain a considerable excess of neutrons compared with stable nuclei with the same number of protons. Some of the excess neutrons therefore are very weakly bound, and in view of the high excitation energy given fission fragments in the process of division, a portion of these neutrons boil off instantly. The average number of prompt neutrons per fission has been extensively investigated, and the values that have been reported vary from 1.5 to as many as 6. The most reliable of these measurements gives values between two and three prompt neutrons per fission, on the average. Although the reported experimental results do not appear conclusive for accuracies greater than this, they tend to indicate an average value of about 2.6. This value can be regarded only as a tentative estimate until experiments demonstrate conclusively the magnitude of the second significant figure. The observed energy distribution of prompt neutrons is found to be not only continuous but also to be very nearly a Maxwellian distribution when the translational component of the fission fragment is subtracted. The super- position of the translational component of the fragment and the Maxwellian distribution bears out the contention that the neutrons are emitted from the fragments and not in the primary fission process. The form of the distribu- tion is consistent with the assumption that at high excitation energies many nuclear levels may be affected and because of their great density they present an essentially continuous spectrum of possible transitions by neutron emission. The most likely value of the mean energy per prompt neutron appears to be approximately 2 mev, and therefore, the total average neutron energy is 4 to 6 mev per fission. Sec. 6.9] FISSION 159 The directional distribution of prompt neutrons has been shown by Wilson [28] to be consistent with the assumption of isotropic evaporation from the moving fission fragments. 6.8. Delayed Neutrons. Delayed neutrons are emitted from fission products during the course of radioactive decay. They are emitted, how- ever, from only a few of the many possible fission products that may be formed, and consequently are low in intensity compared with prompt neutrons. The observed intensity under equilibrium conditions is 1.0 ± 0.2 per cent of the abundance of prompt neutrons [18]. A delayed neutron is emitted only after the initial fission fragment has undergone beta decay. If, after beta emission, the residual nucleus still possesses an excitation energy greater than the neutron binding energy, it may decay by further beta transitions or by neutron emission; the latter process usually reduces the nucleus to the ground state. Although the neu- tron is emitted in an exceedingly short time after the nucleus is reduced to the appropriate excited level, the observed half-time for neutron emission following the primary fission process is controlled by the preceding beta transition and, therefore, has the same half-life. Six such half-life periods have been found for delayed neutrons as shown in Table 25. Table 25. Delayed Neutrons [29] Half-life, sec Energy, mev Yield,* per cent Primary fission fragment 0.05 0.025 0.43 0.420 0.085 1.52 0.620 0.241 4.51 0.430 0.213 22. 0.560 0.166 I137 [18] 55.6 0.250 0.025 Br87 [18] * Relative to total neutron emission. These six periods are observed in the fission of both U236 and Pu239 and presumably are associated with the same fission fragments from either element. 6.9. Alpha Particles. Alpha particles have been found to be associated occasionally with fission of both U235 and Pu239. Farwell et al. [11] observed a continuous energy distribution with a maximum energy of about 16 mev and were able to show that the alpha particles were emitted within 5 X 10-6 sec after the primary fission process. Wollan et al. [20], using photographic plates, found the maximum energy to be 22 mev (40 cm range in air at normal temperature and pressure) and demonstrated that alpha particles were emitted in the primary fission process and not from the fragments. It was 160 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 Table 26. Fission Product Yields The following table is based on data reported by the Plutonium Project in J. Am. Chem. Soc, 2411- 2422 (1946). Only the initial fission fragment and the final product of each of the known chains are listed here, together with the probable yield. For a complete description of the chains, reference to the above report is suggested. Probable nssion Stabl e Probable fission Stable fragment product Fission yield, per cent fragment product Fission yield, per cent Z El A Z El. A Z El. A Z El. A 31 Ga 71 48 Cd 115 49 In 115 0.0008 30 Zn 72 32 Ge 72 1.5 X lO-5 i 48 Cd 116 30 Zn 73 32 Ge 73 10 x io-« 48 Cd 117 50 Sn 117 0.01 32 Ge 74 48 Cd .. 48 Cd .. 32 Ge 75 33 32 As Ge 75 76 50 50 Sn 118 Sn 119 32 Ge 77 34 Se 77 0.0091 40 Sn 120 32 Ge 78 ? 0.02 50 Sn 121 51 Sb 121 0.014 33 33 As As 78 81 34 35 34 Se Br Se 78 81 82 0.125 50 MS 51 50 ■>{£ Sn 122 0.0012 34 Se 79 35 34 Br Se 79 80 50 Sn 123 51 50 Sb 123 Sn 124 0.0044 34 Se 83 36 Kr 83 50 Sn 125 52 Te 125 0.023 34 Se 84 36 Kr 84 0.65 50 Sn 125 ? 35 Br 82 36 Kr 82 2.8 X 10 -« 50 Sn 126 52 Re 126 0.1 35 Br 85 37 36 Rb Kr 85 86 51 Sb 127 53 52 I 127 Te 128 35 Br 87 36 Kr 87 0.026 51 Sb 129 54 Xe 129 35 Br 87 38 Sr 87 52 Te 130 36 Kr 88 38 Sr 88 51 Sb 132 54 Xe 132 3.6 36 Kr 89 39 Y 89 4.6 51 Sb 133 55 Cs 133 4.5 36 Kr 90 40 Zr 90 51 Sb 134 54 Xe 134 5.7 36 Kr 91 40 Zr 91 9.5 52 Te 131 54 Xe 131 2.8 36 Kr 94 40 Zr 94 5 52 Te 135 56 Ba 135 5.9 36 Kr 97 42 Mo 97 53 I 136 56 Ba 136 0.01 40 Zr 96 53 I 137 54 Xe 136 42 Mo 98 53 I 137 56 Ba 137 37 Rb 86 38 Sr 86 2 X 10-s 54 Xe 138 56 Ba 138 37 Rb 92 40 Zr 92 5.1 54 Xe 139 57 La 139 6.3 37 Rb ? 54 Xe 140 58 Ce 140 6.1 36 Kr 93 41 Cd 93 54 Xe 141 59 Pr 141 5.7 39 Y 95 42 Mo 95 6.4 54 Xe 143 60 Nd 143 5.4 42 Mo 99 44 Ru 99 6.2 54 Xe 144 60 Nd 144 5.3 42 Mo 100 54 Xe 145 60 Nd 145 42 Mo 101 44 Ru 101 55 Cs 142 58 Ce 142 42 Mo 102 44 Ru 102 58 Ce 146 60 Nd 146 42 Mo 105 46 Pd 105 0.9 60 Nd 147 62 Sm 147 2.6 43 Tc 107 47 Ag 107 60 Nd 148 46 Pd 108 60 Nd 149 62 Sm 149 1.4 44 Ru 103 45 Rh 103 3.7 60 Nd 150 44 Ru 104 60 Nd 151 63 Eu 151 44 Ru 106 46 Pd 106 0.5 62 Sm 152 45 Rh 109 47 46 Ag Pd 109 110 0.028 61 153 63 62 Eu 153 Sm 154 0.15 46 Pd 111 48 Cd 111 0.018 61 156 64 Gd 156 0.013 46 Pd 112 48 Cd 112 0.011 62 Sm 155 64 Gd 155 0.03 • 48 Cd 113 63 Eu 157 64 Gd 157 0.0074 48 Cd 114 63 Eu 158 64 Gd 158 0.002 Sec. 6.11] FISSION 161 also observed in these experiments that the distribution of alpha-particle tracks tended to bunch about a direction at right angles to that taken by the fragments. The frequency of occurrence of alpha particles appears to be about 1 in 250 fissions of U235 and 1 in 500 fissions of Pu239 [11]. 6.10. Fission Induced by Other Radiations. Neutrons are the most effi- cient means for inducing fission in heavy elements since they are unaffected by the high electrostatic potential barrier, but charged particles and gamma rays will also induce fission when given sufficient energy. Photofission has been investigated with high-energy gamma rays, and the cross sections for uranium and thorium are reported as ou = 0.0035 barn and o-Th = 0.0017 barn, respectively [30]. Alpha particles and deuterons are also known to induce fission, but in the case of deuterons it is not yet certain if the entire particle enters the nucleus or is first stripped of its proton so that only the neutron is captured. 6.11. Fission of Elements below Thorium. Despite the increasing height of the fission barrier in elements with atomic numbers lower than thorium, it was anticipated that fission could be induced in such elements with particles of very high energy. This has been verified by Perlman et al. [31,32] for the elements bismuth, lead, thallium, platinum, and tantalum by bombarding targets of these elements with 400-mev alpha particles, 200-mev protons, and 100-mev neutrons produced by the 18-i-in. Berkeley cyclotron. Bismuth, the most carefully investigated element, exhibits marked differences from fission of uranium by low-energy neutrons. Unlike uranium fission the masses of the bismuth fission products are distributed symmetrically in a single peak about mass 98-99. Also a greater proportion of the products are either stable or /3+ active. A qualitative explanation of bismuth fission is given [32] which suggests that only after about 12 neutrons have boiled off the compound nucleus (Bi + d) does fission become probable; the fissionability parameter Z2/A is then about equal to that of U236. Further, if it is assumed that the fragments retain the same neutron-to-proton ratio as the light bismuth nucleus (n/p = 1.36) then, as has been observed, the fragments with masses less than ~ 100 carry off an excess number of neutrons and are (jr emitters, those of intermediate masses are stable, and the heavier fragments are neutron deficient and therefore ^+ or K capture active. REFERENCES FOR CHAP. 6 1. Hahn, O., F. Strassman: Naturwissenschaften, 27, 11 (1939). 2. Meitner, L., O. R. Frisch: Nature, 143, 239 (1939). 3. Bohr, N., and F. Kalckar: Kg!. Dansk Vid Selskah. Acad., 1939. 4. Bohr, N., and J. A. Wheeler: Phys. Rev., 56, 426 (1939). 5. Breit, G., and E. Wigner: Phys. Rev., 49, 519 (1936). 6. Bethe, H.: Rev. Mod. Phys., 9, 69 (1937). 162 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 6 7. Bethe, H., and R. F. Bacher: Rev. Mod. Phys., 8, 32 (1937). 8. Feenberg, E.-.Phys. Rev., 55, 504 (1939). 9. "The Science and Engineering of Nuclear Power," Vol. 1, Addison-Wesley Press, Inc., Cambridge, Mass., 1947. 10. Jentschke, W.: Z. Physik, 120, 165 (1943). 11. Farwell, G., E. Segre, and C. Wiegand: Phys. Rev., 71, 327 (1947). 12. Plutonium Project: /. Am. Ghent. Soc., 68, 2411 (1946). 13. Feather, N.: Nature, 143, 597 (1939). 14. Wilson, R. R.: Phys. Rev., 72, 98 (1947). 15. Henderson, M. C: Phys. Rev., 58, 774 (1940). 16. Way, K., and E. P. Wigner: Phys. Rev., 70, 115 (1946). 17. Bernstein, S., W. M. Preston, G. Wolfe, and R. E. Slattery: Phys. Rev., 71, 573 (1947). 18. Snell, A. H., V. A. Nedzel, H. W. Ibser, J. S. Levinger, R. G. Wilkinson, and M. B. Sampson: Phys. Rev., 72, 541 (1947). 19. Burgy, M., L. A. Pardtje, H. B. Willard, and E. O. Wollan: Phys. Rev., 70, 104 (1946). 20. Wollan, E. O., C. D. Moak, and R. B. Sawyer: Phys. Rev., 72, 447 (1947). 21. Kanner, M. H., and H. H. Barschall: Phys. Rev., 57, 372 (1940). 22. Jantschke, W., and F. Prankl: Naturwissenschaften, 27, 134 (1939). 23. Flammersfeld, A., W. Gentner, and H. Jensen: Z. Physik, 120, 450 (1943). 24. Lassen, N. O.: Phys. Rev., 68, 230 (1945). 25. Bohr, N.: Phys. Rev., 59, 270 (1941). 26. Fowler, J. L., and L. Rosen: Phys. Rev., 72, 926 (1947). 27. deHoffman, F., and B. T. Feld: Phys. Rev., 72, 567 (1947). 28. Wilson, R. R.: Phys. Rev., 72, 189 (1947). 29. Hughes, D. J., A. C. Dobbs, and D. Hall: Phys. Rev., 73, 111 (1948). 30. Haxby, R. O., W. E. Shoupp, W. E. Stephens, and W. H. Wells: Phys. Rev., 59, 57 (1941). 31. Perlman, I., R. H. Goeckermann, D. H. Templeton, and J. O. Howland: Phys. Rev., 72, 352 (1947). 32. Goeckermann, R. H., and I. Perlman: Phys. Rev., 73, 1127 (1948). 33. BjzSggild, J. K., O. H. Arr0e, and T. Sigurgeirsson: Phys. Rev., 71, 281 (1947). 34. Bohr, N., J. K. B^ggild, K. J. Brostr0m, and T. Lauritsen: Phys. Rev., 59, 275 (1941). 35. B0ggild, J. K , K. D. Brostr0m, and T. Lauritsen: Phys. Rev., 59, 275 (1941). 36. Katcoff, S., J. A. Miskel, and C. W. Stanley: Phys. Rev., 74, 631 (1948). 37. Segre, E., and C. Wiegand: Phys. Rev., 70, 808 (1946). CHAPTER 7 RADIOACTIVITY 7.1. Summary of Radioactivity. Radioactivity refers only to those proc- esses by which unstable nuclei decay by loss of their excitation energy to form known stable nuclear species. These processes are distinct from the primary processes of nuclear interaction in which unstable or excited nuclei are formed. Radioactive decay proceeds at a rate proportional only to the number of unstable nuclei present and is wholly independent of external influences, whereas the primary process of formation depends upon the type and energy of the bombarding radiation. In addition, the primary process of formation of an excited nucleus takes place in a time of the order of 10-10 sec or less, while the probable time for decay of an unstable nucleus is enor- mously longer and varies over the range from 10-7 sec (RaD) to 4.4 X 1017 sec (thorium). All known unstable nuclei decay only by emission of one or more of the following radiations: negatron, positron, neutrino, gamma ray, alpha particle, and neutron. In general, decay proceeds by several discrete energy steps or transitions to lower nuclear quantum levels until the ground state of a stable nuclear species is reached. In most cases this involves the emission of a charged particle and one or more gamma rays. In many instances, particu- larly in medium and heavy nuclei, decay may occur by one of several alter- native processes involving different sets of quantum levels and sometimes different radiations. The probabilities for the alternative processes is given directly by the observed fractions of different radiations when the decay scheme is known. A summary of the processes that are known to occur in radioactive decay is given below. More detailed discussions will be found in those sections describing the specific radiations. a. Negatran Emission (Beta Decay). A beta particle and neutrino are emitted simultaneously and share in any proportion the total fixed energy corresponding to a discrete level transition in the nucleus. The observed beta kinetic energy varies from zero to a well-defined maximum corresponding to the total transition energy. The residual or daughter nucleus is greater in charge by one electronic unit, and the exact atomic weight is diminished by only the mass equivalence of the maximum kinetic energy of the beta particle emitted. The statistics of the nucleus remain unchanged, but the nuclear spin is altered by an integral multiple of h/2ir. 163 164 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 b. Positron Emission (Beta Decay). A positron and a neutrino are emitted simultaneously and share in any proportion the total discrete energy of the level transition. The observed positron kinetic energy may take any value from zero up to the well-defined total transition energy. The residual atom is smaller in charge by one electronic unit, and its exact atomic weight is diminished by an amount equal to the mass equivalence of the maximum kinetic energy plus twice the electron rest mass. The statistics of the nucleus remain unchanged, but the spin is altered by an integral multiple of h/2ir. c. K Capture. An alternative process to positron decay, K capture is often found to compete with positron emission for the same level transition in the transformation proton — > neutron. Unlike positron decay, however, a monoenergetic neutrino is emitted and K x-radiation characteristic of the daughter substance is emitted. The residual atom is smaller in charge by one electronic unit, and its exact atomic weight is diminished by the mass equivalence of the kinetic energy carried off by the neutrino. The statistics of the nucleus remain the same, but the spin is altered by an integral multiple of h/2ir. d. Isomeric Transition (Gamma Emission). Gamma rays are always monoenergetic for any one nuclear level transition, but several gamma rays of different energy hv may be emitted in cascade in the decay of a single atom. The charge of the residual nucleus remains unaltered, the spin is altered by an integral multiple of h/2ir, and the exact atomic weight is reduced by the amount hv/c2. e. Internal Conversion. Although internal conversion is not a nuclear phe- nomenon in the decay process, it is frequently observed to accompany gamma emission. Internal conversion (I. C.) is essentially the photoelectric absorp- tion of a gamma ray by an orbital electron of the atom from whose nucleus the gamma ray is emitted. K electrons are often observed to have the highest probability for emission, L electrons next, etc. The electron is ejected with a kinetic energy equal to the gamma-ray energy hv, minus the binding energy (ionization potential) of the electron in the atom. Ejection of conversion electrons is accompanied by characteristic K, L, M, and possibly N, x-radiation. The probability for the process is given in terms of the conversion coefficient a which is numerically equal to the ratio of the number of conversion electrons ejected to the number of gamma rays emitted: NK + iVL + • • • a = where Nr, Nk, . • • are the observed numbers of gamma rays and K, L, . . . electrons. Sec. 7.3] RADIOACTIVITY 165 /. Alpha Decay. With a single exception (lithium) alpha-particle emission is always monoenergetic. Although only one alpha particle is emitted per disintegration, many energy groups may be observed corresponding to different and more or less probable level transitions in the same species of nucleus. The residual atom is smaller in charge by two electronic units and is diminished in mass by an amount approximately equal to the rest mass of the alpha particle plus the kinetic energies of the particle and recoil nucleus, plus the rest mass of two electrons. 7.2. Law of Radioactive Decay. Radioactive decay is a statistical process following well-established rules. A single radioactive nucleus possesses a fixed probability of disintegration per unit time which is characteristic of the particular isotope and its state of excitation. Aside from these two factors, the probability of decay, and hence the rate of decay of a macro- scopic quantity of the radioisotope, is wholly independent of external influences such as temperature, pressure, chemical reagents, and the means by which it is produced. Since each disintegration is a statistically inde- pendent event, the average number of nuclei which disintegrate per unit time is proportional to the number of nuclei of the particular species in a pre- scribed state of excitation that are present at any instant. f - - where N — number of nuclei present at time / X = disintegration constant; factor of proportionality characteristic of the isotope and its state of excitation In practice the quantity Ar frequently is given any convenient dimension and may be referred to as the number of nuclei, activity, mass, or some wholly arbitrary unit convenient to the particular measuring device. 7.3. Fluctuations. The actual number of disintegrations observed per unit time fluctuates about a mean value A as a consequence of the random character of the disintegration process. The probability of observing M disintegrations per unit time when the average value is A is given by the Poisson probability distribution formula: When the average value is large and the difference A — M is small, the probability distribution may be represented approximately by Gauss' formula; 1 (M-XY- Pu = , e 7\— 166 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 HALF-LIVES (UPPER CURVE) 2 3 4 5 HALF-LIVES (LOWER CURVE) Fig. 47. Sec. 7.5] RADIOACTIVITY 167 An estimate of the statistical error in the measurement of an activity N is expressed usually in terms of the absolute probable error given by r = 0.6745 VN or in terms of the per cent probable error by 1 t% = 67.45 Vn It is assumed, of course, that the period of observation is very small compared to 1/X. 7.4. Simple Decay. The observed decay of a given quantity of radio- active isotope follows a simple exponential law as is readily apparent on integrating the expression dN/dt = —\N in Sec. 7.2. This assumes, of course, that the isotope is not at the same time being produced by some external agent. If N0 is the initial number of atoms of the radioactive isotope, the number of atoms remaining after a time / is N = N0e~M where X = decay constant in units of reciprocal time However, the decay of an isotope is usually expressed in terms of half-life T, which is the time required for an initial number of radioactive nuclei to be reduced by one-half. The number of atoms present at time / is then N = N0e-»-™WT Also frequently used is the mean life r = T/0.693 = 1/X, which is the time required for an initial quantity of radioisotope to be reduced by 1/e. The activity of any substance as a function of the number of half-lives is plotted in Fig. 47 for convenient reference. 7.5. Growth of Radioactivity. When a radioisotope is produced at a constant rate, for example, in a cyclotron or as a daughter substance of N0 N(t) 12 3 4 5 12 3 HALF -LIVES Fig. 48. Growth of a radioactive isotope that is produced at a constant rate, e.g., in a cyclotron, and decay after production is stopped. 168 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 uranium, the number of atoms of the product radioisotope after a time t is N = N0{\ - e -0.6931/T ) where N0 = saturation activity; the activity at which the rate of production of the isotope equals rate of its decay. This is equivalent to the rate of formation divided by X 7.6. Radioactive Substance Produced by Parent of Long Half -life. When a radioactive daughter substance is produced for which the half-life To is short compared with that of the radioactive parent, i.e., T\ )>> T->, and assuming that only the parent substance is present initially, the quantity of the daughter substance after time t is N2 = N0^(l - e 1 1 -0.693*/ T2 ) where N0 = initial quantity of parent substance After many half-lives of the daughter, the parent and daughter are in secular equilibrium and the decay of the latter is governed now by the decay of the parent. The quantity of the daughter is then proportional to the ratio of the half-lives of the two substances: N2 = N0 ^ 1 1 7.7. Parent and Daughter Substances of Comparable Half -lives. When the half-lives of parent and daughter are of the same order of magnitude and only the parent is present initially, the activity of the daughter substance at 10 ii 12 234 56789 HALF -LIVES OF PARENT Fig. 49. Growth and decay of a series of daughter substances in a radioactive chain A-+B—>C-+D->. Only the substance A is present initially. Sec. 7.9] RADIOACTIVITY 169 any later time is given by I 1 — I 2 The activity of the daughter increases to a maximum and then decays after a sufficiently long time at a rate corresponding to the longer of the two half- lives. The ratio of daughter to parent substance in transient equilibrium is N2 = TT\ N0 I 2 — I 1 This mode of radioactive decay is shown in Fig. 49. The area under all curves must be equal since the same number of atoms is involved in the complete decay of parent and daughters. 7.8. Decay of nth Component in a Radioactive Chain. If a given initial quantity N0 of radioisotope decays into a series of radioactive daughter substances, the quantity of the «th successive daughter substance after a time / is given by [1] where N = N0(aie-°-692t/Ti + a2e~°-69Zt/T^ + • • • + ane-°-6m/T») Tn-l ~2.79 53 £)~4.94 H 43Y 1.60 -< 57y 2.15 — 38 18 (3) Sec. 7.10J RADIOACTIVITY A r -99.3 6 1.18 18 \- - 0.7 B 2.25 110 m I ■^ r 1.3 K 41 19 (4 ) 173 .40 K 19 1.42x10 y ■34.5 0" 1.35 -(] 2oCO 40 - 63 K - 2.4 K 7 1.55 -* 40 (5) 19 12 ■I 25 £> 2.07— *{- 75 a" 3.58 r 1.51 20 Ca 42 (6) 21 65 d t SC*6h94P 0.36 »| 71, 12 6 (3 1.49 Y 0.68 -» Tl 46 22 (7) 52 Mn -98 6+2.66 25 21 m 6,5 d >/ -35 (3 0.58 /98 7 0.42 ^ •65 K (8) 54 Mn 25 310 d 100 K •" — 7 0.835 Cr 54 24 56 Mn 25 2.59 h -20 P 0.75 »| - 7 2.06 - -30 $~ 1.04 ►[— 7 1,77 50 p" 2.81 7 0.822 56 Fe 26 (9 26 Fe \- 50 (3 0.26 $ 47 d h50£ °-46' 7 1.30 — »| — 7 11 0 — 59 Co 27 174 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Col- 15 P+0 27 72 df"85 K ' 60l 27CO I- 100 P 0.31 5.3 y I 470 ■* » — 7 0.805 58 2£ y i.i< 7 1.30 60 28 Ni 64 Cu 29 12.8 d ^ a571 H|3ozn + 64 18.5 P 0.657 -42 K - 0.5 K »| 7 1.35 64 28 Ni (13) 63 Zn 30 38.3 m - 88 K, P 235 - 4 8K,p+ 1.4 0 -*[— 7 0.96 ■* K, P+ -*] 7 '-9 ~ Cu 63 29 (K) 65 Zn - 53 K 30 250 d - 1.3 P+ 0.4 -46 K 7 1.14 Cu 65 29 72 Ga I 399 335 3.05 40 P 0.64 -*■ 31 14.3 h 2.52 — i — 1.47 32 P 0.955 — •» -10.5 £~l.48 - 8 &~Z5Z - 9.5 (f 3.15 26.5 7 2.51 7.8 7 1.87 »| 32.9 7 2.21 4.5 7 159 H 4.5 7 1.05 -» 0.84 0.68 24.5 f 0.63* |- 05 J 0.68 100 70.84 ■* Ge 72 32 (16) Sec. 7.10] RADIOACTIVITY t o s 175 76 As 33 26.8 d - 15 £ 1.29 — - 25 p>~2.49 60 p~ 3.04 7 1.2 7 1.75 7 0.55 Se 76 (17) 34 82| h I 35^r h100 P 0>46 36 7 0.5 5 -* 7 0.79 7 1.35 — •■ 82 Kr 36 (95) Tc 43 62 d a/I 0 30 K 40 K 30 K —| — 40 70.570 + 30 7 0.81 3 y 1. 01 "^44^a2°H 42 Mj 177 0.73 -» 45 30 s 82 0 3.55 017 1.25 106 Pd (20) 46 (6-T rules ) I07l Q+ cd h0,31 p a32 48 1-99.27 K 6.7 h U 0.42 K — •» J - 7 0.86 -* — a/yy rUOyj* L 1.34 0.94 0.095 (44 s) 47 0 E Ag 107 (21) ml 2.7 d I 7 0.173 — J 0.247 ■* 111 Cd 48 (22) 112 In 49 23 m IOO7O. 16 — f 1.0 — H .50Sn K./3+l'7-^U Cd 9 m 4^4 0,1 122) 176 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 52 14 _ 1211 Je L»jj, >3 d I 70225 7 0.428 — 17 d K 1 7 0.61 -* 51 121 Sb (23) 128 I 53 25 m I- 7 /Tl.5< [-93 (3~2.0 59 2 7 0.428 -* 128 Xe (24) 54 55 12 .l30l „- [ I ~ I 1—40/3 0.61 —\ — 7 0.417 — 1 —7 0537 6hf-60^ 103 * 70.667 — * 70.744 — » Xe 54 (25) 130 131 53 8.0 d 15 /3~0.3I5 — 85/3 0.600 6/20 7 0.36 -* 55 Cs 133 (29) 1871 w |-7o/3 0.5 X 24.1 h U30£- 1.4 ■40 7 0.086 -* — y 0.101 — ►] — y0.!35 -* 60 y 0.94 1991 79Au |-I00 )S"0.38 3.3 d 100/ - x£6 yO.18 — 30 Hg 199 y 0.62 -• ► 187 Re 75 (30 J (31) Sec. 7.11] RADIOACTIVITY \" REFERENCES FOR DECAY SCHEMES (SEC. 7.10) 1. Bleuler, E., and W. ZuNTi: Helv. Phys. Acta, 20, 195 (1947). 2. Siegbahn, K.-.Phys. Rev., 70, 127 (1946). 3. Siegbahn, K., and N. Hole: Arkiv. Mat. Ast. Fysik, 33A, Xo. 9 (1946). 4. Bleuler, E., W. Boltman, and W. Zunti: Helv. Phys. Acta, 19, 419 (1946). 5. Gleditsch, E., and T. Graf: Phys. Rev., 72, 640 (1947). 6. Siegbahn, K.: Arkiv. Mat. Astron. Fysik, 34A, Xo. 10 (1946); 34B, Xo. 4 (1946). 7. Peacock, C., and R. G. Wilkinson: Phys. Rev., 72, 251 (1947). 8. Osborne, R. K., and M. Deutsch: Bull. Am. Phys. Soc, 22, 11 (1947). 9. Siegbahn, K.: Arkiv Mai. Asiron. Fysik, 33A, Xo. 10 (1946). 13. Bradt, H., et al.: Helv. Phys. Acta, 19, 219 (1946); M. Deutsch, Phys. Rev., 72, 729 (1947). 14. Bradt, H., et al.: Helv. Phys. Acta, 19, 221 (1946). 16. Haynes, S. K.:Phys. Rrc, 74, 423 (1948). 17. Siegbahn, K.: Arkiv Mat. Astron. Fysik, 34A, Xo. 7 (1946). 19. Huber, O., H. Medicus, P. Preiswerk, and R. Steffen: Phys. Rev., 73, 1211 (1948). 20. Peacock, W. C.:Phys. Rev., 72, 1049 (1947). 21. Bradt, H., el a/.: Helv. Phys. Ada, 19, 218 (1946). 22. Trendam, D. J., and H. Bradt: Phys. Rev., 72, 1118 (1947). 23. Burson, S. B., a al.-.Phys. Rev., 70, 565 (1946). 24. Siegbahn, K., and X. Hole: Phys. Rev., 70, 133 (1946). 26. Metzger, F., and M. Deutsch: Phys. Rev., 74, 1640 (1948). 27. Elliott, L. G., and R. E. Bell: Phys. Rev., 72, 979 (1947). 28. Townsend, J., M. Cleland, and A. L. Hughes: Phys. Rev., 74, 499 (1948). 29. Katcoff, S.:Phys. Rev., 72, 1160 (1947). 30. Sullivan, W. H.: Phys. Rev., 68, 277 (1945). 31. Mandeyille, C. E., M. V. Scherb, and W. B. Keighton: Phys. Rev., 74, 601 (1948) 7.11. The Natural Radioactive Series. The three radioactive chains (see Figs. 50, 51, and 52) growing out of the long-lived parent isotopes Th232, AcU235, and UI238, contain those radioactive isotopes that, together with K40 and Rb87, comprised the only radioactive isotopes known before the discover}' in 1932 of artificially induced radio- activity. The members of these series are found to occur in natural sources and in this sense are actually the only ''natural" radioactive series. In recent years, however, numerous short side branches have been added to these series as a result of the discovery of many new isotopes produced artificially. All of these branches consist of isotopes with relatively short half-lives and therefore do not occur naturally. The longest of these branches, as shown in Fig. 50, contains five members, and, although it runs into the uranium-radium series, it has been separately named the protacti- nium series after Pa230, its longest-lived member. A new series, completely independent of the three naturally occurring series, has also been found whose leading members were produced artificially. Although the series starts with Pu241, it has been named the neptunium series after its longest-lived member Np237. This chain would appear to complete 178 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 234 238 UX, —Ul 4.55X10 y 24.1 d 234 99.65 UX2 ••' m 234 0.35 UZ «'7 h RaB RaA Rn 3.05 m 3.825 d I 600 y Ro lo Ull 62 250 y 2.3X10 y 210 « 214 RaC" °-°"% Rac 19.72 m I 32 m \ \ 19.72 m, 99.96 % Pa 210 214 RaD 22.2 y RaC' Em Ra Th 20.8 d 206 (5XI0-7) 2I° Tl — ' RoE . 4.85 d PROTACTINIUM SERIES 4.85 <) STABLE RoG RaF 81 82 83 84 85 86 87 88 89 90 91 92 ATOMIC NUMBER Fig. 50. Uranium-radium series and protactinium series. 231 233 UY — AcU 24.64 h AcK 223 I % •Ac Pa 13.4 y 3.2X10 y .13.4 y, 99 % AcB AcA An ii 2 d 223 ^ 227 AcX RdAc 207 \ J,, AcC'r -^^AcC 2.16 m l 2.16 m,0.3 % 211 stable AcD 7— AcC' \ 81 82 83 84 85 86 87 88 89 90 91 92 ATOMIC NUMBER Fig. 51. Actinium-uranium series. Sec. 7.11] RADIOACTIVITY 179 MsTh ■Th 2 32 6.7 y MsTh, ThB ThA •Tn 6.13 h 224 224 ThX RdTh 1.90 i 206 ThC" -^ ThC 3.i m 60 6 m, 66 % A* ThD ■ThC' 81 82 83 84 85 86 87 88 89 90 ATOMIC NUMBER Fig. 52. Thorium series. Pu \ A/tO y 241 209 213 Tl Bi \ 46 m \ 2.2 m^ \ \ ■At Pb 3.3 h 209 3.2 xio"6 : Po Pa 2 7.4 d Np 225X10 y 500 y Ra 14 d Th 5000 y 1.65X10 y Fa Ac io d Am STABLE Qj 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ATOMIC NUMBER Fig. 53. Neptunium series. , the number of independent series that can be expected to exist. It is seen from Figs. 50, 51, and 52, that the mass number of each member of the uranium-radium series is represented by 4w + 2, where n is an integer. Similarly, the members of the other two natural series are represented by 4w + 3 and 4n, respectively. The new series, it is seen from Fig. 53, is the 180 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Table 27. The Natural Radioactive Series and Alpha Particles Isotope Symbol Half-life Range, cm in air Energy, mev Velocity 3 X 10'° cm/sec Disinte- gration energy, mev Relative intensity Uranium-radium Series Uranium I Ul 238 92 4.55 X 10' y 2.653 4.23 0.0456 4.15 Uranium Xi UX, 234 90 24 d 0- Uranium X21 Uranium Z J UX2 234 91 1.14 m 0- UZ 234 91 6.7 h 0~ Uranium II UII 234 92 2.3 X 105 y 3.211 4.76 0.0479 4.7 Ionium Io 230 90 8.2 X 104 y (2.85) 4.66 0 . 0485 Radium Ra 226 88 1,600 y 3.13 4.791 0.0500 Radon Rn 222 86 3.823 d 4.051 5.4860 0.0540 5.5886 Radium A RaA 218 84 3.05 m 4.657 5.9981 0.0565 6. 1123 Radium B RaB 214 82 26.8 m 0" Radium C RaC 214 83 19.72 m 4.039 5.506 0.0544 5.611 94 3.969 5.445 0.0539 5.549 113 -► Radium C • — RaC 214 84 1.5 X 10~< s 6.908 7.792 9.04 9.724 11.51 11.580 7 . 6802 8.2769 8.941 9 . 0655 9.315 9.4877 9.660 9.781 9.908 10.077 10.149 10.329 10.5052 10.5379 0.064 0 0665 0.0691 0 . 0696 0.0705 0.0711 0.0718 0.0723 0.0728 0.0734 0 0736 0.0742 0.0749 7.829 8.437 9.112 9.241 9.493 9.673 9.844 9.968 10.097 10.269 10.342 10.526 10.709 10« 0.43 (0.45) 22 0.38 1.35 0.35 1.06 0.36 1.67 0.38 1.12 0.23 -►Radium C"« — RaC" 210 81 1.32 m 0- Radium D ( RaD 210 82 22.2 y 0" Radium E RaE 210 83 4.975 d 0- Radium F RaF 210 84 139.5 d 3.845 3.685 5.403 21 (Polonium) (Po) (mean) 3.890 4.016 4.111 4.303 4.449 4.640 4.749 4.838 4.901 5.065 5.113 5.2984 5.303 0.0523 18 19 48 43 79 70 64 49 84 (126) (96) 10^ Radium G RaG 206 82 stable (Lead) (Pb) Actinium-uranium Series Actinium-uranium Uranium Y AcU UY 235 231 7.07 X 10s y 24 . 64 h 4.52 0- Sec. 7.11] Table 27. The RADIOACTIVITY 181 Natural Radioactive Series and Alpha Particlbs— (Continued) Isotope Symbol Half-life Range, cm in air Energy, mev Actinium-uranium Series — {Continued) Protactinium ^Actinium ► Radioactinium •Actinium K* Actinium X <- Actinon Actinium A Actinium B Actinium C 'Actinium C •- ► Actinium C"»~ Actinium D 4 — (Lead) Pa Ac RdAc AcK 231 227 227 >2A AcX 223 An AcA AcB AcC AcC AcC" AcD (Pb) 219 215 211 211 211 207 207 3.2 X 10< y 21 .7 y 18.9 d 21 m 11.2 d 3.92 s 3.20 3.23 3.511 (4.36) (4.17) 84 1.83 X 10-3 s 36 m 2. 16 m 2.0 X 10-3 s 4.71 m stable 692 240 14 45 7 4.69 4.72 5.00 5.0 5 . 429 4.984 6.555 051 019 990 968 924 870 817 766 744 719 674 /3" 719 607 533 8235 561 436 365 0" 618 272 7.680 Velocity 3 X 10>° cm /sec Disinte- gration energy, mev 0 0569 0.0567 0.0566 0.0565 0.0563 0.0560 0.0557 0.0555 0.0554 0.0553 0.0550 0.0552 0.0547 0.0544 0 . 0603 0 . 0592 0.0586 0.0627 0.0594 0.0578 0.0630 4 77 4 80 5 . 09 159 127 097 075 030 975 921 869 847 822 776 5 823 5 709 5 634 6 953 6 683 6 556 6 739 6 383 Relative intensity 80 15 100 15 5 10 5 80 15 60 10 6 4 1 10 1 1 100 19 Thorium Series Thorium Mesothorium 1 Mesothorium 2 Radiothorium Thorium X Thoron Thorium A Thorium B Thorium C Th 232 90 MsThl 228 88 MsTh2 228 89 RdTh 228 90 ThX 224 88 Th 220 86 ThA 216 84 ThB 212 82 ThC 212 83 1.389 X 10'° y 6.7 y 6.13 h 1.90 y 3.64 d 54.50 s 0. 145 s 10 6 h 60.6 m 2.80 (3.67) 4.08 5.004 5.638 .20 0- 0- .420 .335 6825 2818 7744 /s- 083 0.0481 4.34 (0.0527) 5.517 5.431 0.0546 5.7858 0.0579 6 399 0.0602 6 . 903 0.0570 6.200 27.2 182 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Table 27. The Natural Radioactive Series and Alpha Particles — {Continued) Isotope Symbol A Half-life Range, cm in air Energy, mev Velocity 3 X 10"> cm /sec Disinte- gration energy, mev Relative intensity Thorium Series — •(Continued) e 6.044 0.0535 6.160 69.8 (4.730) 5.762 0.0555 5.872 1.8 mean 5.620 5.601 0.0548 0.0544 5.728 5.708 0.16 1.10 -►Thorium C •— ThC 212 84 3 X 10-' s 8.570 9.687 1 1 . 543 8.7759 9.491 10.541 0.0684 0.0712 0.0750 8.947 9.673 10.744 10* 34 190 L-^ Thorium C"»— ThC" 208 81 3.1 m 0" Thorium D 4 ThD 208 82 Stable (Lead) (Pb) Neptunium Series* Plutonium Americium Neptunium Protactinium Uranium Thorium Radium Actinium Francium Astatine Bismuth • ► Polonium • — ► (Thallium)* — Lead i — Bismuth Pu 241 94 Am 241 95 Np 237 93 Pa 233 91 U 233 92 Th 229 90 Ra 225 88 Ac 225 ,89 Fa 221 87 At 217 S5 Bi 213 83 Po 213 84 Tl 209 XI Pb 209 X2 Bi 209 83 500 y 2.25 X 10« y 27. 4d 1 . 63 X lO' y 5 X 103 y 14 d 10 d 5 m 2.1 X 10-2 s 46 m 3.2 X 10-6 s 3.3 h Stable (8- 825 ~ 5 0- 801 31 023 86 8.336 * Recent data have made it possible to construct a fourth natural radioactive series which has the form (in +1). Its probable members and arrangement are given above as reported by Hageman, F., L. I. Katzin, M. H. Studier, A. Ghiorso, and G. T. Seaborg, Phys. Rev., 72, 253 (1947), and by English, A. C, T. E. Cranshaw, P. Demers, J. A. Harvey, E. P. Hinks, J. V. Jelley, and A. N. May, Phys. Rev., 72, 253 (1947). Thallium 209 is the only member that has not been positively identified. The name "Neptunium Series," after the longest lived member, was proposed in accordance with the practice for naming the other three series. hitherto missing 4« + 1 series. Additional radioisotopes that may be found should belong to existing series. For example, mass number 4n + 5 would be merely an existing member or a branch of the 4rc + 1 series. Figures 50 to 53 show the order and the half4ives of members of the four series. In the scheme used here, alpha decay corresponds to a displacement of two units to the left, whereas beta decay appears as a displacement of Sec. 7.12] RADIOACTIVITY 183 one unit to the right and diagonally downward. The ordinate of each member, actually the mass number, is represented by the vertical scale 2Z + Y where Z is the atomic number and Y is an integer. More detailed data concerning the energies and ranges of alpha particles emitted from the members of the series are given in Table 27. 7.12. Seaborg and Perlman Table of Isotopes.1 The following table represents a complete list of all the artificial and natural radioactive isotopes and stable isotopes, together with a number of their important features covering information available by approximately October, 1948, through publications, private communications, and almost all of the restricted distribution reports of the U. S. Atomic Energy Commission, the former "Manhattan District," U. S. Army Corps of Engineers, and the corresponding offices of Great Britain and Canada. With very few excep- tions, the criterion for listing a radioactive isotope has been the actual observation of its radiation. A somewhat more extensive treatment of fission product data available up to August, 1946, may be found in a Pluton- ium Project compilation, "Nuclei formed in fission," /. Am. Chem. Soc, 68, 2411 (1946). The first column lists the atomic numbers and mass numbers of the isotopes. The superscript "ra" following the mass number denotes a metastable isomer of measured half-life of either a stable or unstable ground state, but the isomeric transition need not have been observed. In the second column headed "Class" the degree of certainty of each isotopic assignment is indicated with a letter according to the following code: A = isotope certain (mass number and element certain) B = isotope probable, element certain C = one of few isotopes, element certain D = element certain E = element probable F = insufficient evidence In most cases the class is determined by evaluating the uniqueness of the assignment through chemical separation, reaction type and yield consider- ations, genetic relationships, and type of radiation. In a few cases newer techniques have been used. The term "m.s." in the second column refers to the identification of the mass number by means of a mass spectrograph, 1 The table of isotopes presented on pp. 187-207 is reprinted from Rev. Med. Phys., 20, 585 (1949) by permission of Professors G. T. Seaborg and I. Perlman and the publisher. It was found necessary in the interest of keeping the present volume within reasonable size to omit the exhaustive list of references contained in the original table. Aside from this omission, however, the table is complete in all other details. The explanatory text on this and the succeeding pages is also printed verbatim, except for deleted references and acknowledgments, from the same publication. 184 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 and "res.n.act." (resonance neutron activation) refers to the identification of a nuclear isomer by observing both isomers upon irradiation with filtered neutrons. With the mass spectrographic assignment of mass numbers there are some instances in which the mass number is known with greater certainty than the element. Such cases are assigned the appropriate code letter such as "E" followed by "m.s." The per cent abundance of the stable isotopes is listed in column three. The fourth column lists the type of radiation, with the following meaning for the symbols: jS- = negative beta particles (negatrons) /3+ = positive beta particles (positrons) 7 = gamma rays a = alpha particles n = neutrons er = internal-conversion electrons K = K-electron capture (or in more general terms, orbital electron capture) I.T. = isomeric transition (transition from upper to lower isomeric state) In the cases where it is certain that no gamma rays are emitted, this fact is expressed explicitly in column seven by the term "No 7." Annihilation gamma rays and x-rays are not listed. It may be assumed that x-rays have been observed or actually identified in almost all cases of orbital electron capture listed. The half-life is given in the fifth column. In most cases the determination is direct, either by measuring the decay rate, by weighing a long-lived isotope of known purity, or by comparing the activity with that of a genetically related isotope of known half-life. A number of half-lives are known only from the yield of activity resulting from a nuclear reaction of known or estimated cross section. Half-lives estimated in this manner are indicated by the term "yield." Usually for the cases where more than one value for the half-life has been reported, an attempt has been made to list the best value (an experimental value thought to be taken under the most favorable conditions) rather than a mean value; more than one value is listed where a choice does not seem obvious. Among the natural radioactivities an average value is often used which was taken from an international committee sum- mary report. In the columns headed " Energy of radiation," the energy value is followed by a description of the method used for the energy determination. The beta- particle energies correspond to the observed upper limits of the spectra; in those cases where only the Konopinski-Uhlenbeck extrapolated value has been reported, this is listed, followed by the designation "K.U." For alpha particles reported only by a range the "mean range in air" vs. energy relation- Sec. 7.12) RADIOACTIVITY 185 ship of Holloway and Livingston was used. The methods used for the deter- mination of the energy of the particles (alpha and beta) are described in each case with the aid of the following symbols: abs. = absorption cl. ch. = cloud chamber (with magnetic field in case of beta particles) spect. = magnetic deflection (magnetic spectrograph or spectrometer or counter with magnetic field) calor. = calorimetric measurements ion. ch. = measurement of pulse sizes in ionization chamber or propor- tional counter coincid. abs. = beta- and gamma-coincidence counters with absorbers coincid. = beta- and gamma-coincidence counters (for information on decay scheme — data not necessarily used in the table) spect. coincid. = coincidence counters arranged with a magnetic field The alpha-particle energies listed, where more than a single group exists in high abundance, include the group of highest 'energy and those groups with abundance greater than 10 per cent. Conversion electron energies are listed only when it is not known in which shell internal conversion takes place or when no attempt was made to relate the electrons with observed or unob- servable gamma rays; in all other cases entries are made in the column for gamma rays. The symbols used to describe the methods employed for the determination of gamma-ray energies have the following meaning: abs. = absorption cl. ch. recoil = secondary electrons in cloud chamber with magnetic field cl. ch. pair = positron-electron pairs in cloud chamber with magnetic field coincid. abs. = secondary electrons with coincidence counters and absorbers spect. conv. = internal-conversion electrons with magnetic spectrograph or spectrometer spect. = secondary electrons with magnetic spectrograph or spectrometer cryst. spect. = direct measurement of gamma-ray energy by diffraction in a crystal abs. of e~ = absorption of internal-conversion electrons abs. sec. e~~ = absorption of secondary electrons; coincid. = measurements with gamma-gamma-coincidence counters (for information on decay scheme — data not necessarily used in the table) Be-y-n reaction = measurement of neutron energy from Be-y-n reaction D-y-n reaction = measurement of neutron energy from D-y-n reaction When internal-conversion electrons are emitted, the energy listed in this column is always that of the corresponding gamma-ray transition. Only 186 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 the main gamma rays are listed for the natural radioactive isotopes. In a few instances in which a very short-lived metastable state has been identified as the daughter of the isotope in question, the gamma rays of the daughter may be listed for both parent and daughter. When a semicolon is used, it means that the values listed on each side of it are independent determinations of the same item, e.g., independent deter- minations of the half-life or of the energy of the radiation of a radioactivity. In another usage the semicolon separates the symbols in the "type of radia- tion" columns when there is more than one type of decay (/?""", (3+, a, K, or I.T.) for the radioactivity. The observed nuclear reactions (giving the target element, projectile, and outgoing particle, in order) by which the radioactive isotopes are formed are listed in the last column (p = proton, n = neutron, a = alpha particle, d = deuteron, / = tritium or triton (H3), y = gamma ray, e~ = electron). In cases in which the target material is not the naturally occurring element, but one enriched or depleted in a particular isotope, that isotope is indicated. No means for identifying the source or energy of the projectile is given. For example, deuterons varying from low energies to 200 Mev have been used. In many cases, with high-energy projectiles, multiple particles are ejected. A reaction such as (d-ap2n) is a formal presentation showing what the out- going particles might be and does not mean that the order of leaving the nucleus was determined nor that the a, p, and n were identified. In some cases where the path for reaching the product nucleus can even less definitely be stated the reaction is presented in the form (d-3zl0a) where "$z" indicates that the product nucleus is lower in atomic number than the compound nucleus by three units and "10a" means that it is lower in mass number by 10 units. Where the same isotope has been made by spallation of various target elements with high-energy particles, this is indicated by the symbol "spal." followed by the symbols for the target elements. Stable product nuclei which have been identified by means of the mass spectrograph are indicated by "m.s." The neutron-induced fission reactions of the heavy elements are designated by such symbols as XJ-n, Th-n, Pu-w, and Pa-w, while the gamma ray, deuteron, and alpha-particle-induced fission reactions are designated by symbols such as U-y, XJ-d, and XJ-a. Usually, but not always, "U-w" will mean the slow neutron fission of U235 while "U-d" or "U-a" designated fission products arise from U238. In this last column the method of production for each radioactive fission product is described by these symbols (XJ-n, etc.) together with the designation of its radioactive parent and its radioactive daughter when these are known. Similarly, for the radioactivities of the heavy natural and artificial families there are listed the immediate parent and daughter isotopes. The natural radioactivities without parents are listed as produced by a "natural source." Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 187 Isotope Z A 1 Hi H= H3 2 He' He* He« Li' Li» 4 Be7 Be' Be3 Be10 5 Bm B" B12 6 C« Class Per cent abundance 99.9344 0.0156 1.3 X 10~« 99.9999 7.39 92.61 Type of radiation 0~, 2a K. A m.s. A 100 18.83 81.17 Half-life 12.1 yr; 10.7 yr 0.89 sec; 0.8 sec; 0.85 sec 0.89 sec; 0.88 sec 52.9 days; 43 days 10-" - 10"17 sec calc. 2.5 X 10« 2.9 X 10" yr yield 0.027 sec; 0.022 sec 20 sec Energy of radiation, Mev Particles 0.0185 ion.ch.; 0.0169 ion.ch.; 0.015 abs., cl.ch.; 0.011 abs., cl.ch. 3.7 cl.ch.; 3.7 abs. Al; 3.5 abs. Al 12(/3") cl. ch.; 12QS-) abs. Al; distribu- tion, mean at 2.0(a) 0.055 (each a in cen- ter of mass system) ion.ch. 0.560 abs. Al; 0.58 abs. Al; 0.65 abs. Al 12 cl.ch. 2 abs. 7- rays No y No No y 0.485 spect. 0.485 coincid. abs.; 0.476 abs. Pb; 0.453 spect.; 0.474 spect. No Produced by D-n-7 D-d-p Ke3-n-p Li-n-l Be-d-t B-n-t N-n-< Li-y-p Li-n-p Be-n-a Li-d-p Li-n-7 Li7-n-7 Be-y-p B-n-a hi-d-n Li-p-n B-p-a B-d-an Be-7-n Be-d-p Be-n-7 B-n-p C-n-a B-d-P N ">-n-a B-p-n B ">-/>- h 188 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 6 C" A 0+ 20.5 min; 0.95 cl.ch.; No y Be-a-2n 20.0 min 0.99 spect. coincid. B-d-n B-p-y B-p-n C-y-n C-n-2n C-d-dn C-p-pn C-a-an N-p-a N-n-p3n N-y-p2n 0-y-an(?) O-n-aln Cis 98.9 c» 1.1 C" A 0- 5100 yr; 0.156 No y C-d-p 6400 yr; 4700 yr spect.; 0.154 abs. Al; 0.154 spect. C-n-y N-n-p O-n-a 7 N» A e+ 9.93 min; 1.24 spect.; No y coin- B-a-n 10.13 min 1.25 spect.; 0.92, 1.20 spect. cid.; No y spect. C-d-n C-p-y N-n-2n N-d-t N-7-n 0-n-p3n N« 99.62 N" 0.38 N« A &~, y 7.35 sec; 3.5, 10 abs. 6.2, 6.7 abs. N-n-7 7.5 sec; Al, Cu; 10 sec e~, cl. N-d-p 7.3 sec; cl.ch; 4, ch. pair; O-n-p 8 sec 10.3 cl.ch., abs. 4 abs. Pb, Cu; ~ 6 cl.ch. recoil F-n-a N" A /S-, n 4.14 sec 3.7(0-)O'« recoil — 0~ coincid. abs.; 0.9 (mean)(tt) O16 recoil in ion.ch.; 1.0 (mean) (n) p re- coil in cl.ch. Spal.(O.F, N.Mg.Al, Si.P.S.Cl, K) 8 0>< B 0+7 76.5 sec 1.8 abs. 2.3 abs. N-p-n O" A /3+ 126 sec 1.7 cl.ch. C-a-n "■ N-rf-n N-p-y Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 180 Isotope 7. A 8 O" On O18 Ol» 9 F" pi8 Pl9 P20 10 Ne19 Ne2° Ne21 Ne22 Ne23 11 Na21 Na22 Na" Na2* Class Per cent abundance A B 99.757 0.039 0.204 100 Type of radiation P • 7 0 + 90 51 0.28 9 21 100 /»-. 7 /3+ 0+(~lOO%) 7, no K 0~. 7 Half-life 29.4 sec; 29.5 sec; 27.0 sec 70 sec 112 min 12 sec 20.3 sec 40 sec; 40.7 sec 23 sec 2.6 yr; 3.0 yr 14.8 hr Energy of radiation, Mev Particles 4.5(30 •-, ), 2.9(70%) abs. Al; 4.1 abs.; 3.2 abs. Al 2.1 cl.ch. 0.7 cl.ch.; 0.7 abs. Al; 0.95 (20%). 0.6(80%) cl.ch. 5.0 cl.ch. 2.20 cl.ch. 4.1 abs. 0.58 cl.ch.; 0.575 spect. ; coincid. 1.390 spect., coincid.; 1.4 spect. 7-rays 1.6 abs. No 7; 1.4 cl.ch. recoil 2.2 cl.ch. recoil 1.3 spect.; 1.30 spect. 1.380,2.758 spect.; 1.4 2.8 spect.; 2.87, 2.74 Be-7-H reaction, D-7-n reaction; 2.56, 2.68. Produced by O-7-n 0-n-2n O-n-y F-n-p N-a-w O-d-n O-P-y F-y-2n O-a-pn O-p-n O-d-n O-t-n F-n-2n F-d-t F-y-n Ne-d-« Na-7-a«(?) F-d-p F-n-y Na-n-a F-p-n Ne-d-p Na-n-i> Mg-»-a Ke-p-n Ne-rf-n Mg2i-p-a F-a-n Ne-d-n Na-«-2n big- d-a Na-d-p Na-«-7 Mg-d-a Mg-n-p Mg-y-p Al-rt-a Al-d-pa A\-y-n2p Si-y-n3p(?) 190 I SO TOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Isotope Z A 11 Na" Na26 12 Mg23 Mg24 Mg26 Mg26 Mg« 13 A126 A12« A127 A128 A129 14 Si2' Si 28 Si29 Si™ Si31 Class B Per cent abundance A A A 78.60 10.11 11.29 Type of radiation p-, y 100 92.28 4.67 3.05 /S". y fi-.y Half-life 58. 2 sec; 60 sec; 62 sec 1 1.6 sec 10.2 min; 9.6 min 8 sec; 7.3 sec 6 sec; 6.3 sec 7.0 sec 2.30 min; 2.4 min 6.7 min 4.9 sec 170 min Energy of radiation, Mev Particles 3.4 abs. Al; 2.8 abs. Al 2.82 cl.ch. 0.79(20 %), 1.80(80%) spect.; 1.8 cl.ch.; coincid. 2.99 cl.ch.; 1.8 abs. 3.01 spect.; 2.75 coincid. abs.; 3.3 cl.ch.; 3.0 cl.ch.; 3.10 abs. Al, coincid. 2.5 cl.ch. and abs. 3.74 cl.ch.; 3.54 cl.ch. 1.8 cl.ch. 7-rays 2.76, 2.89 cl.ch. pair; coincid. abs. 1.01, 0.84 spect., coincid.; 0.64, 0.84, 1 .02 spect. 1.05 (single 7) cl.ch. recoil 1.80 abs. sec. e~; 1.80 spect. 1.8 spect.; 2.1 cl.ch. recoil No Produced by Mg-y-p Mg-n-p A\-y-2p Na-i>-K Mg-7-n Mg-d-p Mg-n-7 A\-n-p Mg2s-/)-n Na-a-n Mg-p-n Mg26-£-n Mg-/>-7 Al-7-n Mg-a-p Al-d-p AI-K-7 Si-n-p Si-y-p P-n-or Mg-a-p Si-n-p Si-y-p P-y-2p Al-p-n Mg-a-n Si-7-n Si-d-p Si-n-7 P-n-p S-n-a I Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 191 Isotope Z A 15 P29 P30 P31 P32 P34 16 S31 S32 S33 S36 S36 S3? 17 CI" CI" C135 Class A D A A A Per cent abundance 100 95 . 06 0.74 4. 18 0 016 75.4 Type of radiation P , y P+, y Half-life 4.6 sec 2.55 min 14.30 days; 14.07 days 12.4 sec 2.6 sec; 3.2 sec 87.1 days Energy of radiation, Mev Particles 5.04 min; 5.0 min 2.4 sec; 2.8 sec. 33 min 3.63 cl.ch. 3.0 cl.ch.; 3.5 spect. 1.712 spect.; 1.69 spect. 5.1(75%), 3.2(25%) coincid. abs.; 4.9 abs. Al 3.85 cl.ch. 0.169 spect.; 0.167 abs. Al; 0.166 spect.; 0.17 abs. Al 4.3(10%), 1.6(90%); 4, 1.4 abs. Al 4.13 cl.ch. 2.5 abs.; 5.1, 2.4 cl.ch. 7-rays No 7 2.6 abs.; 2.75 abs. sec. e~ 3.4 cl.ch. recoil Produced by Si-p-n Si-d-n P-7-2w(?) Al-a-n Si-p-n Si-He'-p P-n-2n P-7-n S-d-a Si-a-p V-d-p P-K-7 S-n-p S-d-a Cl-n-a Cl-d-pa Cu-d-15z33a S-n-p Cl-n-a Si-a-n P-p-n S-7-n S-n-7 S-d-p Cl-n-p Cl-d-ct S-n-7 C\-n-p S-d-n S-p-n P-a-n S-d-n S-a-p,n or S-a-d S-t-n C1-H-2K Cl-7-» 192 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 17 CI" A • P+; K;/3" 2 X 10» yr yield p~, P+; ~ 10« yr yield; > 103 yr yield 0.64 OS") abs.; 0.66 03-) abs. Al Cl-n-7 C\-d-i> CI" 24.6 C13" A P~, y 38.5 min; 1.19(36%), 1.60(43 %), Cl-d-p 37 min 2.70(11%), 5.2(53 %) spect.; 1.1, 2.8. 5.0 spect.; coincid. abs. 2.12(57%) spect.; 1.65, 2.15 spect. Cl-n-7 K-n-a Cu-d-13z27a Cl»» B P~ 1 hr Cu-d- 13226a Cu-a-14z28a As-d-17z38a 18 A36 A P+ 1.88 sec; 1.84 sec 4.4 cl.ch. S-a-rc Cl-p-n A3« 0.307 A37 A K 34.1 days No y S-a-n C\-d-2n C\-p-n K-d-a Ca-n-ar A38 0 060 A3» F P~ 4 min K-n-p A" 99 . 633 A" A P~.y 110 min; 1.18, 2.55 1.37 cl.ch. A-d-p 109.4 min (0.7 %) abs. Al, coincid.; 1.5 cl.ch. (K.U.) recoil; 1.3 abs. of e" A-n-y K-n-p 19 K37 F e+ 1.3 sec K-y-2n K38 A P+. y 7.7 min; 2.53 abs. 2.15 co- Cl-a-n 7.5 min Al; 2.3 abs. incid. abs. K-H-2M K-y-n Ca-d-a K'» 93.3 K«« A 0.011 P-. K; 1.8 X 10' yr 1.9 abs. Al; 1.54 Natural K/0- ratio (uncorr. 1.7 cl.ch.; (with K) source ~0.1, 1.9, for K); 1.41 abs. coincid.; > 1;t 1.4 X 10» Al; 1.35 1.55 abs. (14% of P~) yr (uncorr. for K); 1.5 X 10» yr (uncorr. for K) spect. coincid. Pb; 1.5 (with K) abs. Cu, Pb, co- incid. K*> 6.7 Sec. 7.12] SERBORG AND PERLMAN TABLE OF ISOTOPES 193 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles -, -rays 19 K« A 0~, 7 12.4 hr; 2.04(25 %), 1.4. 2.1 abs. A-a-pn 12.44 hr 3.58(75 %) spect. ; ~ 1.8, 3.50 abs. Al, co- incide 3.5 cl.ch. sec. e "; 1.51 spect., coincid. K-d-P K-n-y Ca-n-p Sc-n-a K« B £-. y 22.4 hr 0.24, 0.81 spect. 0.4 abs. Pb A-a-p K« D p- 27 min Ca-n-p K43'44 C p- 18 min Ca-n-p 20 Ca« F /9+ 4.5 min Ca-n-2n(?) Ca" E 1 .06 sec Ca-y-n Ca10 96.96 Ca« 0.64 ' Ca" 0.15 Ca" 2.06 Ca« A &- 152 days; 180 days 0.260 abs. Al; 0.25 spect.; 0.21 No 7 Ca-n-y Ca-d-p Sc-n-p Ti- n-a Bi-d Sc-d-2p Ca" 0.0033 Ca« F fi-.y 5.8 days 1.1 1.3 Ca-d-p Ca" 0.19 Ca" A P~, y 2.5 hr 2.3 abs. 0.8 abs. Pb Ca-d-p Ca-n-y Ca" B fi~ 30 min Ca-d-p Ca-n-y 21 Sc41 A 0 + 0.87 sec 4.94 cl.ch. Ca-d- n Sc" A 0\ -, 3.92 hr; 1.12 abs. 1.65 abs. Ca-a-p 4 hr Al, spect.; 0.4, 1.4 abs. Pb, Cu; 1.0 abs. Pb Ca-d-n Ca-p-n Sc44m A I.T., «-, y 2.44 days; 2.2 days 0.27 spect. conv.; 0.28 abs. of e~ K-a-n Ca-d-n Ca-p-n Sc-n-2n Ti-d-a Sc" A 0+, 7. K 3.92 hr; 1.5 abs., 1.33 abs. K-a-n 4.1 hr spect.; 1.33 abs. Al Pb, Cu, Al Ca-d-n Ca-p-n Sc-n-2n Sc-7-rt Sc""- I.T. Ti-d-a Sc" 100 Sc"m A res. n. act. I.T., 7. e- 20 sec 0.18 abs., abs. of e~ Sc-)!-7 194 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Isotope Z A 21 So" Sc«7 Sc« Sc« Class Per cent abundance 22 Ti« Ti45 Ti« Ti4» Ti60 Ti" 23 V" E D A A Type of radiation 0". 7, K Half-life 85 days 7.95 7.75 73.45 5.51 5.34 0". 7. K(?) 0" 0 . 7 0-. 7 /9+ 3.4 days 44 hr 57 min 0.58 sec 3.08 hr 21 days 6 min 72 days 33 min Energy of radiation, Mev Particles 0.36(0-) spect.; 0.26(0-) abs. Al, coincid.; • 0.4(0") abs. Al; 0.26, 1.5(0-) abs.; 1.49(0") (weak) spect. 0.46 abs. Al 0.64 spect.; 0.57 abs. Al 1.8 abs. 1.2 cl.ch. 1.6 abs. 0.45 abs. Al; 0.36 abs. 1.9 abs. 7-rays 0.88, 1.12 spect.; coincid.; 1.25 abs. Pb; 1.5 abs. Pb; 1.4 abs. Pb No y(?) 0.98, 1.33 spect.; 1.35 spect.; 1.33 abs. Pb No y 1.0 coincid. abs.; 1.02 coincid. abs. Produced by Ca.-a-p Sc-d-p Sc-n-y Ti-d-a Ti-n-p Ca-a-p Ca-d-n Ca.-p-y Ti-n-p Ca-p-n Ca-d-2n Ti-n-p Ti-d-a V-n-a Ca-d-n Ti-n-p Ti-y-p Ca«(2.5 hr) 0 "-decay Ca« (30 min) 0--decay Ca-a-M Ca-a-K Sc-p-n Sc-d-2n Ti-n-2n Ti-y-n Cu-d-8z20a Sc-p-n Ti-d-p Ti-n-y Ti-d-p Ti-n-y Cu-d-8zl4a Ti-d-n Ti-p-n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 195 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 23 V" A 0\ K, y; 16 days 0.72 spect.; 0.98, 1.33 Sc-a-n 0+(58%), 1.0 cl.ch.; spect.; Ti-d-n K(42 %) 0.58 1.05 cl.ch. recoil; 1.50 abs. Pb Ti-p-n Cr-d-a Cu-d-1z\1a v« B K 600 days Xo /3 or e~ No 7 Ti-d-n V51 100 \T62 A /3", 7 3.74 min; 2.05 abs.; 1.46 abs. Y-n-y 3.9 min 2.65 cl.ch. Pb, Fe, Cu; 1.3 abs. Pb Y-d-p Cr-n-p Cr-y-p Mn-w-a 24 Cr" A /3 + , 7 41.9 min; 1.45 abs., 0.18, 1.55 Ti-a-n 45 min cl.ch. abs. Pb Cr-n-2n Cr-y-n y Cu- 90%); spect.; spect. Co-d-p 0". 7 1.25(0-) conv.; 1.5 Ni-n-p (< 10%) spect.; 1.56(0") spect. (with 0") abs. Pb; 1.32 (with B~) spect. Co«i A m.s. 0" 1.75 hr 1.1 abs. Al Xo 7 Co-t-p Ni-7-£ Ni-<2-an Ni»4-f>-a Ni<"-n-/> Cu-n-na Cu-y-2p Cu-d-apn Ks-d-lz\6a Co«2 B 0". 7 13.8 min 2.5 abs. Al, coincid. 1.3 abs. Pb Ni«2-«-/; Cu-n-a Cu-d-ap 28 Ni« A 0+ 36 hr; 34 hr 0.67 abs. Fe-a-n Ni-n-2« Xi-7-n Cu-d-2zSa or Cu-d-2sl0o As-d-6z20a 198 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 28 Ni« 67.76 Ni» B • K, no 0- 5 X 10< yr yield; 16 yr yield ~ 0.05 abs. Al Fe-ot-n Ni-n-7 Ni-d-p Co-d-2n Ni«o 26.16 Ni»i 1.25 Ni»2 3.66 Ni«3 B P- 300 yr yield; long yield 0.05 abs. Al; abs. A, Al Ni-n-7 Ni«2-w-7 Ni«< 1.16 Ni« A /S", y 2.6 hr 1.9 abs. Al 1.1 abs. Pb; 0.280, 0.65, 0.93 spect. Ni-d-p Ni-n-y Ni'*-n-y Cu-n-p Zn-n-a Cuib-n-p Cu-d-2p As-d-6zl2a Ni«« A fir 56 hr As-d-6zlla Bi-d, parent of Cu«i 29 Cu" D fi+ 7.9 min; 10 min Ni-p-n Cu68 B 3 sec Ni-p-n Ni^-p-n Cu'» E 0 + 81 sec Ni-p-n Cu«o A m.s. P+.y 24.6 min 1.8, 3.3 ( < 5 %) abs. Al 1.5 abs. Pb Ni-p-n Ni«0-p-n Ni*°-d-2n Ni^-a-pn Cu-d-pin As-d-5zl7a Cu" B /3+; K 3.4 hr; 3.33 hr 1,205 spect.; 0.9 abs.; 1.23 No 7 Ni-d-n Ni-p-n Ni't-p-n Ni-p-y Ni-a-p Cu-7-2n Cu-d-p3n or Cu-d-p5n As-d-5zl6a CU»2 A /3+, 7 10.5 min; 10.1 min 2.6 cl.ch.; 2.5 abs. Al 0.56 abs. Pb Co-a-n Ni-p-n Ni-p-y Cu-n-2n Cu-7-n Cu-e~-e~n Cu-d-t Zn»2 K-decay Cu« 69.09 Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 199 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 29 Cu" A K(54%); 12.8 hr 0.57 1(0-), 1.35(2.5%) Ni-p-n 0-(31 %); 0.657 (0+) spect. ; Cu-d-p 0+(15%); spect.; 1.34 (weak) Cu-n-y 7(1-5%) 0.58(0-), spect.; Cu-n-2n (with K) 0.66 03+) spect.; 0.57 OS"), 0.64 (/S-) spect. 1.20(weak) coincid. abs. Cu-p-pn Cu-y-n Zn-d-a Zn-n-p As-d-5zl 3a Cu«6 30 91 Cu<»i .4 0". 7 5 min 2.9 cl.ch. (K.U.); 2.58 1.32 abs. Pb Cu-n-y Cu-d-P Zn-n-p Ga-n-a Ni<" 0--decay C'.l" B /3" 56 hr; 61 hr 0.56 abs. Al As-rf-5zlC» i.t. Zn'o 0.620 Zn" B P~, y 2.2 min 2.1 Zn-n-7 Ge-n-a Zn" A 0~, y 49 hr ~0.3 (95 %), ~ 1.6 (5 %) abs. Al U-n, parent of Ga" Bi-d As-d-4z5a 31 Ga" B 0+ 48 min Zn-p-n Ga« A K, e~ 15 min 0.054,0.117 spect. conv. Zn-d-n Zn-p-y Ga«« A P+ 9.4 hr 3.1 abs. Cu-a-n Zn-p-n As-d-3zlla Ge86 decay Ga<" A K, 7, e~ 78.3 hr; 83 hr 0.094, 0.174, 0.187, 0.301 spect.; 0.0925, 0.180, 0.297 spect. conv., spect.; 0.292 spect. Zn-d-n Zn-a-p Zn-p-n As-d-3zl0a Ge« 0+-decay Ga»8 A /9+ 68 min 1.9 abs. Cu-a-n Zn-p-n Zn-p-y (?) Zn-d-n Ga-n-2n Ga-7-n Ge-y-pn Ge-d-a As-d-3z9a Ge«s K-decay Ga«» 60 2 Ga'» A p-.y 20.3 min; 20 min 1.68 cl.ch. (K.U.); 1.65 spect.; 1.62 abs. Al Zn-p-n Zn-a-p Ga-n-7 Ga-n-2n Ga-7-n Ge-d-a Ge-n-p Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 201 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 31 Gp." 39.8 Ga" A 0~. 7 14.3 hr; 0.64(40%), 0.63(24%), Ga-d-p 14.1 hr 0.955 (32 %), 1.48 (10.5 %), 2.52(8%), 3.15 (9.5 %) spect.; — 0.77, 2.3 co- incid. abs.; spect.; 0.8 (-65%), — 3.1 0.84 (100%), 1.05 (4.5 %), 1.59 (4.5 %). 1.87 (7.8 %), 2.21 (33 %), 2.51 (26.5 %) spect.; 0.64 Ga-n-7 Ge-n-p As-d-ap U-n, Zn'* /9~-decay Bi-a Tl-a XJ-a • (-35%) abs. Al (-8%), 0.84 (-46%), 2.25 (—46%) spect..; 2.50 D-7-rc reaction; spect. Ga" B 0- 5 hr 1.4 abs. Al No 7 Ge-n-p Ge-y-p U-n 32 Geee A — 140 min Ge-d-p5n, parent of Ga«« Ge<" A 0+ 23 min Ge-d-p4n, parent of Ga" Ge«8 A K 250 days; ~ 195 days Zn-a-2n As-d-a5n, parent of Ga«8 Ge™ 20.55 Ge" A K, «"(?); 11 days; ~0.6(/S+?) 0.6 abs. Ga.-d-2n K, no 0- 1 1.3 days; of e~ Ga- p-n or«-;^+(?) 11.4 days Ge-d-p Ge-n-y As-d-a2n Ge'i B 0+ 39.7 hr; 40 hr; 36 hr; 38 hr 1.2 abs. Zn-a-n Ga-d-2n Ga.-p-n Ge-n-y Ge-d-p Ge-n-2n Ge-y-n As-d-a2n 202 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 32 Ge" Se-n-a As7' 0+- decay(?) Ge72m A I.T., e~ 5 X 10 7 sec 0.68(e-)co- incid. abs. Ga72 0 "-decay Ge72 27.37 Ge" 7.61 Ge" 36.74 Ge" A 0~, y 89 min 1.1 cl.ch. (K.U.); 1.2 abs. Al Ge-n-7 Ge-d-p Ge-n-2n Ge-y-n As-n-p Se-n-a Ge7« 7.67 Ge77 A 0~, y 12 hr 2.0 abs. Al; 1.9 cl.ch. (K.U.); 1.8 abs. Al Ge-n-y Ge-d-p Se-n-a U-n, parent of As" Tj233.n Ge77m B fir 59 sec 2.8 abs. Al Ge-n-7, parent of As77 Ge" D &-, y 2.1 hr ~ 0.9 abs. Al U-n, parent of As" 33 As" B 0+ 52 min As-d-p5n Se" 0+-decay, As" A K 60 hr parent of Ge"(lld.) As72 B 0+, 7 26 hr 2.78 abs. Al, coincid. 2.4 coincid. abs. Ga-a-n Ge-p-n As-d-pin Se7*-d-a Se72 K-decay As" B K, e~ 90 days 0.052 spect. conv. Ge-d-n Ge™-a-p(?) As" A fi~, 0+, y 17.5 days; 1.3(0-), 0.582 Ga-a-n 19.0 days; 0.9(0+) spect. As-n-2n 16 days cl.ch. (K.U.) As-d-p2n Ge-d-n Se-d-a Ge-p-n Bi-d As76 100 As7« A 0~, y, no fi+; 26.8 hr 1.29(15%), 0.55, 1.20, Ge-p-n 0+, K, y 2.49 (25 %), 3.04(60%) (0~) spect.; 1.70 spect. ; 0.557, 1.22, 1.78 As-d-p As-n-y Se-n-p Se-y-p Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 203 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 33 As78 1.1, 1.7, 2.7(0-) cl.ch.; 0.7, 2.6(0 + ) cl.ch.; coincid. (weak) spect.; 1.94, 0.83 spect.; coincid.; 2.15 (weak), 1.84 (weak), 1.25 (~30%), 0.57 (-70%) spect.; 3.2, 2.2, 1.5 cl.ch. pair Se-d-a Br-n-a As" A $~ 40 hr 0.8 abs. Al V-n, Ge77 0~-decay Th-a Bi-d Ge77(59 sec) 0~-decay As" A (3", y 80 min; 65 min 1.4 cl.ch. (K.U.) 0.27 abs. Pb Br-n-a Se-n-p As78 D 0- 90 min 1.4 (-30%), 4.1 (-70%) abs. Al V-n, Ge" j3"-decay 34 Se7' B 0+ 44 min As-d-6n, parent of As7 1 Se" B K 9.5 days As--i-5n, parent of As72 Se" B /3+; X 6.7 hr 7.1 hr 1.29 abs. Al Ge-a-n Ge70-a-n As- 2.5 yr Al; ~0.8 abs. Al U-n Krso 17.43 U-n m.s. Kj87 B /s- 74 min ~ 4 abs. Al Kr-d-p Rb-n-p V-n, Br8' 0~-decay Krss A 0" 3 hr 2.5 cl.ch. (K.U.) Th-n U-n, parent of Rb88 Sec. 7.12] SRABORG AND PERLMAN TABLE OF ISOTOPES 207 Energy of ra liatii hi, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 36 Krss A 0" 2.6 min; 2.S min U-n, ances- tor of Sr8« V-d Pu-n Kr«° A 0" ~ 33 sec; short U-n, ances- tor of Sr»« Pu-n Kr» B 0" 9.3 sec; 5.7 sec U-n, ances- tor of Sr", ancestor of Y»« V-d Pu-n Kr»2 A f 2.3 sec; < 0.5 min U-n, ances- tor of Y»2 Th-n Pu-n Kr" A 0" 2.2 sec; 2.0 sec U-n, ances- tor of Y»» V-d Pu-n Kr« B 0~ 1.4 sec U-n, ances- tor of Y»« Kr" B 0~ Short U-n, ances- tor of Zr" Pu-n 37 Rb" A m.s. 0+. 7. e~ 5.0 hr 0.9(/J+), 0.2 (e~) abs. Al, spect. 0.8 abs. Pb Br-a-2n Rb«2 A m.s. 0+. 7 6.3 hr; 6.5 hr 0.9 abs. Al 1.0 abs. Pb Br-a-n Kr-d-2n Rb82 D 20 min Br-a-n Rb8* B 0+ ~ 40 days Rb-n-2n Sr-d-a Rb»=> 72.8 Rb F 42 min Ki-d-n Rb F 200 hr Ks-d-n Rb8« A 0". 7 19.5 days; 1.82(80^), 1.081 Rb-n-7 ~ 1 7 days 0.716 (20 %) spect., coincid.; coincid., 1.56 abs.; 1.60 spect.; 1.80 abs. Al spect., coincid.; coincid. Rb-7-n Sr-d-a Bi-d U-n Rb" A 27.2 0". 7. e" 6.3 X 10i» 0.132 0.034, Natural yr; spect.; 0.053, source 5.8 X 10'° 0.25; 0.13 0.082, yr; 0.102, 208 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 37 Rb87 1.2 X 10" yr spect.; 0.144 spect. 0.129 spect. conv. Rb88 A (8- 17.5 min 4.6 abs. Al; 5.1 cl.ch. Rb-n-7 Pa-n U-n, Kr88 0~-decay Th-n Rb8° A (9-. y 15 min 3.8 abs. U-n, Kr8» 0"-decay; parent of Sr«» Rb»° A 0" Short ' U-n, Kr»o 0"-decay, parent of Sr'o Rb91 A /3- Short U-n, Kr" (3 "-decay, ancestor of Y« Rb>»° D P- 80 sec U-n Rb's A 0" Short U-n, Kr<>3 /S "-decay, ancestor of Y»8 Rb84 B 0" Short U-n. Kr»« /3 "-decay, ancestor of Y»" Rb" B 0" Short U-n, Kr" 0"-decay, ancestor of Zr" 38 Sr8« 0.56 SrS6m A I.T., e~, T 70 min 0.1 70 spect. conv. Rb- p-n Sr«6 A K, T 65 days 0.8 abs. Pb Rb-p-n Rb-d-2n Sr*> 9.86 Sr87m A I.T., e~, 7 2.7 hr 0.37 spect. conv.; 0.386 spect. conv. Rb-p-n Sr-n-n Sr-x-rays Sr-e~-e~ Sr-d-p Sr-n-7 Sr8*-n-7 Sr-p-p(?) Y<" K-decay Zr-M-a SrS' 7.02 Srss 82 56 Sr8» A 0- 53 days; 1.50 cl.ch.; No 7 Sr-d-p m.s. 55 days 1.48 Sr-n-7 Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 200 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 38 Sr«> spect.; 1.5 spect. Y-n-p Zr-n-a(?) U-n, Rb" /9"-decay U-d U233-n Th-n Th-a Pu-n Bi-a Bi-d Pb-a Pt-a Sr»° .4 8- 25 yr; 0.61 spect.; No y U-n, Rb»° m.s. — 30 yr 0 6 abs. Al 0~-decay, parent of Y90 U233-M Th-a Sr« A B~, y 9.7 hr; 1.3(40%), ~ 1 .3 abs. Zr-n-a 10 hr 3.2(60%) abs. Al Pb U-n, Rb" 0~-decay, parent of Y91 (-60%) and Y»i™ (~40%) Th-n Th-a Pu-n Bi-a Pt-a Pb-a Bi-d Sr»2 A a- 2.7 hr U-n, parent ot Y»2 Th-n Th-a U-7 Sr»s A s- 7 min U-n, Rb« /3~-decay, parent of Y»3 Sr»< B 6- ~ 2 min U-n. Rb« 0~-decay, parent of Y»4 Sr»' B 3- Short U-n, Rb" j3~-decay, ancestor of Zr" 39 Y*7»> B I.T., e~, y 14 hr 0.5 abs. Sr-d-n St-P-h 210 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 39 Y«7 A K 80 hr No 7(?) Rb-a-n Sr-p-n Sr-d-n V88 A P + 2.0 hr 1.65 abs. Al; 1.2 cl.ch. (K.U.) Sr-d-n Sr-p-n Y-n-2n Y88 A K, y; /3+ 105 days 0.83 03 + ) 0.908, Sr-p-n m.s. (0.19 %) spect. 1.853,2.76 spect.; 0.908,1.89 spect. coincid.; 0.95, 1.92 cl.ch.; 1.87 Be-7-n; 2.8(1 %) D-7-n Sr-d-2n Y-n-2n Y89 100 Y90 A 0- 62 hr; 2.35 spect.; No 7 Y-d-P m.s. 65 hr 60 hr 2.16 spect.; 2.6 cl.ch. (K.U.); 2.5 abs. Al Y-n-7 Zr-n-£ Zr-d-a Ch-n-a U-n, Sr»« P "-decay Bi-d Bi-a Pt-a Tl-a Y»i"> A I.T., 7, e" 51.0 min; 0.61 abs. Zr-n-p (~9%) 50 min Pb, abs. Al of e~ U-n, Sr« /3"-decay Y»i A /s- 57 days; 1.53 spect.; No 7 Zr-n-p m.s. ■ 61 days 1.6 abs. U-n, Sr" ^"-decay; Y»»» I.T. U233-n U-d Th-n Pu-r, Bi-d Y»2 A /3", 7 3.5 hr 3.5 abs. Al; 3.6 abs. Al ~labs Pb Zr-n-p U-n, Sr« /3 "-decay Th-n Pu-n ^93 A 0", 7 10.0 hr; 11.5 hr 3.1 abs. Al 0.7 abs. Pb U-n, Sr»s /3"-decay Th-n Pu-n Y»* B /?", 7 20 min Zr-n-p U-n, Sr»< /3 "-decay Pu-n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 211 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 39 Y" B 0- Short U-n, Sr" /3~-decay, parent of Zr" 40 Zrs» A e~, y, I.T. or K 4.5 min Y-p-n Zr-n-2n(?) Zrs» A e+ 80.1 hr; 78 hr 1.07 abs. Al; 1.0(/9+) cl.ch. (K.U.), abs. No 7 Y-d-2n Y-p-n Zr-n-2n Mo-n-a Zr90 51 46 Zr9" 11 23 Zr" 17 11 Zr9« 17 40 Zr" A 0-. y. e~ 65 days; 0.394 0.73(93 %), Zr-n-7 65.5 days; (98%), 0.23 Zv-d-p 63 days 1.0(2 %) spect.; 0.42 (95 %), 1.0(5%) abs. Al (93 %), 0.92(7%) spect. convi.; 0.80 abs. Pb Mo-n-a U-n, parent of Cb"6 (35 days) and Cb96 (90hr)(?) U233-M Pu-n U-a Bi-d Th-a Zr»» 2.80 Zr97 B ft-.y 17.0 hr 2.2 abs. Al; 1 abs. ~ 0.8 abs. Pb Zr-n-7 Mo-n-a U-n, Sr" /3"-decay, parent of Cb9' U-a Th-a Pu-n Zr E 5 sec Zr-n-7 (?) Zr E &' 18 min Zr-n-7 (?) Zr F 0- 90 min ~ 1.5 abs. Zr-d-? Zr E /3- 70 hr 1.17 cl.ch. (K.U.) Zr-n-? 41 Cb E 4 min Zr-/)-n(?) Cb E 12 min Zr-p-n(}) Cb E 38 min Zt-p-nd) Cb»° B /3+. y 15.6 hr; 18 hr; 21 hr ~ 1 abs. Al 1 abs. Pb Zr- p-n(?) Zr-d-2n Mo92-(/-a Mo-d-a Cb9"" A I.T., e-, y 62 days; 60 days; ~ 55 days ~ 0.15 abs. of e~; 0.94 Zx-d-n Mo»W-a» 212 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 41 Cb" /I • 0-, 7 10.1 days; 1 1 days 1.38 cl.ch. (K.U.); 1.38; 0.59 1.0 Zx-p-n Cb-n-2n Ch-d-t Mo-n-p Cb»2 A 0-, y 21.6 hr 1.2 abs. Al 0.6 abs. Pb Ch-d-t Mo**-d-a Cb93 100 Cb"m F I.T. 42 days Cb-x-rays Cb94m A I.T., e~ 6.6 min 1.3 coincid. 0.058 abs. Cb-n-7 (-99.9%), abs. Al of «"; 1.0 Ch-d-p 0-(~O.l %) abs. Pb Cb" A > 104 yr Cb-n-7, Ch94" I.T. Cb96m A I.T., e~ 90 hr; 0.216 U-n, Zr" (100 %) 80 hr spect.; 0.24 spect. conv. 0~-decay (-2%), parent of Cb9" Mo"-d-a Cb" A 0~. 7. e~ 35 days; 0.146 0.75 spect.; Zr" 37 days spect.; 0.15 abs. Al; 0.154 spect. 0.79 spect.; 0.775 spect. conv. ; 0.92 co- incid. abs., coincid. 0"-decay Mo-d-a Mo^-d-a U-n, Zr»6 /3~-decay (-98%) Cb»« A e-.y 2.8 days; 3 days; 4 days 1.8 abs. Al 1 abs. Pb, coincid. abs. Zr-p-n Zr-d-2n Mo-d-a MoK-d-a Cb" A /3". T 68 min; 75 min 1.4 abs. Al 0.78 abs. Pb Mo-n-p Mo-y-p Mo100-d-an U-n, Zr" 0~-decay Cb9« A 0- 30 min Mol00-d-a 42 Mo92 15.86 Mo93 B 0 + , 7 6.70 hr; 7hr 0.3, 0.7 1.6 Zr-a-n Ch-P-n Ch-d-2n Mo-d-p Mo93 F /3+ 17 min 2.65 cl.ch. (K.U.) Ch-d-2n Mo-n-2n Mo-7-n Mo-d-p Mo« 9.12 Mo" 15.7 Mo96 16.5 Mo97 9.45 Mo98 23.75 Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 213 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 42 Mo" A P~. 7 67 hr; 1.3 abs. Al; 0.4 abs. Cu, Zv-a-n 66.0 hr 1.5 abs.; 0.24, 1.03 coincid. abs. Pb; 0.24 (20%), 0.75(80%) spect.; 0.77, 0.815, 0.84 spect.; 0.71 co- incid abs. Mo-d-p Mo-n-y Mom-n-y Mo-n-2n U-w, parent of Tc99™ U2M-„ Th-n Th-a Pu-n Bi-a Bi-d Tl-a Pt-a Mo100 9.6 Mo101 A P~. 7 14.6 min 1.0, 2.2; 1.8 cl.ch. (K.U.) 0.3, 0.9 Mo-n-7 Mo™-n-7 U-n, parent of Tc101 Mo102 D 0" 12 min U-n, parent of Tc102 Mo>°5 B 0- Short U-n, ances- ■ tor of Ru>°5 43 Tc'2 B P+, y 4.5 min 4.3 abs. 1.3 abs. Mo92-rf-2n Tc92.93 C /3+, 7 2.7 hr 1.2 abs. 2.4 abs. Pb Mo92-d-2n Mo-p-n Mo-d-n Tc94m B I.T., e~ 53 min 0.0334 spect. conv. Mo-p-n Mo9W-2n Tc»« B /S+;K(65 %), < 53 min 2.4703+) 0.380, Mo-p-n 7 spect. ; 2.503+) abs. Al 0.873, 1.48, 1.85, 2.74 spect. Mo94-d-2n Tc»6 A K, 7, «-; 0+ 56 days; 0.4 03+) 0.25, 0.84 Mo-d-n (~ l %) 52 days; 62 days cl.ch. abs. Pb; 0.201. 0.57, 0.81, 1.01 spect., spect. conv., coincid. Mo-p-n Mo»B-rf-2n Tc« A K. 7. e~ 20.0 hr 0.762, 0.932, 1.071 spect. conv.; 0.78 abs. Pb; 0.8 abs. Pb Mo-p-n Mo-d-n MoM-d-2n /3+-decay Tc9« A K, «"(?), 7 4.30 days; 0.64 (*-) 0.312, Cb-a-n 4.33 days abs. Al; no 0.771, Mo-p-n 214 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 43 Tc96 - P~, no e~, -0.8(0"?) spect. 0.806, 0.842, 1.119 spect. conv., spect., coincid.; 0.92 spect. ; 0.8 abs. Pb Mo-d-n Ru-n-p Mo9«-d-2n To97"1 A I.T., c 90 days; 93 days; 95 days 0.097 spect. conv. ; 0.108 abs. of e~ Mo97-d-2n Mo-d-n Mo-j>-n Ru»7 K-decay Tc97 A > 100 yr Mo97-d-2n, Tc""* I.T. Tc9* B fi-\ K(?), 7 2.7 days; 1.3 abs. Al; 0.9 abs. Pb; Mo98-d-2n 2.8 days 0.75 abs. Al 1.0 abs. Pb Ru-n-p Tc99"1 A I.T., e~, y 6.0 hr; 5.9 hr; 6.6 hr 0.136 spect. conv. ; ~0.18 abs. Cu, Pb Mo99 0~-decay Ru-n-p U-n, Mo»9 fi "-decay Th-n Tc'» A 0- 9.4 X 106 0.32 abs. Al; No 7 Tc99™ I.T. m.s. yr; 4.7 X 106 yr; ~ 3 X 106 yr yield ~ 0.4 abs. Al; ~0.3 abs. Al U-n Tc100 B 0". 7 80 sec 2.3 abs. Al 0.6 abs. Pb Tc99-n-7 Mo100-d-2n Tc<101 F 0" 36.5 hr Mo-p-n Tc<101 E 0" 18 sec Mo-p-n Tcioi A P~, 7 14.0 min 1.3; 1.1 cl.ch. (K.U.) 0.30 Mo101 P "-decay U-n, Mo101 0 "-decay Ru-y-p TC102 D /3- < 1 min U-n, Mo102 /3 "-decay Tc<104 F K(?), 7 60 days Ru-n-p Tc106 B 0- Short U-n, Mo106 /3 "-decay, parent of Ru106 44 Ru96 F 20 min Ru-n-2n(?) Ru" A e+, k, 7 1.65 hr 1.1(0+) abs. Al 0.95 abs. Pb Mo-a-n Mo92-a-n Ru-n-2n, parent of Tc96 Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 215 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 44 Ru9» 5.68 Ru97 A K, y, e- 2.8 days; 3.0 days 0.23 abs. Pb Mo!t-a-n Rn-d-p Ru-n-7. parent of ■pc97"1 Ru" 2.22 Ru» 12 81 RU100 12.70 Ru><» 16.98 Ru102 31.34 Ru»W A P~. 7 42 days; 0.25; 0.56 abs. Ru-d-p 41 days; 0.3(95 %), Pb; 0.4 Ru-n-7 45 days; 0.8(5 %) abs. Pb V-n, parent 37 days abs. Al; 0.75 abs. Al of Rhi°3"i U233-M Th-n Pu-n Bi-d Pb-a Ru104 18.27 RUI06 B 0~. y 4.5 hr; 1.4 abs. Al; 0.76 abs. Ru-n-7 4.4 hr; 1.5 abs.; PL; 0.7 Ru-d-p 4 hr 1.3 abs. Al abs. Pb V-n, Tci°6 0 "-decay parent of Rhios Th-n Bi-a Pb-a Tl-a Pt-a Ru109 A 0- 1.0 yr; ~ 0.03 abs. No 7 V-n, parent m.s. 290 days Al; very soft of Rh10« TJ233.„ V-d Th-n Th-a Pu-n Bi-d Ru107 D &~ 4 min ~ 4 abs. Al V-n, parent of Rh">7 45 Rh'»° B K, y, e~, /3+ 19.4 hr; 0.6(e-). 1.2 abs. Pb; Ru-d-n (~5%) 21 hr 3.0G8+) spect. 1.8 abs. Pb Pcjioo K-decay Rh>°> B K, t. e- 4.3 days; 5.9 days 0.35 abs. Pb. spect. conv. Ru-d-n Pd'°i K- and /3+- decay Rh'°2 A /S-, /3+, 7. K 210 days; 1.04 (0~), 0.46 Ru- 1.0 spect.; 0.29, 0.42, 0.50, 0.62 spect. No 7 1.06, 0.69 spect.; 1.63, 1.06, Produced by Pd-n-y, parent of RhlOSm Pd-7-n Pd-d-p Pd-M-7 Ag-n-p Ag-d-2p Ag-t-Ue^ U-n, parent of Ag">»" TJ233-W Pu-« Pd-d-p Pd-n-y U-n, parent of Agi" Th-n U-n, parent of Agi" Th-n Th-a Bi-d Pu-w Pd- p-n Sb-d-21a5z Pd-p-n Pd-p-n Rh-a-n Pd-d-n Pd-p-y Pd-p-n Ag-n-2n Ag-d-t Ag-y-n Ag-e~-e~n Ag-d-p2n Cd-n-p Rh-a-n Pd-d-n Pd-p-n 218 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of ra diation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 47 Agios 0.72(?) spect. Ag-n-2n Ag-d-P2n(?) Cd-n-p Sn-d-? Agio? 51.35 Agl07m A I.T., e", 7 44.3 sec; 40 sec 0.093 spect. conv.; 0.094 spect. conv. Ag-n-n Ag-x-rays Ag-e~-e~ Cdio' A'-decay Agios A P- 2.3 min; 2.4 min 2.8 cl.ch. Pd-p-n Ag-n-7 Ag-7-n Ag-e~-e-n Agi07-n-7 Ag-d-p Cd-n-p Agl09m A I.T., e~, 7 40.4 sec; 40 sec; 39.2 sec 0.087 spect. conv.; 0.088 spect. conv. Pdi°» i8~-decay Ag-n-n Ag-x-rays Ag-e~-e~ Cdio» A'-decay Agios 48.65 Agno A /S", 7 24.2 sec; 22 sec; 28 sec 2.6 abs.; 2.8 cl.ch. (K.U.) Ag-n-7 Agios-n-7 Cd-n-p Cd-y-p Agno A K, 7, tr\ (»- 225 days 1.3 abs. Al; 1.40(9 %), Ag-n-7 res. n. act. 0.38 abs. Al; 0.59 spect. 0.90 (47 %), 0.66 (44 %) spect conv., spect.; 0.650, 0.925, 1.51 spect.; 0.6 abs. Al Ag'oa-n-7 Ag-d-p Agui A 0" 7.5 days ~0.24(?), 1.0 abs., ~ 0.8 abs. No 7 Pd-d-n Pd-a-p Cd-n-p Cd-y-p V-n, Pdi" /3~-decay Tj233.n V-a Th-a Pu-» Bi-d AgH2 A /3_, 7 3.2 hr 3.6 abs. Al; 2.2 cl.ch. 0.86 abs. Al Cd-n-p Cd-y-p Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 219 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 47 Ag'i2 In-n-a V-n, Pd112 0~-decay U"3_n V-a Ag"3 A 0- 5.3 hr 2.2 abs. Al; 2.0 abs. Al No 7 V-n Cd^-y-p Ag E 0-,7 22 min ~ 3 abs. Al V-n 48 Cd106107 D (S+ 33 min Cd-n-2n Cd106 1.215 Cd107 .1 K(~100%), 6.7 hr 0.32 (0 + ) 0.84 (weak) Ag-p-n 7(4%), spect. spect.; Ag-d-2n 0+(O.3 %) * 0.53 abs. Pb; 0.7 abs. Ag-a-p3n Cd"*-n-y Sb-d-16a4z or Sb-d-18a4z Sn-d-? Cd108 0.875 Cd109 A K 330 days Ag-d-2n Ag-a-pn Cd108M-7 Sn-rf-? Sb-4 0.61 Sn"5 0.35 Sn»« 14 07 Sn''7 7.54 Sn"s 23.98 222 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by SO Sn<"» E 0" 25 min Sn-n-7 Cd-a-n Sn<»« £ 0- 3 hr Cd-a-n Sn"9"> D I.T., 7, e~ 13 days; 14 days 0.13 («") spect. 0.17 abs. Pb Cd-a-n Sb-d-a Sn"» 8.62 Sni2" 33.03 Sn»« A 0- 28 hr;26hr 0.4 abs. Al No 7 Sn-d-p Sn-n-7 Sn^o-d-p Th-a Sni2i-i23 C 0- 130; days; 136 days 1.5-1.6 abs. Al; 1.2 No 7 U-m U233-M Th-a Sni22 4.78 Sn>12» D P~ ~ 80 hr; 60 hr 0.76 abs. Al U-» U-a Sn'23 D /3->7(?) 10 days; 11 days; 9 days 2.6 abs. Al; 2.5 abs. Al Sn-d-p Sn-w-7 U-n U"3-W Sni2< 6.11 Sn12s B /?-. 7 10 min; ~ 2.2 abs. ~ 0.74 abs. Sn-d-p 9 min Al Pb Sn-M-7 Sn1^ D /?- 40 min ~ 3 abs. Al Sn-d-p Sn™-d-t Sn-n-2n Sn12i B /9- 36 min 1.5 abs. Al Sn^o-d-p Sni=o E /3" 17.5 days 1.7 U-M U233-M Sn>i2» E P- 7.0 days 1.8 U-M Sni26 D /3~. y 70 min; 80 min 0.7 or 2.8 abs. Al 1 .2 abs. Pb U-m, parent of Sb"« Sn>i" D P~ ~ 20 min U-M 51 Sb117 D K, =» A 0 + 17 min 1.53 cl.ch. Sn-d-n Sn-p-n Sn120-rf-2M Sb-n-2n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 223 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 51 Sbi2" Sb-7-n Sb-d-t Sb-p-pn Sbi=° B K, 7. e~ 6.0 days 1.1 abs. Pb Sni2°-rf-2n Sb-d-p2n Sb121 57.25 Sbi-" A I.T., e~ 3.5 min 0.14 abs. of e~ Sb-n-7 Sbl=I-M-7 Sb1" A P~, 7. e~ 2.8 days 1.36, 1.94 spect. ; 0.81, 1.64 cl.ch., abs.; 1.19, 1.77 co- incid. abs., abs. Al 0.57 spect. conv. ; 0.96 coincid. abs.; 0.80 spect. Sn-d-2n Sn-p-n Sb-d-P Sb-n-7 Bi-d Sb"« 42.75 Sb"« A P~. 7 60 days 2.37. 1.62. 1.00, 0.65, 0.48 spect.; spect.; coincid. abs., 0.74, 2.4S spect.; 2.25, 0.53 spect.; 1.53 abs.; 0.654 spect.; 0.67, 2.45 coincid. abs. 2.04(weak), 1.708, 0.732, 0.654, 0.608, 0.121 spect., spect. conv.; spect.; 1.72 spect.; 1.82 coincid. abs.; 1.67, 1.71 Be-7-M re- action; 1.70 cl.ch. pair Sb-d-P Sb-n-7 I-n-o: Sn-d-2n Sb1**" A I.T., 0-, 7 21 min 0.02 (I.T.) abs. of e~ Sb-n-7 Sbl23-W-7 Sb"*» A /3-, 7; I.T. 1.3 min 3.2 abs. Al 0.014(I.T.) abs. of e~ Sb-n-7 Sb123-M-7 Sb'25 A 0-. 7 2.7 yr; sev- 0.3(65 %), 0.55 abs. Sn-rc-7, eral yr 0.7(35 r"c) abs. Al; 0.56 Pb; 0.6 abs. Pb /3~-decay, parent of Te126m Sn-d-n U-B Tj233-n Th-a Sb> «b E 0- 28 days 1.86 U-n Sb"« D /3- 60 min 2.8 or 0.7 abs. Al U-n, Sni-o 0~-decay Sb1" A 0-, 7 93 hr; 90 hr 1.2 abs. Al; 0.8 0.72 abs. Pb U-n, parent of Te'-? TJ233.M Pu-n 224 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Isotope Z A 51 Sb129 Sb1" Sb1" Sb1" 52 Te<118 Tei is Te"» Te120 Te121m Te121« Te121 Tei" Tei" Tei2< Tei 26 Class B A B D B B Per cent abundance Type of radiation 0.091 2.49 0.89 4.63 7.01 0- 5 min p- < 10 min fi- < 10 min 0+ 2.5 hr K 6.0 days K, y. e~ Half-life 4.2 hr I.T.. e-, y I.T.. y K, 4.5 days 143 days; 125 days Energy of radiation, Mev Particles 0.2, 0.5(e-) spect. 5 X 10-8 sec 17 days 7-rays No 7(?) 1.4 abs. Pb 0.0365(?), 0.082, 0.0885, 0.159, 0.213 spect. con v.; 0.0820, 0.0883, 0.136, 0.1573, 0.2108 spect. conv.; 0.05 spect. conv., abs. Ag; 0.22 abs. Pb 0.23 co- incid. abs. 0.61 abs. Pb; 0.615 spect. conv. Produced by U-n, parent of Tei2» Pu-n U-n, parent of Te132 U-n, parent of Te1" Th-n U-n, parent of Te"« Sb-d-? Sb-d-Sn, parent of Sb118 (3.3 min) Sb-d-4n, parent of Sb119 Bi-«i Sn-a-n Sb-d-2n Sb-p-n Te121m (143 days) I.T.. par- ent of Te121 Sb-d-2n Sb-p-n Te121m (143 days, 5 X 10-* sec) I.T. Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 225 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 52 Te'^m A I.T., e~ ~ 60 days ~0.12( A I.T., e- 30 hr 0.177 spect. conv. Te-M-7 Te-d-p U-n, parent of Tei3i Tei3i A &~ 25 min Te-d-p Te-n-y U-n, Te!3i»» I.T., par- ent Of 1131 Te"2 B 0~, 7 77 hr 0.36 abs. Al; ~ 0.3 abs. 0.22 abs. Pb U-n, Sb"2 /3"-decay, parent of I1M Th-n Th-a Pu-n Tei'3 A P~ 60 min U-n, parent of 1133 Pu-M 226 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 52 Tei" B • P~ 43 min U-n, Sb"4 l8~-decay, parent of 1134 Th-n Pu-n Tei36 A P~ < 2 min U-n, parent of I136 Te D P~ ~ 1 min U-n 53 I1" A P+ 4.0 days Sb-or-n Te-p-n Bi-d 1126 B K, no p 56 days ~ 0.1 (weak) («"?) No y, no e~ Te-d-n Bi-d 1126 A P~, 7 13.0 days 1.1 abs. 0.5 abs. Pb Sb-a-rc Te-d-n Te-p-n \-n-2n I-7-W Bi-d 1 127 100 J128 A P~, 7 24.99 min 1.59(7 %) (by diff.), 2.02(93%) spect.; 1.05, 2.10 cl.ch. (K.U.) 0.428(7 %) spect.; 0.4 abs. Pb 1-n-y Te-d-2n Te-p-n J 129 A P~ Long U-n J 130 A P~, 7 12.6 hr 0.61, 1.03 spect. coincid. 0.417, 0.537, 0.667, 0.744 spect. conv., spect., coincid. Te-d-ln Te-p-n Cs-n-a Th-n(?) I129_w_7 J131 A P~, 7. e~ 8.0 days 0.595 spect., coincid.; 0.687 cl.ch. 0.367,0.080 spect., spect. conv., coincid.; 0.65(15%) abs.; 0.4 abs. Pb Te-d-n U-n, Te"i /3~-decay U233-n U-a Th-a Pu-n 1132 B P~, 7 2.4 hr 0.9, 2.2 abs. Al; ~ 1.35 abs. 0.6, 1.4 abs. Pb; 0.85 abs. U-n, Te132 /3"-decay, parent of Xe"2 XJ233.n U-a Th-n Sec. 7.121 SEABORG AND PERLMAN TABLE OF ISOTOPES 22' Isotope Z A 53 I"3 J134 1 136 J138 1137 J138 1139 I 54 Xe>2« Xe1*6 Xei" Xe"' Xe'28 Xe129 Xe130 Xe13' Xe132 Xe™ Class A B D D D D F B B Per cent abundance 0.094 0.088 Type of radiation 0 . 7 0 . y fi-.y 1 90 26 23 4 07 21 17 26 96 £ . 7 0", « I.T.(?),e-, t * . 7 Half-life 22 hr; 20.5 hr 54 min 6.7 hr; 6.6 hr I.T., e~ 1.8 min; 86 sec 22.0 sec; 22.5 sec; 18 sec 5.9 sec 2.6 sec 30 days 75 sec 34 days Energy of radiation, Me\ Particles 1.4 abs. Al; 1.1 cl.ch. 7-rays 1 1 days 1.40(25 %), 1.00 (40 % ). 0.47 (35 % ) spect.; 1.4 abs. Al; 1.6 abs. 6.5 abs. Al 0.56(mean) (n) abs. paraffin ; 0.7 (mean) (n) p re- coil in cl.ch. 0.55 abs. Pb; 0.528 spect. > 1 abs. Pb 1.6 abs. Pb; 1.3 abs.; 1.27, 2.00 spect. Produced by 2.9 abs. Pb 0.175,0.125 spect. conv. 0.9 abs. of e~ U-n, Te133 0~-decay, parent of Xe133 U-a Pu-n Pb-a U-n, Te134 /3-decay Th-w U-a Pu-n U-n, Te136 /S~-decay, parent of Xe136, or parent of Xe136m (-10%), Xe'3» (~90%) Th-w Pu-n U-a U-n, parent of Xe"8 U-n, parent of Xe137 Pu-n U-n, ances- tor of Cs138 U-n, ances- tor of Ba139 Xe-n-p l-p-n Xe-n-y l-p-n \-d-2n U-n m.s. U-n m.s. Xe-n-n 228 1S0T0PIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 54 Xe"3 A P~. y, e~ 5.3 days; 0.34 abs.; 0.085 abs. Te-a-n 5.4 days 0.049 (e~) abs.; 0.260 abs. Al; Cu, Pb Xe-d-p Xe-n-y Cs-n-p 0.42 abs. Al Ba-n-a U-tt, I133 /3_-decay Xe134 10.54 U-n m.s. Xe'" A 0~, y. 9.2 hr; 0.93 spect.; 0.247 Xe-d-p *-(10%) 9.4 hr 0.95 abs. Al; 0.9 abs. Al; 1.0 abs. Al spect.; 0.25 abs. Pb Ba-n-a U-n, I"6 /3~-decay, Xe«smI.T. Xe136"* A 7; I.T., y, e~ 15.6 min; 10 min 0.52 spect.; ~ 0.5 abs. Pb; 0.6 abs. Al of e~ Xe-rt-7 U-n, lias /3"-decay, parent of Xe"6 Xe1" 8.95 U-n m.s. Xe137 D 68 min Xe-d-p Xe1" B 0- 3.8 min; 3.4 min 4 abs. Al Xe-n-y U-n, Ii" 0~-decay, parent of Cs137 Xe"8 D 0- 17 min U-n, parent of Csi38 Xe1" A 0- 41 sec; ~ 0.5 min U-n, parent of Cs"" Th-tt Xe1" A fi~ 16 sec; < 0.5 min; 9.8 sec U-n, ances- tor of Ba140 Th-tt XJ-d Xe1" A P~ 1.7 sec U-n, ances- tor of Ce1" V-d Xe1" A fi~ ~ 1.3 sec U-tt, ances- tor of Pr143 Xe1" A 0- Short U-tt, ances- tor of Ce144 Xe1" D /s- 0.8 sec; short U-m, ances- tor of Pr14* 55 Cs130 B 30 min I-a-n Cs131 B K, 7, e~ 10.2 days; 10.0 days No 7; 0.145 abs. of e~ Ba"! AT-decay Cs"2 B K, 7. e~ 7.1 days 0.6( 20 yr 0.36 abs. Pb, abs. of «-; 0.085, 0.320 abs., abs. of e~, cl.ch. Ba-ra-7 Bai33*" I.T. Ba134 Ba135m D 2.42 I.T., y, e- 28.7 hr 0.28(«~) abs. Al 0.34(weak) abs. Pb Ba-n-7 Ba-d-p U-a Ba135 6.59 Ba136 Ba137m A 7.81 I.T., y, e- 2.63 min; 2.5 min 0.626(e") spect., coincid.; 0.7 (<:") abs. Al, coincid. 0.663 spect. conv., spect.; 0.75 abs. Pb Csi" /3~-decay Ba-n-7 Ba137 11 .32 Ba138 Ba139 .4 71.66 0', 7 84 min; 85 min; 86 min 2.27 spect.; 2.3 abs. 0.163, 1.05 spect. conv., abs. Pb, coincid.; 0.6 abs. Pb, Cu Ba-d-p Ba-n-7 ha-n-p Ce-n-a U-n, Cs"9 /3 "-decay U-7 Th-w Pu-n Bau0 A m.s. 0". 7. e~ 308 hr; 12.8 days; 12.5 days 1.05 spect.; 0.4(25 %), 1.0(75%) abs. Al; 1.2 abs.; 1.1 abs. 0.529 spect.; 0.54 spect., spect. conv.; 0.5(25 %) abs. Pb U-n, Xe"o (and Cs1") /3 "-decay, parent of La»° U233-n V-d U-a Th-n Th-a Pu-n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 231 Energy of radiation, Mcv Isotope Class Per cent Type of Half-life Produced Z .4 abundance radiation by Particles 7-rays 56 Ba141 A 0~. 7 18 min U-n, Cs14' 0~-decay, parent of La14' Th-n U-7 Ba142 D P~ 6 min U-n, Cs142 P "-decay, parent of La"* Th-n U-7 Ba143 B P~ < 1 min U-n, parent of La143 Th-n Ba144 A (J- Short * U-n, de- scendant of Xe'", ancestor of Ce144 Ba146 D /»" Short U-n, de- scendant of Xe145, ancestor of Pr'« 57 La<139 D 0 + 10 min 2.1 abs. Al Ba-d-n La1" B K. 7 19.5 hr; 17.5 hr 0.88 abs. Pb Cs-a-2n Ba.-d-n Ba-p-n Cei" /3+-decay La136 B 0+ 2.1 hr 0.84 abs. Al No 7 Cs-a-rc La'37 A m.s. > 400 yr Cei" K-decay La138 0.089 La139 99.911 La>4° A IS". 7 40.4 hr; 0.90(20%), 0.335(2 %). Ba-rf-7(?) m.s. 40.0 hr; 1.40 0.49(5 %), La-d-P 39.5 hr (70%). 2.12 (10 %) spect. ; 1.41 abs. Al, spect.; 1.45 spect.; 1.8 abs. 0.87 (10%), 1.65 (77 %), 2.3(6 %) spect.; 0.335 1 % 1,0.49 (7 %), 0.83 (14%). 1.63 (74%), 2.3 (4%) spect.; 2.49(weak) D-y-n reaction La-n-7 Ce-n-p U-n, Ba>40 /3~-decay U233-n Th-« Pu-n 232 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 57 Lai" A 0" 3.7 hr; 3.5 hr 2.9 abs. Al No 7(?) U-n, BaUI /3"-decay, parent of Ce"i Th-n Lai" D P~, 7 74 min; 77 min U-n, Bai*2 fi~- decay Th-n Lai" A P- 20 min; 15 min U-n. Bai" 0~-decay, parent of Cei" Lai" A &- Short U-n, de- scendant of Xei", parent of Cei" Lai" D 0- Short U-n, de- scendant of Xei«, ancestor of Pri« 58 Cei" B P + ~ 16 hr La-4« 17.18 Nd>4' A 0-, 7. e~ 11.0 days; 0.4(40%), 0.58(40%) Nd-n-7, 11.1 days; 0.9(60%), abs. Pb parent of 12.1 days 0.03 (e") abs. Al; 0.76 abs. coincid.; 0.45 abs. Pm14' U-n 234 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 60 Nd"» 5.72 Ndi« B • 0- 7(?) 1.7 hr; 2.0 hr 1.6 abs. Al; 1.5 abs. Al Nd-n-7 Nd-d-p Nd-n-2n, parent of Pm14»(?) Nd160 5.60 Nd160 E 0- ~5 X 101" yr 0.011 abs. air Natural source Nd'" E P- 21 min Nd-n-7 Nd1" F 0- Short Nd-n-7, parent of Pm1" 61 Pm'« B K, e", 7 ~ 200 days; ~1 yr 0.67 abs. Pr-a-2n Nd-d-n Pm E p-,y 2.7 hr 2 Nd-p-v Nd-d-n Nd-a-£ Pm E /3", 7 16 days 1.7 Nd-d-n Pm147 A P- 3.7 yr; 0.223 No 7 U-n m.s. ~4 yr; 2-3 yr spect.; ~ 0.2 abs. Al; 0.20 abs. Al U233-n Nd-n-7, Nd147 0~- decay Pm"' .4 m.s. 0', 7 5.3 days 2.5 abs.; 2 0.8 abs. Pm147-n-7 Nd-p-n Nd-d-2» Nd-a-p Pm149 A 0~, 7 47 hr; 1.1 abs. Al 0.25 (weak) Nd-n-7, Nd m.s. 47.5 hr; 55 hr abs. Pb 0--decay U-n Pu-n Pm F /3" 12.5 hr Nd-d-n Pm'ii F 0~ 12 min Nd-n-7, Nd1" 0-- decay 62 Smi« 3.16 Sm1" F m.s. > 150 days; > 72 days 0.242, 0.95 spect. conv., abs. Pb Sm-w-7 Sm"' 15.07 Sm148 11.27 Sm14» 13.84 Sm'so 7.47 Sm1" A m.s. 0~ ~20 yr 0.06 abs. Al No 7(?) Sm-n-7 U-n Sm'52 26.63 Sm>« B a 1.0 X 10'2 2.14 photo- Natural m.s. yr (total Sm); 1.2 X 1012 yr (total Sm) film track; 2.0 cl.ch. source Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 235 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 62 Sm1" A 0~. y\ e~ 47 hr; 0.78 abs. Al 0.0695. Xd-a-n m.s. 46 hr * 0.103 spect. conv.; 0.57 (weak), 0.10 abs. Pb, Cu; ~0.6, 0.11 spect. ; 0.61 (weak), 0.11 abs., coincid. abs. Sm-n-7 Sm-n-2« Sm-" 22.53 Smi" B &~, y 25 min; 1.9 abs. Al; ~ 0.3 abs. Nd-a-n 21 min 1.8 Pb Sm-n-7 Sm- 20 yr; 0.9 spect.; 1.1 abs. Pb; Sm-154 D 0" 60 min — 2.5 abs. Al U-n 64 Gd1" 0.20 Gd153 B K, e~, y 155 days; 0.22, 0.40 0.102 spect. Eu-d-2n m.s. 155-170 days; ~ 110 days (weak)(e~) abs. Al conv.; 0.083, 0.270 abs. Cu, Pb Gd-n-7 Gd1" 2.15 Gd166 14.78 Gd158 20.59 Gd157 15.71 Gd168 24.78 Gd190 21.79 Gd181 D P~.y 18.0 hr; 20 hr 0.85 0.3 Gd-n-7 Gd-d-p Gd D 8.6 days Gd-n-7 Gd1" B P~. y 4.5 min 1.5 spect. 0.37 Gd-n-7 65 Tb1" D K 4.5 hr Eu-a-3n Tb163 D K, e~ 5.1 days 0.15, 0.4(e") abs. Al Eu-a-2n Tb1" D /S+, K, 7. e~ 17.2 hr 2.603+), 0.22, - 1 (e-) spect., abs. Al 1.4 abs. Pb Eu-a-3w Gd-£-n Tb1" D K, e- ~1 yr O.l(e-) abs. Al Eu-a-2rt Tb169 100 Tb180 A (3- 3.9 hr Tb-n-7 Tb190 A /3". 7 73.5 days; 0.546, 0.086, Gd-»« Eri" Er'«8 Eriss Erl«9.171 Er"0 Er"» Class El-"' A res.n.act. A m.s. D C B D A m.s. B F B Per cent abundance 0 . 0902 2.294 18.88 25.53 24.97 28.18 100 0 1 1.5 32.9 24.4 26.9 14.2 Type of radiation I.T., e~ 0~, 7 K(?) K(?), y, e- 0\ K, 7 K, e~ 0- 0- /S", 7. e- Half-life 1.25 min 145 min; 140 min; 2.5 hr 0', 7 ~ 20 min 60 days 4.5 hr 7 days 35 min; 47 min 27.0 hr; 27.5 hr; 27.3 hr; 30 hr 1.1 mm 9.4 days 6 min; 7 min 7.5 hr; 5.7-7.1 hr; 12 hr Energy of radiation, Mev Particles 20 hr 0.13(e-) abs. Al 0.42, 0.88, 1.25 spect.; 1.20 abs. coincid.; 1.18 spect.; 1.40cl.ch. 0.6, 0.16(e") abs. Al 2.O03 + ), 0.3 (e-) spect., abs. Al 0.4(«-) abs. Al 0.7 abs. Al 1.8 abs. Al; 1.9 abs.; 1.6 abs. 0.33 spect. 1.49(6 %), 1.05 (71 %), 0.67 (22 %) spect., coincid. 0.6 abs. Al 7-rays 0.091, 0.37, 0.78 spect. conv., spect.; 1.1 abs. coincid.; ~ 1, 0.37 spect. 1.1 abs. Pb No 0.81(22 %) 0.31 (71 %), 0.113 (71 %) spect., spect. conv. Produced by Dy-H-7 Dy"W-w-7 Dy-n-7 Dy164-n-7 Tb-a-3w Tb-a-2n Dy-d-2n Dy-p-n Tb-a-n Dy-J-s T>y-p-n Ho-w-2«(?) Dy-p-n Ho-n-y Er-n-2n(?) Er-n-7 Er-n-7 Er-n-7, parent of Tm'7"" (70%), Tm'"i (30 %) Er-n-7 238 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 69 Tm'« B 0+, K, 7, e~ 7.7 hr 2.1 (0+), 0.24, ~ 1 («-) spect., abs. Al 1.5 abs. Pb Ho-a-3n Tm'" B K, 7. e~ 9 days 0.21 (e-) abs. Al 0.22, 0.95 abs. Pb Ho-a-2n Tn-d-5zl6a Tm167.168 C K(?), e~ ~ 100 days 0.16, 0.5( i 127 days; 0.98 spect.; 0.83 spect. Tm-d-p ~ 125 1.1 abs. Al conv., Tm-n-7 days; 105 spect. days Tmi'1"- B I.T., e~ 2.5 X 10-» sec 0.113 spect. conv.; 0.1 coincid. abs. of e~ Eri"(7.5hr) jS "-decay Tm'" B P~ 500 days 0.1 abs. Al; 0.100 spect. Er>"(7.5hr) 0"-decay 70 Ybi68 0.06 Yb1"9 B K, 7. «-(?) 33 days; 33.5 days; 32.5 days 0.2, 0.4 abs. Pb, co- incid. Tm-rf-2n Yb-n-7 Yb»« 4.21 Yb>" 14.26 Ybm 21.49 Yb"« 17.02 Ybui 29.58 Ybl76 A 0", 7 99 hr; 0.50, 0.13 0.35 abs. Yb-n-7 m.s. 100 hr; 102 hr abs. Al; 0.45 cl.ch. Pb, co- incid. Yb"« 13.38 Yb»» B /3" 2.4 hr; 2.7 hr; 3.5 hr; 1.9 hr 1.3; 1.15 cl.ch. Yb-n-7 71 Lu>™ B K, 7, e-, 0+ 2.15 days 1.7(0+), 0.1(«-) spect., abs. Al 1.5 abs. Pb Tm-a-3n Yb-d-2n Ta-rf-3zl3a Lu"' B K(?), 7. «" 9 days 0.17,0.7(e-) abs. Al Tm-a-2n Yb- 100 days 0.11, 0.22 (e~?) abs. Al Tm-a-2n Yb-d-2n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 239 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 71 Lu1" 97.5 Lu"« A 2.5 0". (33 %), 7.3 X lO'o 0.215 abs. 0.260 abs. Xatural 7! K(67 %) yr (uncorr. for K); 2.4 X 10'° yr (corr. for K) Al, spect.; 0.40 abs. Al Pb source Lu1""" B 0- 3.67 hr; 3.75 hr; 3.7 hr; 3.4 hr 1.04 abs. Al; 1.15 abs. Al; 1.25 cl.ch. No 7 Lu-d-p Lu-n-7 Lu-x-rays Lu'7' A 0~, 7 6.8 days; 0.440 abs. 0.2 abs. Lu-n-7 m.s. 6.6 days; Al; 0.52 Pb; 0.2, Lu-d-p 6.9 days abs. Al; 0.47 cl.ch. 1.3 (weak) abs. Pb Hi-d-a 72 Hf"< 0.18 Hfi« B K, 7, e~ 70 days 0.3 (e~) abs. Al 0.3, 1.5 abs. Pb Lu-d-2n Lu-p-n Hfl74 5.30 Hfi" 18.47 Hf"« 27.10 Hfl79 13.84 Hfwo 35.11 Hfisi A ts-.y 46 days; 0.460 0.485, Hf-M-7. 55 days spect. ; 0.45 abs. Al; 0.42 abs. Al; 0.28 abs. Al, co- incid.; 0.63 abs., coincid. 0.347, 0.134, 0.087 spect. conv.; 0.342, 0.128, 0.472 spect. conv., coincid.; 0.52, 0.30 abs. Pb; 1.4 coin- cid. abs.; 0.52, 0.13 abs., coin- cid. abs. parent of Ta181m Hf« D I.T., e~(}) 19 sec 0.19(«") abs. Al Hf-n-7 73 Ta17« B K, 7. e~ 8.0 hr 0.12, 0.18, l.2(«~) abs. Al 1.7 abs. Pb Lu-a-3n Ta.-d-p6n Xa177 B K, e~ 2.66 days 0.1 («-) abs. Al Lu-a-2« H(-d-2n Ta.-d-p5n Ta178'177 C K, e", or 0^ 16 days l.lGr?) abs. Al Lu-a- n m-d-2n 240 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 73 Ta'so A K, r, y; /3-(?) 8.2 hr < 0.5(e-?) abs. Ta-n-2n Ta-7-n Ta181n» A I.T., 7, e- 2.0 X 10"6 0.12(e-) 0.128,0.472 Hfim sec; coincid. spect. 0~-decay 2.2 X 10-B abs. conv., sec coincid.; 0.20, 0.49 coincid. abs. Tarn 100 Ta182 A /3-, t, e~ 117 days; 1.0 abs.; 1.22(57%). Ta-M-7 113 days 0.98, 0.32, 0.050; 0.53 spect.; 1,13 (37 %), 0.22(4%), 0.15(2 %) Ta-d-p 0.499 spect.; 1.1 abs. Al, coincid. spect., spect. conv.; 1.6(Z2); 0.23 abs. Pb 'J,a182m E I.T.(?) 0.40 sec Ta-n-7 Ta'82 B P-. 7(?) 16.2 min 0.2 abs. Al Ta-rt-7 74 W179'178 C K, e~, 7 135 min 0.15, 0.45 (e") abs. Al ~0.5, 1.2 abs. Pb Ta-8* A P~, K, 7 50 days; 0.22-0.26; 0.17, 1.05; W-p-n 52 days O.l(e-), 0.22, 0.86(e"?) abs. Al 0.85; 0.17, 1 spect. conv., abs. Pb W-./-H Ke-n-2n Re las 37.07 Re »88 A 0- 92.8 hr; 1.07 abs. Xo 7 W-d-2n m.s. 90 hr Al; 1.05 cl.ch. W-p-n Re-7-M Re-n-7 Re-«-2w Re-d-p Re187m .4 I.T., «-, 7 0.65 X lO^6 sec < 0.13(<--) coincid. abs. \\r187 /3--decay Re187 62.93 0- 4 X 101- yr 0.043 abs. Al Natural source Re 188 A 0~, y, e~ 18.9 hr; 2.05 abs. 0.16, 0.48, Re-n-7 m.s. 18 hr Al; 2.5 cl.ch. (K.U.); 2.5 abs.; 0.12(e-), 0.23 03-) coincid. abs. 0.64, 0.94, 1.43 spect.; 0.7 abs. Pb; 1.39 coin- cid. abs., coincid. Re-d-p U-a-19s54o 76 0si<>4 0.018 Os186 B K, 7 97 days; 94.7 days 0.75 abs. Pb Re-d-2n Os-n-7 Os188 1.59 Os187 1.64 Os188 13.3 Os189 16.1 Os19° 26.4 Osi'i B 0~. 7. tr 15.0 days; 0.142 0.039,0.127 Os-n-7 16.1 days; spect.; spect. U-a-18z51a 17 days < 0.16 abs. Al; conv.; 0.13 abs. 242 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 76 0s>9» 0.35 abs. Al; 0.64 coincid. abs. Pb; 0.129 spect. conv. Os>92 41.0 Os193 A 0", 7 32 hr; 1.5 abs. Al; 1.17 abs. Os-w-7 31.9 hr; 0.95 abs. Pb; 1.58 Os-d-p 30 hr Al; 1.15 abs. Al; 0.14( K-decay Tl 201 D K 75 hr Pb201 K-decay T1202 B K(?), 7. r 11.8 days; 13 days 0.40 Hg-d-2n Tl-n-2n -pi 203 29.1 T1204 B p- 2.7 yr; 3.5 yr 0.80 abs. Al; 0.87 cl.ch.; 0.77 spect. No 7 Tl-n-7 Tl-d-p XI 206 70.9 T1206 A p- 4.23 min 1.65 abs.; 1.77 abs. Al Xo 7 Tl-n-7 Tl-d-p Pb-y-p RaE2io a-decay 246 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Isotope Z A 81 AcC"2°7 ThC"208 fj 209 RaC"2i° 82 Pb"" Pb200 Pb201 Pb203 Pb204 Pt)204lT Pb206 Pb207 Pb208 Pb209 RaD2io Class A A D B Per cent abundance 1.5 23.6 22.6 52.3 Type of radiation P , 7 /»". y K K K, e~, 7 I.T.(?) or K(?)« K-de- cay, par- ent of Tl"» Bi2°o A'-de- cay, par- ent of Tl2°° Tl-rf-4« Tl-d-2n T\-p-n Pb-n-2n Pb™*-n-2n Pb-7-» Tl-d-n Tl-d-3n Pb-n-n Pb-x-rays Bi204 A"-decay Pb-d-p Pb-n-y Bi-n-p p0213 a-decay Natural source, RaC"2'° Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 247 Isotope Z A 82 RaD^io AcB2u ThB2'2 RaB2i< 83 Bii" Bil98 Bii" Bi200 Bi204 Bi208 Bi208 Bi209 RaE-'io Class A E D B B B F A Per cent abundance 100 Type of radiation P . 7 P , 7 Half-life 36.1 min 10.6 hr 26.8 min Energy of radiation, Mev Particles spect. 0.5, 1.40 abs. Al 0.36 spect. 7-rays conv. ; several weak lines of lower energy 0.8 abs. 0.65 spect. a; K( n a; K or; K K, e- 7 K(?), e~, y K (9-(~ 100%); a(10 -4_ 10-5 ft) 2 min 9 min 27 min 62 min; ~ 100 min 12 hr 6.4 days Short 5.0 days 6.2 ion.ch. 5.83 ion.ch.; — 5.5(a) ion.ch. 5.47 ion.ch., abs. mica; ~ 5.5(a) ion.ch. 5.15 ion.ch.; — 5.5(a) ion.ch. 0.2(e-), ~0.8(e-, weak) spect., abs. Al 1.1703") spect.; 4.77(a) calc. 0.74 abs. of e~; 0.93 abs. of e~; 1.1 abs. Pb; —0.4, 1.1 abs. Pb X.j Produced by /3 -decay, RaC':" a-decay, parent of RaE2io Natural source, AcA='5 a-decay, parent of AcC2n Natural source, ThA2ia a-decay, parent of ThC2i2 Natural source, RaA2is a-decay, parent of RaC2i< Pb-d-? Pb-i-? Pb-d-? Pb-d-? PbWi-d-2n Tl-a-3n, parent of PD204m (~4%) Tl-a-3n Pb-d-2n Pb2°7-d-3n po206 A."-decay Bi-n-2n Natural source, RaD2>° /3"-decay, parent of Po210 and Tr-os 248 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 83 RaE2'" Bi-d-p Pb-a-pn Bi-n-y A a(99.68 %) 2.16 min 6.619 Natural AcC'n 7! 0~ (0.32 %), y (a,84 %), 6.273 (a,16%) spect. source, AcB2n 0--decay, parent ot AcC'211 and AcC"2°7 At2" a-decay A a(33.7 %),y; 60.5 min 6.081 Natural ThC2'2 /3"(66.3 %), 7 (a,27 %), 6.042 (a.70 %) (a, others, 3%) spect.; 2.2003") spect. source, ThB2i2 ^"-decay, parent of ThC'212 and ThC"208 At2" a-decay, A /3"; a(2 %), 47 min; ~ 1.3 03") At217 Bi213 (4%) 46 min abs. Al; -1.2 03-); 5.86(a) ion.ch.; 6.0(a) ion.ch. a-decay, parent of p0213 A a (0.04%); 19.7 min 5.505 Natural RaC2i< 0" (99.96%), 7 (a,45 %), 5.444 (a,55 %) spect.; 3.1503") abs. Al, spect. 1.8 source RaB2H /3~-decay, At2" a-decay, parent of RaC'2H and RaC'210 D a; K 40 min 5.56(a) Pb-a-7n 84 Po2"3 ion.ch. D a; K 4 hr 5.35(a) Pb-a-5n p0206 ion.ch. A K (-90%), 9 days 5.2(a) Pb204-a-2«, p0206 7, e~; a (~ 10 %) ion.ch. 0.8 abs. Pb parent of Bi206 A K(~ 100%), 5.7 hr 5.1(a) Pb20«-a-3n po207 7;a(0.01 %) ion.ch. 1.3 abs. Pb B a 3yr 5.14 ion.ch. Pb208-a-2n po208 No 7 Pb2»'-a-3w Bi-d-3n Bi-p-2n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 249 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 84 Po2i° .4 a. 7 138 days; 5.298 0.773 spect. Natural 140 days spect.; 5.303 spect. conv.; 0.8 (weak) abs. Pb source, RaE2i° /3 "-decay Pb-a-2n Bi-d-n At210 K-decay AcC'2ii A a 5 X 10-3 sec 7.434 spect. Natural source, AcC2n /3"-decay At211 A'-decay ThC'212 A a 3.0 X 10"' sec; 3.4 X 10-' sec;, 2.6 X 10-' sec; 3 X 10"' sec 8.776 spect. Natural source, ThC2l2 /9"-decay Em2" /3-decay p0213 A a 4.2 X 10"« sec 8.336 ion. ch.; 8.30 ion.ch. Bi213 0"-decay, parent of Pb209 Em!" a-decay RaC'2" A a 1.5 X 10-1 sec; 1.55 X 10"* sec; 1.4 X 10-« sec 7.680 spect. Natural source, RaC2^ 0--decay, parent of RaD'-'» Em2i8 a-decay AcA21& A a(~ 100%); 0-(5 X io-«%) 1.83 X 10-3 sec 7.365 spect. Natural source, An2i» a-decay, parent of AcB2n and At21* ThA2>« A a(~ 100%); 0"(O.O14 % | 0.158 sec 6.774(a) spect. Natural source, Th220 a-decay, parent of ThB2'2 and At2" RaA2'8 A a(99.96<"c); 0-(O.O4 %) 3.05 min 5.998(a) spect. Natural source, Rn222 a-decay, parent of RaB2" and At2" 250 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Class Per cent Type of Half-life Produced Z A abundance radiation by Particles 7-rays 85 At*" D «; K(?) 1.7 hf 5.76(a) ion. ch. Bi-a-6n At208 D «; K(?) 4.5 hr 5.66(a) ion. ch. Bi-a-4n At210 A K, y 8.3 hr 1.0 Bi-a-3«, parent of po210 At211 A a(40%); K(60%) 7.5 hr 5.89(a) ion. ch.; 5.94 (a) abs. Bi-a-2n Th-a 25a7z U-a-31a9z At212 A a 0.25 sec Bi-a-w At214 B a Very short 8.78 ion.ch. Fr2>8 a-decay At21* A a ~ 10-« sec; short 8.00ion.ch.; 8.4 ion.ch. Natural source AcA2'6 0~-decay, parent of AcC2" pr219 a_-decay, parent of AcC2" At21« A a 3 X 10-" sec; ~ 10-3 sec; short ( < 54 sec) 7.79 ion.ch.; 7.64 ion. ch. Natural source, ThA2" 0"-decay, parent of ThC2'2 Pr220 a-decay, parent of ThC212 At217 A a 0.018 sec; 0.021 sec 7.02 ion.ch.; 7.00 ion. ch. pr221 a-decay, parent of Bi21» At218 F a Several sec(?) 6.72 ion.ch. Natural source, RaA2'8 £"-decay, parent of RaC2" 86 Era'" A a Very short 8.07 ion.ch. Ra220 a-decay, parent of ThC'212 Em2" A a ~1 X 10-3 sec 7.74 ion.ch. Ra221 a-decay, parent of P0213 Em2'8 A a 0.019 sec 7.12 ion.ch.; 7.1 ion.ch. Ra222 a-decay, parent of RaC'2'" , Sec. 7.121 SEABORG AND PERLMAN TABLE OF ISOTOPES 251 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z A by Particles 7-rays 86 An*" A a 3.92 sec 6.824(82%) (others 18%) spect. Natural source, ACX223 a-decay, parent of AcA2is Tn"o A a 54.5 sec 6.282 spect. Natural source, ThX224 a-decay, parent of ThA2i« Rn222 A a 3.825 days * 5.486 spect. Natural source, Ra226 a-decay, parent of RaA2i« 87 Fr2is B a Very short 7.85 ion.ch. Ac222 a-decay, parent of At2" prju A a ~ 0.02 sec 7.30 ion.ch. Ac=23 a-decay, parent of At2" pr220 A a 27.5 sec; ~ 30 sec 6.69 ion.ch. Ac224 a-decay, parent of At21" pr22I A a 4.8 min; 5 min 6.30 ion.ch. AC225 a-decay, parent of At!" Pr223 A 0-. 7 21 min 1.20 cl.ch. 0.090 abs. Natural (AcK) Al source, Ac227 a-decay, parent of AcX223 88 Ra22o A a Short 7.49 ion.ch. Th221 a-decay, parent of Em2i» Ra22i A a 31 sec 6.71 ion.ch. Th225 a-decay, parent of Em!" Ra222 A a 38 sec 6.51 ion.ch.; 6.5 ion.ch. Th22« a-decay, parent of Em2!8 252 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 88 ACX223 A a, y 11.2 days 5.717(55%) 5.606 (36 %), (others 9 %) spect. Natural source, RdAc»7 a-decay, AcK»3 /9~-decay, Ac 223 K-decay, parent of An2i» U-a-19a6z U-rf-17a5z ThX22« A a 3.64 days 5.681 spect.; 5.66 ion. ch. Natural source, RdTh228 a-decay, parent of Xh220 U-a-18a6z U-d-16a5z Ac"< K-decay Ra225 A 0" 14.8 days; 14 days ~ 0.2 abs. Al; < 0.05 abs. Th22« a-decay, parent of Ac 226 Ra22« A a, y 1622 yr; 1631 yr; 1590 yr 4.791 spect. 0.19 Natural source, Io230 a-decay, parent of Rn222 Ra22' A 0" Ra.-n-y, parent of AC22V MsThi228 A P- 6.7 yr < 0.015 cl. ch.; 0.053 spect., abs. Al Natural source, Th232 a-decay, parent of MsTh2228 89 AC222 B a Short 6.96 ion.ch. Pa22 0.3 U-K-7, 23 min; Al; 1.2 (weak) parent of \ 23.2 min; abs. Al; abs. Pb; NP23S 23.54 min 1.12, 2.06 (weak) spect. 0.073, 0.92 spect. conv., abs. Pb V-d-p 93 Np2" A a, K 53 min 6.2(a) ion. ch. V-d-9n, parent of Pa227 U236.J.6„ Vn-™-d-itl Np234 B K, y 4.40 days; 4.4 days 1.9 abs. Pb Pu23< A-de- cay(?) U233.^.M U"*-d-3n Pa-a-w XJ233.a.p2n U235-a-£4n \jm-p-2n Np»« B K;a 435 days; 5.06(a) No t(?) V^-d-2n (~0.1 %) 400 days ion.ch. V^-a-pn V™>-a-p3n Np!" A 0-,y 22 hr 0.5 abs. Be Parent of pu236 \Jw-d-n V-d-4n U233-a-/> \Jni-a-p2n Np-d-t Xp-a-att NP237 A a 2.20 X 10« yr; 3 x 10« yr 4.77 ion.ch.; 4.75 abs. air; 4.73 abs. Al; IJ237 /3"-decay, parent of Pa233 258 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 Energy of radiation, Mev Isotope Per cent Type of Half-life Produced Z A abundance radiation Particles 7-rays by 93 Np2" 4.72 abs. mica Np238 A P-, V, e~ 2.10; 2.0 0.22, 1.39 1.2, 0.075 Parent of days abs. Al; 1.0 abs. Al abs. Pb, abs. of e~; 1.1 abs. Pb PU238 U"8_(f-2n V-d-2n Am2« a-decay U-a-p3n V-a-p Np-n-7 Np-d-p Np239 A &-, y, e~ 2.33 days; 0.68, 0.33, 0.057, XJ23S 2.3 days; 0.090 abs.; 0.061, /3~-decay, 2.35 days 0.47 abs.; 0.14, 0.40, 0.63 abs. Al; 0.78 abs. Al; 0.288. 0.403, 0.673, 1.179 spect. 0.067, 0.206, 0.227, 0.275 spect. conv. ; 0.2094, 0.2280, 0.2774, numerous softer 7's spect. conv.; 0.22, 0.27 spect. conv., spect. parent of PU23« V-d-n U-a-p2n 94 Pu232 B a 22 min 6.6 ion.ch. Tj236-a-7n, parent of TJ228 pu234 A a;K 8 hr; 8.5 hr 6.2 ion.ch.; 6.0 ion.ch. U233.a-3n, parent of TJ230 and Np234(?) PU23« A a 2.7 yr 5.75 ion.ch.; 5.7 ion.ch. Np23« 0~-decay Cm"o a-decay, parent of TJ232 U235-a-3rt U233.a.n U-a-6n Np-a-/)4n Np-d-3n PU237 B K 40 days No y U236-a-2n U-a-5n Np-d-2n Sec. 7.12] SEABORG AND PERLMAN TABLE OF ISOTOPES 259 Energy of radiation, Mev Isotope Class Per cent abundance Type of radiation Half-life Produced Z .4 by Particles 7-rays 94 Pu238 A a 92 yr; 89 yr; 40 yr 5.51 abs. air; 5.5 abs. air, Al; 5.4 abs. Al; 5.493 ion.ch. Np238 /S~-decay Cm242 a-decay yp-d-n V-a-4n U235.a.„ Pu»« A a, y, e~ 2.411 X 10« 5.15 abs. 0.42, 0.2 \p239 yr calor.; air; 5.1 (weak) /S-decay 2.44 X 104 abs. air; abs. Pb; Natural yr 5.16 cl.ch.; 5.140 ion. ch.; 5.159 ion.ch. 0.05, 0.3 (weak) abs. Pb, Al source U-a-3n pu240 A a ~ 6000 yr yield 5.1 ion.ch. U-a-2n PU241 A p-;<* ~10yr 0.01-0.02 U-a-n, m.s. ( ~ .002 % ) yield OS-) abs. hydro- carbon; 5.0(a) calc. parent of Am24i and TJ237 95 Am238 D K(?) 1.5 hr Pu-rf-3n Am239 B K(~100%), 12 hr 5.77(a) 0.285 abs. Pu-d-2n e~. y; ion.ch. Pb. abs. Pu-p-n a(~ 0.1 %), of e~ Xp-a-2n Am240 B K, 7. e- 50 hr; 53 hr 1.3 abs. Pb, abs. of e~ Pu-d-n X p-a- n Am24i A «. 7 490 yr; 5.48 ion.ch.; 0.062 abs. PU241 510 yr 5.45 ion. ch. Pb 0 "-decay Am242"> A 0- 16 hr; 17 hr 0.8 abs. Al Am-n-7. parent of Cm242 Am2i2 A a(~ 0.2 %), ~ 400 yr ~0.5 OS-) abs. Al; 5.2(a) calc. Am-n-7, parent of Cm242 ancj Np238 96 Cm238 B a ~ 2.5 hr 6.50 ion.ch. Pu-a-5n Cm2gKa3(d — d0)g where tj = viscosity of medium a = radius of drop v = velocity of drop d = density of drop d0 = density of medium g = acceleration due to gravity In order to obtain accurate and reproducible determinations of the density from the rate of fall, it is essential to choose a medium, drop size, and operat- ing temperature that will give falling times short enough for convenience but with sufficient spread to give the required sensitivity over the range of densities that will be encountered and to keep these factors constant. The originators of this method used a mixture of bromobenzene and xylene as the medium [11,12]. By varying the proportions of these substances one can obtain mixtures having a wide range of densities. The differential vaporization that occurs, however, causes the composition of the mixture to change from day to day. Keston et al. [14] introduced the use of 0-fluoro- toluene, which has a density convenient for measuring deuterium oxide con- Sec. 8.7] INDIRECT METHODS FOR MEASURING DEUTERIUM 273 centrations of 0 to 3 per cent at 26.8°C and which avoids the differential vaporization of a binary system. w-Fluorotoluene may be used for the same concentration range at 19.3°C. These toluenes have the further advantage of lower viscosity and therefore greater sensitivity. They may be obtained from the Eastman Kodak Company or synthesized by a procedure analogous to that for fluorobenzene [49]. For higher concentrations of deuterium oxide, o-fluorotoluene is unsatis- factory because the precision of the method falls off rapidly as the difference between the density of the water and the reference liquid increases. For samples containing 10 to 40 per cent deuter um oxide, solutions of phenan- threne in a-methylnaphtha ene have been shown to be superior reference liquids [50]. Neither of these components is particularly volatile. The exact viscosity of o-fluorotoluene has not been published, but it is estimated that that of a-methylnaphthalene is about three times as large; so for the same density difference, the drops fall more slowly in the latter medium. The dimensions of the tube containing the medium are not critical except that the inside diameter should be greater than three times the diameter of the drop to avoid wall effects. The fiducial marks should be as far apart as possible (about 20 cm) to provide maximum sensitivity and the best average rate of fall. Another 20 cm should be allowed above the top mark to ensure thermal equilibrium between the drop and the medium by the time the drop reaches the first mark, and about 10 cm should be allowed below the lower mark to avoid end effects. The size of the drop is controlled through the use of a mechanical micro- pipette. The size is not critical and may be 5 to 45 mm3 [54], but it is impera- tive that it be uniform in any set of determinations, including the associated calibration. It is desirable to use as small a drop as possible to minimize the quantity of water needed for an analysis, but the sensitivity of the method increases with the square of the radius [54]. Variations in drop size introduce a percentage error in velocity which is two-thirds the percentage error in volume. For falling velocities of the order of 1 cm per sec, the variation in drop size must be less than 0.1 per cent. The designs for several satisfactory micropipettes have been published [14,55-58]. The accompanying drawing (Fig. 58) illustrates the one used by the authors [59]. It is somewhat less bulky than other published instru- ments but provides the required precision. The barrel K is made from a 34-cc glass tuberculin syringe and is joined to the capillary with cobalt glass. Mercury is displaced by the advancement of a piece of K6_in- diameter drill rod driven by a micrometer head. A mechanical stop A assures uniformity of the angle through which the micrometer is turned. With the sample in the capillary, the tip is lowered about 1 cm below the surface of the medium and a drop formed. The drop is released by raising the pipette slowly and 274 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 8 allowing the surface tension of the medium to pull the drop from the capillary tip. The relative density of water and the medium vary so greatly with tem- perature that the temperature must be kept constant to ±0.001°C. This is accomplished by mounting the tube in a well-stirred water bath of about 100 liters capacity and carefully controlling the bath temperature. Some form of automatic temperature regula- tion is required. Baths with the required control are available com- mercially. Many designs for thermo- stats have been published [62-68]. If the bath temperature is to be above room temperature, a temperature-sensitive element such as a volume of mercury with a large surface-volume ratio or a bimetallic strip may be used to control the current of an immersion heater through a relay or thyraton circuit. In a thermostat that uses a relay, the dis- continuous input is the fundamental obstacle to the attainment of perfect constancy of temperature. Amplifier devices may be used to give a continuous but variable input, but these also have a finite sensitivity. The Guoy principle, applying a vertical oscillating motion to the contacting wire of an expansion thermoregulator, provides an intermedi- ate type of control between simple on- and-off control and continuous control and has been used to hold the tempera- ture of a 100-liter water bath constant within + 0.0002°C for several hours [66]. There is some advantage in having the bath temperature below room temperature [56]. This may be effected with the same kind of thermoregulators, but by controlling the flow of cold water through the bath instead of controlling a heater. Many difficulties are avoided by having the apparatus in a constant-temperature room and oper- ating near room temperature. The multiple-enclosure principle of Tian may also be used to decrease the effects of ambient variations [68,69]. Under the conditions used in this method, the rate of fall does not follow Stokes' law perfectly, and it is necessary to establish a calibration curve by Fig. 58. Micropipette. A, stop; B, bracket; C, pinion; D, stand; E, micro- meter; F, plunger (}4.6 m- diameter drill rod); G, packing; H, rubber washer; /, lead washer; A", barrel; L, capillary. Sec. 8.8] INDIRECT METHODS FOR MEASURING DEUTERIUM 275 V7777777? ^ V77777777, plotting the densities of several mixtures of known density against the reciprocals of their falling times. The deviation from Stokes' law may be calculated from the differences between the reciprocals of the times of fall of the known mixtures and that of pure water [54]. Depending upon the range of concentrations being determined, this method gives a precision in density of about 1 to 4 parts in 106, corresponding to 0.001 to 0.004 per cent of deuterium. The errors introduced in the combustion and purification processes are larger and may raise the maximum over-all error to 0.02 per cent of deuterium. 8.8. Diffusion Gradient. This method is similar to the falling-drop method in that the density of a drop of the liquid to be tested is determined by introducing the drop into another liquid with which it is immiscible. It differs chiefly in that the reference liquid is so prepared that it presents a linear gradient of density and the drop falls only to an equilibrium position at which the specific gravity of the surrounding medium is equal to its own. The density of the drop is found by comparing the equilibrium position of the unknown sample with the posi- tions of other drops of known density. This method offers the advantage of avoiding the errors due to convection currents inherent in the falling-drop method [15-17,70]. Figure 59 shows the type of tube used in this method [15]. The tube is mounted in a vertical position to the depth indicated by A in a thermo- stated water bath. A gradient suitable for determination of the deuterium in deuterium oxide-water mixtures containing between 0 and 10 per cent deuterium oxide may be prepared from two bromobenzene-kerosene mixtures, the lighter one having a density of about 0.99 and the heavier a density of about 1.02 [70]. The tube is placed in the thermostat (regulation to +0.01 is sufficient), and the heavier mixture is poured in up to the middle of the tube connecting the two bulbs. Next the lighter mixture is brought to the bath temperature and added cautiously through a funnel with a filter up to the level shown at B in Fig. 59. In order to obtain a uniform distribution of the two mixtures in Fig. 59. gradient. Tube for diffusion 276 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 8 the connecting tube, a stirrer is lowered to the center of the tube and slowly pulled up and down in the tube for about ten cycles. After standing about 48 hr, the gradient is sufficiently linear to be used in carrying out measure- ments. The early papers on this method [15] recommended saturating the kerosene-bromobenzene mixture with water at a suitable vapor pressure, but in deuterium measurements this is undesirable because of exchange. Although it is true that if the gradient is used exclusively for deuterium analysis the various levels of the gradient do tend to become saturated with the proper deuterium oxide-water ratios, exchange may still occur while the drop is settling, and it is best to keep the gradient unsaturated. The tube is calibrated by determining the equilibrium positions of drops of known density. In use, several drops covering the density range in which the experimental drops are expected to lie are introduced in the left side of the tube and an experimental drop on the right side. After 15 min the relative positions are determined with the aid of a cathetometer. As in the falling- drop method, the size of the drops is not critical within reasonable limits (about 0.1 to 10 mm3), but those used must be uniform. The pipette can be somewhat simpler than the type needed for the falling drop, the micro- constriction type being satisfactory [71]. As described above, this method gives a precision of only +0.1 per cent of deuterium, but by simultaneously increasing the drop size and decreasing the range of the gradient (using mixtures of densities 0.995 and 1.005, for exam- ple), a precision of 5 parts in 106 can be achieved [72]. REFERENCES FOR CHAP. 8 1. Washburn, E. W., and E. R. Smith: U.S. Nat. Bur. Standards J. Research, 12, 305 (1934). 2. Smith, E. R., and M. Wojciechowski: Rocznicki Chcm., 16, 104 (1936). 3. Lamb, A. B., and R. E. Lee: /. Am. Chcm. Soc, 35, 1666 (1931). 4. Richards, T. W., and J. W. Shipley: /. Am. Chcm. Soc, 34, 599 (1912). 5. Richards, T. \X ., and J. W. Shipley: /. Am. Chcm. Soc, 36, 1 (1914). 6. Richards, T. W., and G. W. Harris: /. Am. Chcm. Soc, 38, 1000 (1916). 7. Gilfillan, E. S., and M. Polanyi: Z. physik. Chcm., A166, 254 (1933). 8. Gilfillan, E. S.: /. Am. Chcm. Soc, 56, 406 (1934). 9. Greene, C. H, and R. J. Voskuyl: /. Am. Chcm. Soc, 56, 1649 (1934). 10. Greene, C. H, and R. J. Voskuyl: /. Am. Chcm. Soc, 61, 1342 (1939). 11. Barbour, H. G., and W. F. Hamilton: Am. J. Physiol., 69, 654 (1924). 12. Barbour, H. G., and W. F. Hamilton: /. Biol. Chcm., 69, 625 (1926). 13. Rittenberg, D., and R. Schoenheimer: /. Biol. Chcm., Ill, 169 (1935). 14. Keston, A. S., D. Rittenberg, and R. Schoenheimer: /. Biol. Chcm., 122, 227 (1937). 15. Linderstrom-Lang, K., and H. Lanz Jr.: Compt. rend. trav. lab. Carlsberg, ser chim., 21, 315 (1938). 16. Linderstrom-Lang, K., O. Jacobsen, and G. Johansen: Compt. rend. trav. lab. Carlsberg, ser. chim., 23, 17 (1938). 17. Lowry, O. H, and T. H. Hunter: /. Biol. Chcm., 159, 465 (1945). Chap. 8] INDIRECT METHODS FOR MEASURING DEUTERIUM 277 18. Lewis, G. N., and D. B. Luten Jr.: J. Am, Chan. Soc, 65, 5061 (1933). 19. Crist, R. H., G. M. Murphy, and H. C. Urey: J. Chan. Phys., 2, 112 (1934). 20. Urey, H. C, and G. K. Teal: Rev. Mod. Phys., 7, 34 (1935). 21. Clemo, G. R., and G. A. Swan: J. Chan. Soc, 1942, 370 (1942). 22. Farkas, A.: "Light and Heavy Hydrogen," Cambridge University Press, London, 1935. 23. Sachsse, H., and K. Bratzler: Z. physik. Chem., A171, 331 (1934). 24. Oliphant, M. L. E., B. B. Kinsey, and Lord Rutherford: Proc. Roy. Soc. (London . A141, 22 (1933). 25. Topley, B., and W. P. K. Wynne-Jones: Nature, 134, 574 (1934). 26. Lewis, G. N., and R. T. Macdonald: J. Am. Chem. Soc, 55, 4730 (1933). 27. LaMer, V. K., W. C. Eichelberger, and H. C. Urey: J . Am. Chan. Soc, 56, 248 (1934). 28. Kistiakowsky, G. B., and R. I. Tichenor: /. Am. Chan. Soc, 64, 2302 (1942). 29. Dole, M., and R. L. Slobod: /. Am. Chan. Soc, 62, 471 (1940). 30. Stokland, K., E. Ronaess, and L. Tronstad: Trans. Faraday Soc, 35, 312 (1939). 31. Swift, E., J. Am, Chem. Soc, 61, 198 (1939). 32. Johnston, H. L.: J. Am, Chem. Soc, 61, 878 (1939). 33. Longsworth, L. G.: /. Am. Chem. Soc, 59, 1483 (1937). 34. Swift, E.: J. Am. Chem. Soc, 61, 1293 (1939). 35. Voskuyl, R. J.: Thesis, Harvard University, 1938. 36. Emulus, H. J., ct al,: J. Chem, Soc, 1934, 1207 (1934). 37. Dorsey, N. E.: "Properties of Ordinary Water-substance," Reinhold Publishing Corporation, New York, 1940. 38. Dole, M.: /. Am, Chem. Soc, 57, 2731 (1935). 39. Dole, M.: /. Chem. Phys., 4, 268 (1935). 40. Dole, M.: /. Am. Chem, Soc, 58, 580 (1936). 41. Swartout, J. A., and M. Dole: /. Am, Chan, Soc, 61, 2025 (1939). 42. Dole, M., and G. Jenks: Science, 100, 409 (1944). 43. Dole, M., R. C. Hawkins, and H. A. Barker: J. Am. Chem, Soc, 69, 226 (1947). 44. Chang, Tsing Tien, and Jen Yuan Chien: /. Am. Chem. Soc, 63, 1709 (1941). 45. Adams, L. H.: J. Am. Chem. Soc, 37, 1181 (1915). 46. Bauer, N.: in "Physical Methods of Organic Chemistry," A. Weissberger, ed., p. 719, Interscience Publishers, Inc., New York, 1945. 47. Crist, R. H., G. M. Murphy, and H. C. Urey: J. Chem. Phys., 2, 112 (1934). 48. Keston, A. S.: in "Medical Physics," Otto Glasser, ed., p. 661, Year Book Publishers, Inc., Chicago, 1944. 49. Blatt, A. H., ed.: "Organic Syntheses," Collective Volume II, p. 295, John Wiley & Sons, Inc., New York, 1943. 50. Frilette, V. J., and J. Hanle: Anal. Chem,, 19, 984 (1947). 51. Gabbard, J. L., and M. Dole: /. Am. Chem. Soc, 59, 181 (1937). 52. Hall, N. F., and T. O. Jones: /. Am, Chem. Soc, 58, 1915 (1936). 53. Birge, R. T.: Rev. Mod. Phys., 13, 233 (1941). 54. Cohn, M.: in "Preparation and Measurement of Isotopic Tracers," Edwards Bros, Inc., Ann Arbor, Mich., 1946. 55. Hochberg, S., and V. K. LaMer: hid. Eng. Chem., Anal. Ed., 9, 291 (1937). 56. Fenger-Ericksen, K., A. Krogh, and H. Ussing: Biochem. J ., 30, 1264 (1936). 57. Rosebury, F., and W. E. Van Heyningen: hid. Eng. Chan,, Anal, Ed., 14, 363 (1942). 58. Fetcher, E. S., Jr.: hid. Eng. Chem., Anal. Ed., 16, 412 (1944). 59. Robertson, J. S., and W. Siri: To be published. 278 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 8 60. Cross, P. C, and P. A. Leighton: /. Chem. Phys., 4, 28 (1938). 61. Farkas, A., and H. W. Melville: "Experimental Methods in Gas Reactions," The Macmillan Company, New York, 1939. 62. Harkins, W. D., and F. E. Brown: /. Am. Chan. Soc, 38, 246 (1916). 63. Beattie, J. A.: Rev. Sci. Instruments, 2, 458 (1931). 64. Roebuck, J. R. : Rev. Sci. Instruments, 3, 93 (1932). 65. La Pierre, C. W.: Gen. Elec. Rev., 35, 403 (1932). 66. Weber, R. L.: "Temperature Measurement and Control," The Blakiston Company, Philadelphia, 1941. 67. American Institute of Physics: "Temperature," Reinhold Publishing Corporation, New York, 1941. 68. Swietoslawski, W. : "Microcalorimetry," Reinhold Publishing Corporation, New York, 1946. 69. Tian, A.: /. Chem. Phys., 20, 132 (1923). 70. Anfinson, Chris: in "Preparation and Measurement of Isotropic Tracers," pp. 61-65, Edwards Bros., Inc., Ann Arbor, 1946. 71. Levy, M.: Compt. rend. trav. lab. Carlsberg, sir. chim., 21, 101 (1936). 72. Ussing, H.: Personal communication. 73. Ussing, H. and A. Wernstedt: Skand. Arch. Physiol., 83, 169 (1940). 74. Lifson, N., V. Lorber, and E. J. Hill: J.Biol. Chem., 158, 219 (1945). CHAPTER 9 MASS SPECTROGRAPHS 9.1. Aston Mass Spectrograph. An arrangement of electric and magnetic fields devised and perfected by Aston [1,2] was the first employed for exten- sive and accurate measurements of isotope masses and relative abundances. A highly collimated ion beam emerging from the slits Si and So, as shown in Fig. 60. Aston mass spectrograph. Fig. 60, passes through a strong uniform electric field between two parallel electrodes which deflects the ions by a small angle v m where / = length of path between plates V = deflecting voltage on plates v = initial ion velocity e = ion charge m = ion mass The defining vane F then permits only ions within a small prescribed range of velocities to enter the uniform magnetic field H. The angular deflection in the magnetic field is given by the expression

move on circular trajectories with radii of curvature given by Sec. 9.6] MASS SPECTROGRAPHS 285 1 + _ sin — -=. + j8 H cos — ^ J cm 2 a/2 a V2/ The relation between the source distance / and the local plane distance L is IL - (I + L) JL Cos * - £ = 0 and the velocity dispersion in the focal plane in terms of linear units is d = {ia(l — cos — -p. -\ — \/~2 sin — ^= ] cm-volts To achieve complete velocity focusing, the velocity dispersion of the magnetic field must compensate exactly for that produced by the electro- static analyzer. Since the edge of the magnetic field coincides with the focal plane of the analyzer and pi = mvi/eH, this condition is satisfied when d = 2(3p0. This condition is exactly met fpr only one radius of curvature in the magnetic field, and all other radii focus imperfectly at the 180-deg position and hence exhibit progressively wider images with greater distance from the focused value of e/tn. The widths of these foci are given by the expression d(po — pi) 8 = Po It is apparent that when a limiting resolution is required the final focal image width can be made smaller by reducing the dispersion d with a defining vane placed behind the focal plane of the electrostater analyzer, i.e., in the plane AB, Fig. 64. 9.6. Bainbridge -Jordan Double -focusing Mass Spectrograph. Direc- tional and velocity focusing is accomplished in a mass spectroscope developed by Bainbridge and Jordan [7], first by deflection of ions in an electrostatic analyzing field through an angle of ir/y/l, and then in a uniform magnetic field through a mean angle of x/3 radians. With the geometrical arrange- ment used (Fig. 65) the small dispersion in velocity accompanying directional focusing for ions of a particular value of m/e is canceled by the velocity focusing in the magnetic field. The focal plane over a large mass range is not strictly flat, but over a considerable range about the exactly focused value of m[e it is sufficiently flat to allow accurate comparison of both mass and abundance. A considerable advantage inherent in this design of spec- trograph is derived from the accurately linear mass scale for a broad range about the exactly focused m/e. In some instances this is highly desirable since it greatly facilitates accurate comparison of masses. The relation between the voltage applied across the condenser plates of 286 JSOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 the electrostatic analyzer and the accelerating voltage for any ion that traverses the central path between the plates is expressed by Ve = 2F0log where Ve = analyzer voltage V ' o = accelerating voltage or energy of ion in central path r\ = radius of inner condenser plate ri = radius of outer condenser plate In traversing the electrostatic analyzer, ions of energy V, differing slightly from V0, are focused into an energy spectrum in the focal plane of the analyzer 5^~\" Fig. 65. Bainbridge-Jordan double-focusing mass spectrograph. [A'. T. Bainbridgc and E. B. Jordan, Phys. Rev., 50, 282 (1936).] and again diverge before entering the magnetic field. The linear displace- ment of an ion from the central path in the focal plane of the analyzer for an ion of energy V, to a close approximation, is given by d = 2ReB where Re = radius of central path through electrostatic analyzer and V0- V B = V0 Only those ions in the central path with a particular value of m0/e are deflected by the magnetic field through exactly 60 deg when the magnetic field satisfies the relation H Rm\ 2m„Vn where Rm = radius of curvature for the ion m0/e traversing the central path through the magnetic field Under these conditions the ion enters and leaves normal to the edge of the magnetic field, and ions of the same m0/e but with different energies are Sec. 9.7] MASS SPECTROGRAPHS 287 deflected through a smaller or greater angle to be focused at a distance \/l Rm along the central path from the edge of the magnetic field. The displacement of the focus from the apex of the magnetic field along the line AO for such ions is D = IRmo. Actually, only those ions of mass m0 for which Re = Rm and which enter and leave the magnetic field normal to its edge are focused exactly on this line. The error in the focus for other masses however is small for a considerable range in mass about m0. The width of the final focus of mass m0 for which the conditions above hold is 8 = Rma* where a = one-half angular divergence of beam entering electric field from the source, or sum of slit widths 2 X slit separation The maximum geometrical resolving power for ions on the central path, defined as the mass separation equivalent to the width of the focal image (complete separation), can be calculated from m0 Rm Am0 ARm The resolving power falls off slowly on either side of m0 owing to the increasing image width from imperfect focusing. 9.7. Trochoidal-trajectory Mass Spectrograph. A combination of crossed uniform electric and magnetic fields has been proposed which accomplishes complete focusing of ion beams with large initial angular divergence and energy spread [8]. Ions injected into a region containing a uniform electric and magnetic field arranged at right angles are known to follow trochoidal trajectories that converge to a single point for any one value of m/e (see Fig. 66). The shapes of the ion trajectories in terms of field strengths and initial conditions is given in rectangular coordinates by the equations x = a(\p — yp0) + p(sin ^„ — sin \p) y = L — p cos yp = p(cos <^0 — cos \J/) Ec- m , _ lirEc-m 0 = lira = — jjr, — Since a and b are proportional to m/e and not the initial angle or energy, all ions of the same m/e converge to a point or a line image located at a distance of x = b from the source. It also follows from this that the mass scale is strictly linear over the whole mass range. The secondary generating 288 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 radius p is given by P = where y = eH mc l/2 &c* 2Ec Y Y\0 + W ~~H Vo C°S 6) v0 = initial velocity of ion The resolving power for this type of instrument is given by m b Am Ab Ions of different m/e can be focused on a single collecting electrode by altering the accelerating potential V0 and the deflecting potential V (= Ed CURTATE CYCLOID ION PATH PROTATE CYCLOID ION PATH Fig. 66. Trochoidal ion trajectories in crossed electric and magnetic fields. [W. Bleakney and J. A. Hippie, Phys. Rev., 63, 521 (1938).] where d is separation of the condenser plates) in direct proportion, i.e., CV = V0 where the constant C depends upon the design parameters of the instrument. When this condition is fulfilled, ions of any m/e traverse the same path for the proper values of V and V0. If the design parameters are chosen to make p < a, the ion trajectory is a curtate cycloid. If p > a, the ion trajectory is that of a protate cycloid (see Fig. 66). 9.8. Ion Sources. The ion sources used in mass spectrographs are either high-voltage discharges or bombardment by low-energy electrons emitted from a hot filament. Both have been widely used, and the choice depends to some extent on the application intended for the mass spectrograph. There is some advantage in using the spark-discharge source for solid mate- rials since the electrodes can be coated with or made of the sample material and little difficulty is encountered in producing ions. Furthermore, the construction and operation of this kind of source is usually simpler than hot- filament sources. On the other hand, filament sources regulated with appropriate circuits give exceedingly stable and reproducible operation over Sec. 9.8] MASS SPECTROGRAPHS 289 a long period of time and probably produce ions with smaller spread in energy. Particular advantage is gained for the analysis of gases and vapors with these sources since very small quantities need be used for complete quantitative analyses. a. High-voltage Discharge Source. Ions may be produced in high-voltage sources either by spark discharge in a vacuum chamber or by a steady dis- charge in an atmosphere of gas at low pressure. The first type of discharge is frequently convenient for the direct ionization of metallic substances. It avoids, among other things, the use of a discharge gas which would produce a spectrum of its own. The sample material can be used as the high-voltage electrode, or when this is impracticable, it can be inserted into a hollow electrode in some usable form, i.e., as a stable salt, an alloy, or a mixture. Suitable high-voltage electrode materials include any of the metals that are stable in a vacuum at elevated temperatures. The material used, how- ever, should not produce ions with values of m/e near similar values expected from the sample unless they can be used for a comparison spectrum. The discharge takes place in a small gap between the two electrodes which are connected to a tesla coil or some similar high-voltage spark device. Some of the ions that are formed drift to the edge of the discharge in the gap where they then fall through an accelerating potential maintained between the dis- charge electrodes and a third electrode. This voltage determines the final energy of the ions passing through the analyzing fields. The second type of high-voltage discharge takes place between a grounded cathode and a high-voltage anode in an atmosphere of gas at low pressure. Satisfactory operation is usually obtained with a potential of approximately 15,000 volts. Unless the gas itself is to be measured, either neon or argon is usually used. Ions formed in the discharge column are accelerated toward the cathode in the electric field of that part of the discharge known as the cathode fall which extends nearly to the anode or to within a distance from it determined by the space-charge sheath thickness. A portion of the ion beam emerges from the discharge tube through a slot in the cathode and is then collimated by an appropriate arrangement of slits, as shown in Fig. 68. Solid substances that are to be analyzed may be placed on or near the cathode, or in the case of some metallic elements, the cathode can be made wholly of the sample material. Otherwise it is used in the form of a suitable compound, such as a halide salt if it has a vapor pressure greater than 10_; mm Hg at several hundred degrees centigrade. In general, the combined effects of heating and sputtering by positive ions striking the cathode will ensure an ample concentration of sample material in the discharge for the production of ions. b. Sources with Electron Emission from a Filament. This type of source is the most widely used at the present time because of its ease of control. 290 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 stability, adaptability to routine analyses of gases and vapors, and the small energy spread of the ions it produces. The general scheme of this type of source is illustrated by the example shown in Fig. 69. The sample material is admitted to a small closed ioniza- FiG. 67. Spark discharge ion source. Ions formed in the discharge between the end of the anode A and the wall of the cathode C are accelerated and focused through slit S. [A . E. Stow and W. Rail, Atomic Energy Commission Report, MDDC-45 (1946).] tion chamber whose dimensions are of the order of a centimeter. Ionization is produced by a stream of electrons which enter through a collimating slot at one end and traverse the chamber to be collected at the opposite side by an anode. A fraction of the ions that are produced diffuse out through a slit Fig. 68. High-voltage gas-discharge ion source. Ions are formed in the gas discharge maintained between the anode A and hollow cathode C. Those ions passing through the cathode are then collimated by slit 5 before entering the analyzing fields. Material to be analyzed may be introduced as a gas, or if solid, may be deposited on the cathode. [A'. T. Bainbridge and E. B. Jordan, Phys. Rev., 50, 282 (1936).] in one side of the chamber and are then accelerated in an electric field main- tained by an appropriate slit or electrode system. The filament may be made of tungsten or tantalum and used in the form of a helix or a short thin ribbon, usually about 0.001 in. thick. Heating current for filament cross sections commonly used is about 5 amp, alternating Sec. 9.8] MASS SPECTROGRAPHS 291 current or direct current. Collimation of the electron stream is obtained with the aid of small electro- or permanent magnets which provide a field of at least several hundred gauss in the region of the ionization chamber. Electrons emitted from the filament move freely along the lines of force but have low mobility in a transverse direction. On the other hand, ions, because of their greater mass, can cross the field with relative ease when leaving the chamber. Electrons, therefore, leave the filament only in the direction of ^ 0, -f IT Fig. 69. Simple ion source. Gas introduced through the tube G is ionized in the chamber / by the stream of electrons (vertical broken line) emitted from the filament F maintained at 75 to 150 volts negative with respect to /. The electron stream is defined by the magnetic field // and collimating slot C. Ions that diffuse to the exit slit are accelerated and focused by slits S. [W. Siri, Rev. Sci. Instruments, 18, 540 (1947).] the anode or electron catcher to which they are accelerated by a potential of about 100 volts. In nearly all cases, the total electron emission is less than 1 ma. Of the fraction of electrons that enter the chamber through the collimating slot, a large proportion either is lost to the walls by repeated collisions with gas molecules and ions or is captured by ions. The remaining electrons pass through the chamber to be collected at the anode. Filaments are operated emission limited and require good thermal and emission regula- tion to ensure stable and consistent operation since the ion-beam current is a rather sensitive function of the emission current. The slit system through which the ion beam passes serves both to accelerate the ions to their final velocity before entering the analyzing fields and to 292 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 focus the beam to the smallest possible angular spread. Numerous com- binations of electrodes have been used to achieve these effects, and two examples are shown in Figs. 69 and 70. Permanent gases and vapors of volatile liquids are introduced directly into the ionization chamber through capillary tubes in which the flow is Fig. 70. Ion source developed by Nier. Gas introduced at G is ionized in the chamber / by stream of electrons emitted from filament F. The electron stream is defined by slot C and by the magnetic field produced by permanent magnets. Ions are accelerated and focused into a narrow beam by slit system S. Electrical leads are brought into the vacuum tube through Kovar seal K. [A. O. Nier, Rev. Sci. Instruments, 18, 398 (1947).] regulated by a valve or throttling device [9-11]. Solid substances can be analyzed usually by one of several methods listed below. Sublimation or Distillation: Some metals, e.g., lithium, calcium, aluminum, and magnesium, and certain compounds of less volatile elements, usually in the form of solids, can be distilled from a hot filament or furnace in or near the ionization chamber. Sputtering: Substances that sputter readily will frequently give a measur- able spectrum when a small quantity is inserted in the ionization chamber Sec. 9.11] MASS SPECTROGRAPHS 293 near the exit slit. This effect sometimes produces an undesirable back- ground spectrum when light elements are used in the construction of the ionization chamber, e.g., glass, tin, or aluminum. Carriers: Heavy metals sometimes can be transported by a stream of chlorine or fluorine which forms halides of the metals. Most of these halides, however, condense at room temperature, and it is therefore necessary to maintain the sample and gas at an elevated temperature until it enters the ionization chamber. 9.9. Detector Requirements. The accuracy of measurements of relative abundance of isotopes or of the constituents of a sample under analysis depends largely upon the sensitivity, linearity, and stability of the device used to measure the focused ion beams of different m/e. This places severe requirements on the detector since the ion currents may range in magnitude from less than 10-16 up to 10-9 amp. Hence, in addition to a high order of sensitivity, the response of an accurate mass spectrograph should be repro- ducible and linear over a range of beam intensity at least of the order of 103. 9.10. Photographic Plates. The applications that have required the greatest accuracy have been determinations of isotope mass (relative to O16 = 16.00000). In nearly all such determinations photographic plates have been employed for ion detection. Since they are essentially an inte- grating device, exceedingly small ion currents can be detected by prolonged exposure, and fluctuations in the current will not affect the accuracy of measurements of relative beam intensities. Both abundance and mass measurements are made from a microphotometric recording of the focal images on the photographic plate. The relative area under the intensity curve of a focal image gives directly the relative abundance, and the distance between maxima gives the relative masses in the appropriate mass scale for the instrument. When a wide range of beam intensities is analyzed, the response of photographic plates cannot be considered linear. In such cases it is nearly always necessary to make several exposures of different values of integrated current on the same plate. For the greatest accuracy, calibration of the emulsion response of the plates should be carried out for a wide range of integrated currents and ion velocities. Since it is known that the emulsion darkening, i.e., number of grains reduced, varies markedly with the ion velocity, this latter effect may be appreciable over the length of the spectrum usually photographed at any one time. Photographic emulsions should be uniform and show little or no fog in development. Further, it is important in abundance measurements that no solarization occur around the most dense images. 9.11. Electrical Devices. The earliest electrical devices for detecting ion beams in mass spectrographs were electroscopes and electrometers. These instruments are current-integrating devices and hence unsuited to rapid 294 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 mass analyses. They have, therefore, been wholly replaced by vacuum- tube amplifiers which provide the requisite sensitivity and also permit less sensitive meters and recording instruments to be used. Most frequently, the first stage of an amplifying system is an electrometer- type vacuum tube coupled directly to the ion-collecting electrode of the mass spectrometer. These tubes usually contain four elements and are designed to draw very small grid currents and to operate with plate potentials of only 7 to 20 volts. The input signal is applied to the second grid, or what is normally the screen grid. Several electrometer tubes with very high sensitivities and suitable characteristics have been designed especially for this type of application. The FP-54 [12] is the most sensitive of these tubes and can be used for con- tinuous indication of ion currents as small as 10-15 amp. Several other elec- trometer tubes are also available such as the Vx-41 [13] and the 38, 954, and 959 [19] which, though somewhat less sensitive, are, under some conditions, more stable. The output from the electrometer tube may be used directly to drive a sensitive galvanometer, or the signal can be further amplified by successive stages of d-c amplification. The signal voltage driving the grid of the electrometer tube is derived from the voltage E developed across a grid resistor of the order of 108 to 1011 ohms through which the ion current passes to ground. The maximum sensitivity that can be achieved in circuits of this type is limited by the average voltage e produced in the resistor by thermal agitation. This is given [14-16] approximately by the relation e1 = brTRAf where T = absolute temperature A/ = frequency band passed by amplifying system Assuming that the minimum detectable ion current i0 is that which produces across the resistance R a voltage equal to e, then i0 = 1.29 X 10- R Although it is apparent that the signal-to-noise ratio can be improved by using a high input resistance, values of R greater than 1011 ohms are difficult to obtain and still more difficult to maintain at a constant value. Variations in temperature and particularly in surface resistance are sometimes difficult to control and, together with variation in the effective resistance with signal voltage, may lead to drift and transient changes in the sensitivity of the instrument. More important still is the tendency of some resistors to polarize, thus introducing a long signal decay time. The band-pass fre- Sec. 9.11] MASS SPECTROGRAPHS 295 quency can be made very small only when the ion current is changed very slowly. If the mass spectrum is scanned as it is in nearly all automatic recording mass spectrometers, A/ must be sufficiently wide to allow the galvanometer or recording device to follow faithfully the rapid increase and decrease in ion current as each mass peak sweeps past the collecting electrode; otherwise resolution is lost because adjacent mass peaks overlap, or alter- natively, time and labor are sacrificed in waiting for the signal voltage to decay to the base-line level. For the same reason it is also important to reduce to a minimum the shunting capacitance of the input to the electrometer tube by making the lead from the collecting electrode as short as possible COLLECTING ELECTRODE 25-30 VOLTS Fig. 71. Balanced-bridge electrometer circuit. Resistance i?l is usually of the order of 1010 ohms. If an FP-54 electrometer tube is used, the filament current is about 90 ma and R2 is chosen to give a filament bias of about — 4 volts. The other circuit constants are chosen to give the required grid and plate voltages and adjusted to give zero galvanometer current for zero input signal. The total resistance R3 + i?4 + R5 across the galvanometer should equal the critical damping resistance for the galvanometer. If an inverse feedback d-c amplifier is coupled to the output, R\ is connected to the feedback return lead instead of to ground. Except for the galvanometer and the divider R5, the entire electrometer circuit should be carefully shielded and shock mounted. (See also reference 22.) and by using shields of large diameter, thus making A/ sufficiently wide to pass the audio-frequency Fourier components of a slow pulse. Considerable care must be exercised in mounting and shielding electrometer tubes since their high sensitivity also makes them highly microphonic and extremely sensitive to stray electric and magnetic fields. Drift, transients, and microphonics are best avoided by carefully shock mounting the tube in a rigid brass or copper can which is then evacuated to prevent sound trans- mission and changes in the surface resistance of both the grid resistor and the surface between the tube terminals, mainly by the removal of water vapor. The conventional electrometer circuit is a balanced-bridge network such as that shown in Fig. 71. For the FP-54 the power supply is 25 to 30 volts. 296 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 depending upon the circuit values used, and it may be supplied from batteries or an electronic supply. If the latter, it should be extremely well filtered and very highly regulated in order to avoid drift and short period transients. Extreme care must be taken in the assembly of such circuits to eliminate contact potentials, acid soldering flux, short leakage paths, etc., and all # u — !i — l A A A A A -O Fig. 72. Typical example of current amplifiers that are now used for measuring steady currents as small as 10~15 amp. The negative feedback, d-c amplifier shown here was developed by Nier especially for use with mass spectrometers. The power supply voltage for the plates is 225 volts, and the voltage at A is adjusted for a filament current of 150 milliamperes. Precision wire-wound resistors are indicated by PWW. [Redrawn from A. O. Nier, Rev. Sci. Instruments, 18, 398 (1947).] Rl = 4 X 1010 ohms, IRC type MG-6 R2 = 5,000 ohms, PWW R3 = 20,000 ohms, PWW i?4 = 40 ohms, PWW R5 = shunt to limit filament current in Fl to 20 ma R6 = 12 steps of 13 ohms each, PWW Rl = 200,000 ohm potentiometer R$ = 20,000 ohm potentiometer R9 = 200,000 ohms, PWW RIO RU, RU = 1 megohm, 1 watt R12 = 7,500 ohms, 10 watts i?14 = 35,000 ohms, PWW R\5 = 10,000 ohms, PWW it 16 = 15,000 ohms, PWW CI = 100 MMfd, variable condenser C2 = 0.02 MMfd, 400 volt condenser VI = VX-41 (Victoreen Instrument Co.) V2 = 12SJ7 V3 = VR75 74 = 12J5 resistive elements should be wound from zero temperature-coefficient wire. The use of long leads from the output to a galvanometer or recording device is permissible. The nonlinear characteristics of the electrometer tube over the range of currents (10~14 to 10-10 amp) which is ordinarily measured must be accurately compensated. In manual or static measurements the electrometer-gal- Sec. 9.12] MASS SPECTROGRAPHS 297 vanometer circuit is used as a null indicator. When a mass peak has been maximized on the galvanometer, an accurately linear voltage from a poten- tiometer or decade-battery circuit is applied to the bottom of the input grid resistor, deflecting the galvanometer back to the base line. The peaks are then found in terms of millivolts rather than centimeters of deflection and are as accurately measured as the applied back voltage is linear. A more satisfactory method that is rapidly replacing the simple electrometer- galvanometer circuit is found in the use of a high gain inverse-feedback amplifier coupled directly to the output of the electrometer stage. With a d-c amplifier gain of 5,000 to 10,000 and 100 per cent negative feedback to the input resistor of the electrometer circuit, the over-all voltage gain of the system is very nearly 1, but the output voltage is accurately proportional to the input. In addition to its linearity, this type of amplifying system has high inherent stability, usually not found in the simple balanced bridge elec- trometer circuit, and a response time considerably shorter than most record- ing mechanisms. An example of this type, of circuit, developed by Nier [13], is shown in Fig. 72. Other detector circuits have been proposed which utilize a-c amplifiers and a pulsed ion beam to provide the necessary audio-frequency signal. In one system this is done by oscillating the ion-beam radius in the magnetic field at a frequency of approximately 200 cps by oscillating the accelerating voltage [10]. The pulse received by the collecting electrode as the beam sweeps past is amplified and observed on an oscilloscope in which the linear sweep is synchronized with the beam-sweep frequency. Alternatively, after amplification the pulse may be rectified to operate a d-c recording meter. A second scheme accomplishes essentially the same result by pulsing the ion source [18]. 9.12. Mass-spectrometer Recording Systems. Routine mass spectrom- eter analyses are now usually carried out by automatically scanning and recording the entire mass range or those portions of the spectrum which may be of interest. The scanning may be done by slowly varying either the electric ion accelerating field or the magnetic field. Some advantage is to be found in the latter method in that the magnetic field varies only as w-- . whereas the electric accelerating field varies directly with m~l and, therefore, often involves an inconveniently large range in voltage. A serious dis- advantage of voltage scanning sometimes arises from voltage discrimination, an effect that is important primarily in isotope analyses where the increased accelerating voltage for smaller mass favors the observed beam currents of the lighter components of the isotopes. Whether or not this effect is present in all types of ion sources is not yet certain, but when it is present it appears to be an involved function of the source geometry, the electric field strength, and the accelerating voltage difference between any two masses. 298 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 Among the various recording mechanisms that have been developed, the most straightforward is direct recording of the galvanometer light beam on a moving strip of photosensitive paper. With several identical galvanometers connected in series and each shunted for a different sensitivity, a wide range of ion currents can be recorded on a narrow paper strip since the shunts or sensitivities can be chosen so that at least one galvanometer trace remains on the paper for the largest expected beam currents. More complex record- ing systems now in use employ standard recording instruments, usually recording potentiometers such as the Speedomax.* Scale contraction in these instruments is accomplished by automatic shunt selection which provides a stepwise sensitivity approximating a logarithmic scale over the width of the recording paper [20]. A further modification of the automatic shunt-selection system enables the top of a peak to be recorded on a linear scale while a large portion of the center of the peak is contracted by a non- linear scaling factor which depends upon the amplitude of the peak [21]. 9.13. Mass-spectrometer Errors. Relative mass-abundance measure- ments made with a mass spectrometer are subject to many possible errors, some of which are inherent in the instrument and others in the isotopic species themselves. The observed ion currents of several isotopes do not always represent exactly the mass abundance but must be corrected for one or more of the effects that lead to errors. The more important sources of errors are described below. a. Inlet-sample Flow Rate. The lighter of two molecules flows through the leak or capillary at a higher rate than the heavier component in accordance with the laws of diffusion. If the system allows free molecular flow, i.e., if the mean free path is very much greater than the capillary radius and the pressure gradient through the leak is small, then the flow rate is inver- sely proportional to the square root of the molecular weight. This effect is particularly important in isotopes of very light mass, e.g., H2 and HD. b. Pump-out Rates. As in a, the rates at which substances are pumped out of the spectrometer tube favor the lighter masses and, with a liquid nitrogen or oxygen trap, also the condensible vapors. To some extent this may tend to compensate a. c. Voltage Discrimination. The ion current varies somewhat with accel- erating voltage, i.e., electric field strength at the source. If several mass peaks are measured by voltage scanning, the lighter masses are enhanced progressively by the higher accelerating voltage required to focus them on the collecting electrode. Among the isotopes of light elements the effect can be quite large. It can be avoided, however, by magnetic field scanning or by using several collecting electrodes properly located to receive the ion beams of the different isotopes simultaneously. * Leeds and Northrup Company. Sec. 0.14] MASS SPECTROGRAPHS 299 d. Background. The presence of a background of peaks due to residual gas can introduce serious errors when they appear at mass positions of the less abundant sample components. The only reliable correction is elimina- tion of the background in the region of the spectrum in which mass peaks of the sample components will appear. Except for certain organic com- pounds, water vapor is the most difficult of the common substances to outgas. Once the system has been exposed to water vapor, a prolonged bake-out with the entire spectrometer tube maintained at an elevated temperature is necessary to remove the water vapor peaks at masses 16, 17, and 18. Also frequently observed are mercury or hydrocarbon peaks due to vapors from the diffusion pump. e. Incomplete Resolution. Peaks of large amplitude may be sufficiently wide at the bottom to overlap the adjacent mass position, thus making a correction necessary for the amount of overlap. This effect arises from poor slit- and magnetic-field adjustment, inadequate collimation, metastable ions [28], or a long time constant in some part of the detecting circuits. /. Nonlinearity of Detecting Circuits. This can be avoided by the use of 100 per cent feedback in the electrometer-amplifier system or by use of a null method. g. Instability of Electrical Circuits. This includes primarily the emission current and voltage and the detecting circuits. If drift and short period fluctuations cannot be avoided, it is necessary to take a sufficient number of readings to give a statistically reliable average. h. Overlapping Spectra. Molecules containing more than one atomic species, each with several isotopes, frequently form combinations of different isotopes but with the same total mass, e.g., carbon dioxide. Determination of the abundance of the separate isotopes or of the molecule is sometimes possible only by analysis of its entire spectrum. 9.14. Hydrogen. The hydrogen isotopes are measured in the form of hydrogen gas. Water vapor is impracticable because of the great difficulty in ridding the system of it, the inconsistency of results, and the needless complication by the oxygen isotopes. Attempts to use hydriodic acid have met with consistent failure. The hydrogen gas sample is usually obtained by reduction of water derived from the original labeled substance. This is most conveniently done by passing the water vapor through a quartz tube containing zinc grains main- tained at a temperature of 350°C. The collected hydrogen is then toeplered into a small glass sample bottle for transfer to the gas sampling-system of the spectrometer. Hydrogen-isotope analysis is somewhat complicated by the formation of H3 in the ionization chamber under conditions that depend upon the pressure, the source geometry, and the accelerating field strength [24]. The formation of 300 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 H3 and other combinations of hydrogen and deuterium depend primarily on the pressure, and under the most general conditions the molecules and masses shown in Table 32 may be observed [24]. Table 32. Hydrogen Molecule Masses .Mass Molecule Variation withP 1 H P,P2 2 H2 P D P,P* 3 HD P H3 P2 4 D2 P H2D P2 5 HD2 P2 6 D3 pi When the concentration of deuterium is small, of the order of 1 per cent or less, it can be assumed that all the deuterium is bound as HD and measure- ments of only masses 2 and 3 are necessary. Mass 3 is the sum of HD and H3, but since HD ~ P and H3 ~ P2, by plotting the observed values of the ratio (HD + H3) aP + PP~ H, yP where a,/3,y = constants of proportionality against the pressure, or against H2 to which the pressure is proportional, a straight line is obtained. By extrapolating the line to zero pressure (H2 = 0) the intercept on the ordinate gives directly the ratio a/y = HD/H2. When the concentrations of hydrogen and deuterium are comparable, a more complete analysis is indicated. 9.15. Carbon. Carbon is usually introduced into the mass spectrometer as carbon dioxide. Its preparation from the sample substance is straight- forward. Carbon dioxide driven off by combustion of the substance is absorbed in sodium hydroxide and the solution neutralized by addition of ammonium nitrate or ammonium chloride in excess. Barium chloride is then added in excess to precipitate the carbonate which is filtered or cen- trifuged, washed with water, and dried in an oven at 1 10 to 135°C. If the ini- tial alkali solution is weak, i.e., < IN, barium chloride can be added directly. A few milligrams of dried barium carbonate are transferred to a single-ended quartz microcombustion tube which is connected to the sampling system. After preliminary heating under vacuum to drive off Sec. 9.16] AfASS SPECTROGRAPHS 301 occluded gases, the quartz tube is heated to 1100°C in a gas-oxygen flame until the barium carbonate is completely dissociated. A detailed discussion of carbon-isotope chemistry will be found in reference 25. Determination of the ratio C13/C14 is obtained directly from the mass peaks 44 and 45 corresponding to C12016016 and C13016016 + C12016017, respectively. The contribution of C12016017 to mass 45 is usually negligible. Masses 12 and 13 can also be used, but the beam intensities are considerably smaller than for the molecular ions. They are not, however, difficult to measure, and more important, they are not affected by the oxygen isotopes. In terms of the ratio R of the intensity of C12 (mass 12 or 44) to C13 (mass 13 or 45) the atom per cent concentration of C13 is %C13= 100 R + l where R = C12 reading/C13 reading 9.16. Nitrogen. The relative abundance of the nitrogen isotopes 14 and 15 in a sample substance is determined from measurements of the nitrogen molecule masses of 28, 29, and 30. The preparation of the nitrogen from the organic sample material requires first its reduction to ammonia and then oxidation of the ammonia to free N2 by hypobromite [26]. The ammonia obtained from the sample substance is contained in 0.05iV hydrochloric acid which is boiled down to drive off dissolved gases and then transferred to a nitrogen generating system. With the system evacuated, hypobromite is added to oxidize the ammonia according to the reaction 2NH3 + 3NaOBr -+ N2 + 3H20 + 3NaBr The nitrogen is toeplered into a small sample bottle equipped with a stopcock and transferred to the spectrometer sampling system. For N15 concentrations of the order of 1 per cent and less, only masses 28 (N14N14) and 29 (N14N15) need be measured. The probability for forma- tion of N15N15 is negligibly small. The atom per cent of N15 in the sample is 100/29 100 c/„ TV15 = ■ = — /o x> 2/28 + /29 2R + 1 where 728 = ion current of mass 28 (N14N14) ( I29 = ion current of mass 29 (N14N15) ' R = p*/pf> When the concentration of N15 is greater than several per cent, it is necessary to measure masses 28, 29, and 30 since the contribution of N15N15 becomes appreciable. The atom per cent of N15 is then /o ^ - 2(/28 + /29 _j_ J30) 302 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 It is obviously important in measuring nitrogen to avoid air leaks, dis- solved or adsorbed air in the solutions, in the sampling system, or in the spectrometer. The presence of air contamination is made evident by the oxygen peak at mass 32. If the ratio of the nitrogen 28 peak to the oxygen 32 peak for normal air has been determined previously for the spectrometer, a correction for a small per cent of air contamination can be made readily from the measured intensity of the O2 peak which, when multiplied by the N/O ratio, gives the required mass 28 correction. 9.17. Oxygen. The abundance of the oxygen isotopes in 018-enhanced samples may be determined from measurements of the oxygen molecule masses 32, 33, 34, etc., or by introducing the oxygen as carbon dioxide and measuring masses 44, 45, and 46. If the concentration of O18 is a few per cent or less, contributions by molecules of the form Ol7017, 017018, and Qi8Qi8 are entirely negligible and only masses 32, 33, and 34 are measured. The atom per cent of O18 is then % O18 = 100/ :u 2(/32 _J_ J33 _|_ /34) where P2 = intensity of mass 32 In = intensity of mass 33 I3i = intensity of mass 34 A similar analysis is applied for measurements of oxygen in the form of carbon dioxide. Neglecting the contributions by C13016017 and C13016018, masses 44, 45, and 46 give the atom per cent of O18 by the formula above. For high concentrations of O18 it may also be necessary to measure mass 47. Air contamination is important, but if its percentage is small its contribu- tion to the measured peaks can be corrected. This may be done by measur- ing the nitrogen 28 peak. If the ratio of the oxygen 32 mass to nitrogen 28 mass for normal air is known for the instrument, the appropriate corrections are made as indicated in the last section for nitrogen. The oxygen atomic masses 16, 17, and 18 usually cannot be measured accurately because of the background of water-vapor peaks. REFERENCES FOR CHAP. 9 1. Aston, F. N.-.Phil. Mag., 38, 709 (1919). 2. Aston, F. N.: "Isotopes," Edward Arnold & Co., London, 1924. 3. Dempster, A. H.: Pkys. Rev., 11, 316 (1918). 4. Herzog, R.: Z. Physik, 89, 786 (1934). 5. Mattauch, J., and R. Herzog: Phys. Rev., 50, 617 (1936). 6. Shaw, A. E., and W. Rall: Atomic Energy Commission Report MDDC-45,1946. 7. Bainbridge, K. T., and E. B. Jordan: Phys. Rev., 50, 282 (1936). 8. Bleakney, W., and J. A. Hipple: Phys. Rev., 53, 521 (1938). 9. Nier, A. O., E. P. Nery, and M. G. Inghram: Rev. Set. Instruments, 18, 191 (1947). Chap. 9] MASS SPECTROGRAPHS 303 10. Siri, W.: Rev. Sci. Instruments, 18, 540 (1947). 11. Honig, R. E.: /. Applied Phys., 16, 646 (1945). 12. Lafferty, J. M., and J. H. Kingdon: J. Applied Phys. 17, 894 (1946). 13. Nier, A. O.: Rev. Sei. Instruments, 18, 398 (1947). 14. Forrester, A. T., and W. B. Whalley: Rev. Sci. Instruments, 17, 549 (1946). 15. Johnson, J. B.: Phys. Rev., 32, 97 (1928). 16. Nyqutst, K.:Phys. Rev., 32, 110 (1928). 17. Washburn, H. W., H. F. Wiley, S. M. Rock, and C. E. Berry: Ind. Eng. Chem., Anal. Ed., 17, 74 (1945). 18. Anker, H. S. : Symposium on the Use of Isotopes in Biological Research, Chicago, 1947. 19. Nielsen, C. E.: Rev. Sci. Instruments, 18, 18 (1947). 20. Hlpple, J. A., D. J. Grove, and W. M. Hickam: Rev. Sci. Instruments, 16, 69 (1945). 21. Grove, D. J., and J. A. Hlpple: Rev. Sci. Instruments, 18, 837 (1947). 22. Penick, D. B.: Rev. Sci. Instruments, 6, 115 (1935). 23. Neer, A. O.: Rev. Sci. Instruments, 11, 212 (1940). 24. Bleakney, W.: Phys. Rev., 41, 32 (1932). 25. Calvin, M., C. Heidelberger, J. Reid, B. Tolbert, and P. Yankwich: "Isotopic Carbon," John Wiley & Sons, Inc., New York, 1948. 26. Rittenberg, D.: "Preparation and Measurement of Isotopic Tracers," p. 31, Edwards Bros., Inc., Ann Arbor, Mich., 1947. 27. Dempster, A. J.: Phys. Rev., 51, 62 (1937). 28. Hipple, J. A.: Phys. Rev., 71, 594 (1947). CHAPTER 10 GEIGER-MULLER COUNTERS 10.1. General Properties. Geiger-Miiller tubes are a form of high-gain, gas-filled, amplifying diode operated at potentials below the continuous dis- charge voltage. Their essential function is that of a triggering device in which a voltage pulse is produced by a discharge initiated by an ionizing particle. The accumulation of negative charge, reaching a magnitude of the order of 10-8 coulomb, is collected at an anode where it can be detected by appropriate instruments. The usual form of Geiger-Miiller tube consists of a cylindrical cathode and a coaxially mounted wire anode sealed in a tube containing one of various possible gas mixtures, usually at reduced pressure. Designs, materials, and gas mixtures of many varieties are used, the choice depending largely on the kind of radiation to be detected and to some extent on special purposes. The tubes commonly used vary in size from 0.3 to 10 cm in diameter and from 2 to 50 cm in length, and for most tubes the anode wire, usually tungsten, is about 0.02 to 0.1 mm in diameter. The size, duration, and general character of the discharge in a counter tube is independent of the specific ionizing power of the initial particle. Thus an electron and an alpha particle produce the same pulse as observed on an oscilloscope screen although the latter particle produces 103 to 105 times as many ion pairs per centimeter of path. One ion pair, if formed in the sensitive region of the tube, is sufficient to trigger the discharge which sub- sequently involves roughly 1010 ion pairs. The first part of the discharge occurs rapidly. Electrons released by the initial ionizing particle drift rapidly to the central anode wire. In the high electric field close to the wire the electrons acquire sufficient energy between collisions to ionize the neutral gas molecules releasing additional electrons which further contribute to a Townsend avalanche. Thus the initial number of free electrons is increased by a factor of 108 to 1010. Because of the high mobility of electrons, this part of the process is completed in a microsecond or less. The less mobile positive ions, however, remain as a positive space charge surrounding the anode along its entire length [1,2], and the subsequent behavior of the discharge depends upon the composition of the gas used to fill the counter, more generally, depending upon whether it is a quenching or nonquenching gas. 10.2. Non-self-quenching Counters. When a counter tube contains monatomic, diatomic, or certain triatomic gases, the discharge tends to 304 Sec. 10.2] GEIGER-MULLER COUNTERS 305 maintain itself and the counter tube is said to be non-self-quenching or "slow." Following the generally accepted qualitative description of the processes given by Montgomery and Montgomery [3] and other writers [4], the presence of the residual slow-moving positive ion sheath greatly modifies B ^ €> ^. ^ ^^ B- Fig. 73. Typical counter-tube designs. A. Bell counter. Wire anode, thin mica window, and chemically deposited silver cathode (beta particles). B. Point counter. Ball anode, thin mica window, and alternative inserted copper cylinder cathode (beta particles). C. Thin glass window counter (beta particles). D. Immersion counter. Thin glass wall, deposited silver cathode. Shown immersed in sample liquid (beta particles). E. Cylindrical counter. Thin glass wall and deposited silver cathode for beta particles. Heavy wall and copper mesh cathode for gamma rays. the electrostatic field gradient surrounding the anode, thus quenching the avalanche by preventing the remaining free electrons from acquiring suffi- cient energy between collisions to cause further ionization. The positive ions then drift to the cathode in a time of the order of 10-4 sec. At the 306 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 cathode surface they are neutralized by ejecting an electron from the wall. This is immediately followed by the emission of one or more photons from each atom as it returns to the ground state. For some gases such as argon, helium, and hydrogen, the emitted radiation lies in the ultraviolet and BF mnn//l/niiitiiiuuiiiiii>ii/iiiii ^VW-^ZZ3- s }JJ/Jj>j>j>rtjsji, /,, i /,//,,, , j / r , / f f r f , f -? Fig. 74. Easily constructed metal counting-tube designs. A. Cylindrical brass or copper tube counter using Kovar seals (cosmic rays, gamma rays, and neutrons). B. Copper "bell" counter with Kovar seal pump out and anode lead (gamma rays and neutrons). C. Arrangement of radiator in fast neutron counters showing hydrogenous layer coated on a thin platinum plate. D. Bell counter with mica window and with mounting for standard sample position (beta particles). possesses sufficient energy to eject photoelectrons from the counter walls where it is absorbed. Although the photoelectric efficiency is of the order of one ejected electron per 104 photons, if 1010 ions are formed in the discharge process, the probability of electron ejection is high and consequently the discharge is continued. In addition, positive ion bombardment of the cathode at potentionals normally used in operating counter tubes frequently Sec. 10.3] GEIGER-MV LLER COUNTERS 307 results in the direct ejection of free electrons which may also continue the discharge. A third mechanism observed by Ramsey [5] and others occurs when the initial avalanche is small. Photons emitted by those ions in the avalanche which capture an electron before reaching the cathode can eject photoelectrons which then maintain the discharge in what is observed to be a series of diminishing pulses. Discharges in tubes containing only mono- or diatomic gases, consequently, will, with certain exceptions, continue so long as the anode potential is maintained. Quenching is accomplished in such tubes only by some external device such as a high resistance, usually of the order of magnitude of 109 ohms, or by an electronic circuit which reduces the anode potential below the threshold voltage after the initial part of the pulse and until the positive ions are collected. These counters have revolving times of several times 10-4 sec when appropriate external electronic quenching circuits are used, but they may be as long as 10-2 sec with simple resistance quenching. The minimum resolving time is limited by the positive ion transit time. 10.3. Self-quenching Counters. The addition of polyatomic gases such as methane, alcohol, and amyl acetate to counter tubes alters the process in a way to quench the discharge following the Townsend avalanche without the use of external quenching circuits, and such counter tubes are called self- quenching or "fast" counters. The resolving times of such counters is usually of the order of 10~4 sec. The principal function of the polyatomic quenching gas is to prevent further production of electrons following the completion of the initial Town- send avalanche. This is accomplished mainly by reducing photoemission and secondary electron emission from the cathode walls [4]. The effectiveness of polyatomic gases in absorbing photons is due to the diffuse vibration-rotation interaction absorption bands present in the ultra- violet region of their spectrum. Radiation emitted by excited argon, helium, and most other permanent gases lies between 1,020 and 790 angstroms and can, therefore, be absorbed by such molecules as methane and alcohol, which have continuous or band absorption spectra blanketing this region. In addition to absorbing radiation, it is equally important that the quenching- gas molecules do not reemit the absorbed photons but have, instead, a strong tendency toward releasing the excitation energy by photodecomposition. This appears to be valid for all polyatomic gases exhibiting quenching properties. Secondary electron emission from the cathode is effectively reduced by two mechanisms. (1) The monatomic and diatomic ions formed in the initial ionization process are prevented from reaching the wall by the process of electron exchange with neutral polyatomic molecules with which they collide with a frequency of roughly 102 to 103 times per centimeter of path. 308 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 This process is possible only when the ionization potential of the quenching gas is less than that of the nonquenching gas [4], The photons emitted in the process are absorbed in turn by other polyatomic molecules. (2) The quenching-gas ions, formed either by the initial ionizing event or by electron exchange, are neutralized by electron ejection from the wall, but they exhibit a greater probability for decomposition than for ejection of a free electron or for radiative capture. Altogether, the probability of secondary electron production appears to be 1 electron per 1010 ions [6,7] and these can be absorbed by the slow-moving residual quenching-gas ions. The presence in a counter tube of appreciable quantities of negative ion- forming gases such as 02, H20, and the halogens considerably alters the mechanism of discharge and with it the desirable operating characteristics. VOLTAGE Fig. 75. Effects of gases on G-M plateau. 274 (1944).] A. Pure methane B. 1.5 cm argon added C. 1.5 cm water added VOLTAGE [S. A. Korff and R. D. Present, Phys. Rev., 66, A. Pure methane B. 1.5 mm air added C. 6.0 mm air added The slow collection time of negative ions compared with electrons tends to prolong the discharge time and frequently leads to the complete disappearance of the Geiger-Miiller plateau [4], as seen in Fig. 75. 10.4. Pulse and Voltage Characteristics. Voltage pulses as observed with an oscilloscope increase rapidly to a maximum value in a time of the order of 1 microsecond, corresponding to the collection time of the electrons. Follow- ing the pulse maximum or pulse rise time, the anode voltage, which has actually been depressed, slowly recovers to normal potential as the residual positive ions are swept out. During the first part of the pulse, referred to as the dead time, the counter is wholly insensitive to a second ionizing event. As the voltage recovers beyond a critical value, a second ionizing event may produce at successively later intervals a larger pulse until, at the termination of the recovery time, a normal pulse voltage is again produced, as shown in Fig. 76. Both the dead time and recovery time appear to have durations of about 10-4 sec or less for self-quenching counters. Voltage characteristics of counters are determined by observing the Sec. 10.4] GEIGER-MULLER COUNTERS 309 counting rate for increasing anode voltage. The important characteristic of a Geiger-Muller, or discharge, counter is the existence of a well-defined plateau voltage region over which the counting rate does not increase appre- ciably. Normally this region of the curve should be flat and the counting rate should not increase more than 2 to 5 per cent per 100 volts over an Fig. 76. Counter pulse characteristics. [H. G. Slever, Phys. Rev., 61, 38 (1942). _i UJ at OTENTIA ENTIAL J / L i / i I I j i L I < J 1 z 5 5» Q. > / o o / > > > 1- 7 ATIO ING 5 / Q C9 - / -> z O z -> : / o fr H 8 tr i- c 3 cr : i / i < z 3 t < c / y uj o < 1- c c / £ Q. o CI r> CI r> K y f o 2 UJ 3 Z o X UJ < o s VOLTAGE Fig. 77. Counting-rate characteristics of counters as a function of anode voltage. interval of 100 to 300 volts, although shorter plateaus are satisfactory with well-regulated voltage supplies. The following voltages are frequently referred to because they are asso- ciated with characteristic properties of counter tubes at various potentials (see Fig. 77). 1. Starting voltage. This is the lowest voltage at which counts are observed. It depends largely on the sensitivity of the detecting circuits used. 2. Proportional threshold voltage. This is the lowest voltage at which pro- 310 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS Chap. 10 portional pulses are observed. It is often identical with the starting voltage, depending upon the sensitivity of the detecting circuits. 3. Geiger-Miiller threshold voltage. This is the lowest voltage at which all pulses have the same height. 4. Operating voltage. This is the normal voltage at which a counter is operated. Usually it is in the lower half of the plateau region. 5. Overvoltage. This is the difference between the operating voltage and Geiger-Miiller threshold voltage. In a similar way, certain voltage ranges are distinguished by characteristic behavior of the counter tube. The voltage ranges usually referred to are given below (see Fig. 78). | 1- Z O Z o UJ _l cc o o 3 UJ on in 13 UJ UJ CC o 2 o CC UJ M UJ CC O u. UJ m 2£ UJ Z H _l < z o z o K z < CC 1- UJ IS CC V) O O i- < z p < DC z I UJ _) 3 o Si z < or M < 1 O DC OL ^^ o UJ CC o V) a Q. CD s o o UJ DC / ALPHA PARTICLE CC UJ _l _l s o _i r / CC / UJ / o / COSMIC RAY UJ k VOLTAGE Fig. 78. Ionization produced in counters as a function of anode voltage. Montgomery and D. D. Montgomery, J . Franklin Inst., 231, 447 (1941).] [From C. G. 1. Region of a few volts above ground potential within which some of the positive and negative ions formed by an ionizing particle recombine before reaching the anode or cathode. 2. Ionization-chamber region, usually in the order of tens of volts. In this region the initial ions formed by the primary particle are collected but do not multiply appreciably. Recombination is negligible. 3. Proportional region. The pulse produced by an ionizing event is proportional to the initial number of ions formed for any fixed operating voltage. 4. Geiger-Miiller transition or limited proportionality region. Pulses are no longer strictly proportional, and large pulses may exhibit some of the characteristics of the Geiger-Miiller region. 5. Geiger-Miiller region. Each event produces a discharge in which pulse size is independent of initial intensity of ionization and the counting rate remains essentially independent of voltage. Sec. 10.6] GEIGER-MULLER COUNTERS 311 6. Continuous-discharge region. This is characterized by corona, glow, and finally, arc discharge. 10.5. Filling Gases. The most frequently used filling gas is a mixture of argon (80 to 95 per cent) and alcohol (5 to 20 per cent) at a total pressure of 5 to 40 cm Hg. Although nearly all permanent gases have been used, either alone or in various mixtures, argon is probably the most useful since it has a large cross section for ionization, a sufficiently high ionization potential to allow electron transfer with most polyatomic molecules, does not form negative ions, and is readily available. Many quenching gases other than ethyl alcohol can be used such as ethane, amyl acetate, ethyl ether, and tetraethyl lead. Heavy polyatomic molecules may also be used, and some increase in useful counter life will usually be found because of the greater number of decompositions required to reduce it to a nonquenching gas. However, their use in most counters is undesirable since they lead to a longer resolving time due to the low mobility of heavy ions. Gases that have strong tendencies to form negative ions should normally be avoided [4,9]. These include primarily oxygen, carbon dioxide, water vapor, and the halogens. However, under special conditions they can be used successfully in small amounts [11,14]. It has also been pointed out by Present [36] that chlorine and bromine can under certain conditions be used as quenching gases. 10.6. Counter-tube Life. The useful life of self-quenching counters appears to be dependent to some extent upon the volume of gas in the counter [8]. With each discharge approximately 1010 ion pairs are formed, and in the process a small fraction of the polyatomic molecules are decom- posed into smaller fragments, some of which still retain quenching properties. Ultimately, however, an appreciable fraction of the complex molecules is reduced to free oxygen, hydrogen, carbon, and simple molecules which remain partly as nonquenching gases and partly as an accumulation of crud on the cathode. The counter performance tends to become erratic and finally no longer self-quenching and must be refilled. Assuming that 108 to 1010 quenching gas molecules are decomposed per discharge and an initial number of molecules of approximately 1020, the approximate life of a counter is then of the order of 1010 counts. In practice it is found that the smallest counters retain their quenching property for only a few months at best when in con- stant use, whereas larger counters, with volumes of the order of 75 cc, have useful lives of a year or more under similar conditions. Counters containing only permanent gases should exhibit no change with time, barring leaks or deterioration of the mechanical and electrical properties of the tube itself. The effective life of self-quenching counters can be prolonged somewhat by operating the counter at a voltage in the lower end of the plateau and by increasing the total gas volume without, at the same time, increasing the sensitive volume in which the discharge takes place. The latter method has 312 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 Table 33. Filling Gases Used in Counters From S. C. Brown, Nucleonics, 2, No. 6, 10 (1948). 1st ex- Ioniza- Meta- Gas Formula citation tion stable Emission or absorption poten- poten- level, spectrum, angstrom units tial, ev tial, ev ev Acetone CH2COOCH3 10.1 3,300-2,940 abs. bands Acetylene C2H2 11.6 2,400-2,090 abs. bands Ammonia NH3 10.5 1,620-1,450 abs. bands Argon A 11.6 15.7 11.5 1,048 emission Boron trifluoride . . BF3 Bromine Br2 12.8 1,500 abs. continuous Carbon dioxide .... C02 14.4 1,360-600 abs. bands Carbon disulfide . . . CS2 10.4 3,800-1,200 abs. bands Carbon monoxide . . CO 14.1 Carbon tetra- chloride ecu 4,600-2,300 abs. bands Chlorine Cl2 12.8 1,500 abs. continuous CHC12 2,200 abs. continuous C2H6OH 11.3 1,633-1,602 abs. bands 1,518 abs. diffuse < 700 abs. continuous Ethyl bromide C2H6Br 10.24 2,850-1,900 abs. continuous < 1,700 abs. diffuse Ethyl chloride C2H6C1 < 1,700 abs. continuous Helium He H- 20.5 11.5 24.5 15.4 19.7 None 854 emission Hydrogen 1,215 emission Hydrogen sulfide . . . H2S 10.4 1,600-1,190 abs. bands Krypton Kr 9.9 13.9 9.87 1,236 emission Mercury Hg 10.4 5.43 1,850 emission Methane CH4 14.4 < 1,450 abs. continuous Methyl iodide CH3I 10.12 3,600-2,110 abs. continuous 2,100-1,215 abs. diffuse Neon Ne NO 16.6 21.5 9.5 16.5 736 emission Nitric oxide Nitrogen N2 6.1 15.5 6.27 Nitrogen dioxide . . . N02 11.0 5,700-2,200 abs. bands Nitrous oxide N20 12.9 3,000-1,760 abs. continuous 1,520-1,056 abs. bands < 1,000 abs. continuous Oxygen 02 6. 12.5 3,5,9 Pyridine C2H6N 9.8 < 2,500 abs. continuous Sulfur dioxide S02 13.1 3,800-1,529 abs. bands Water H20 13.0 1,240-983 abs. bands Xenon Xe 8.3 12.1 8.27 1,470 emission Sec. 10.7] GEIGER-MULLER COUNTERS 313 been successfully employed to increase by several times the useful life of very small counters [8]. By attaching a bulb of larger dimension to the counter outside the sensitive region to serve as a reservoir, the percentage decom- position of quenching gas per discharge can be made very much smaller. 10.7. Low-voltage Counter Tubes. A considerable reduction in the Geiger-Muller threshold of counter tubes containing conventional gas mix- tures can be achieved by reducing the total gas pressure. The minimum threshold voltage of most counters containing permanent gases is found at pressures near a few centimeters of mercury, below this the threshold again increases very rapidly with decreasing pressure. With a quenching gas present, the minimum threshold for counters of moderate size is near 500 volts and without a quenching gas, somewhat lower. In practice, however, a substantial reduction in the threshold by this means is impracticable since the reduced pressure is accompanied by a marked decrease in the counter-tube efficiency and ultimately, below 5 to 10 cm Hg, by the alteration or even loss of the Geiger-Muller plateau. It is well known that the threshold voltage also decreases with the diameter of the cathode and to some extent with the diameter of the anode wire, but the reduction effected by the use of very small anode-wire diameters is not very great and is severely limited for mechanical reasons. Geiger-Muller and proportional counters with very low thresholds can be made, however, with highly specific mixtures of permanent gases and suitable cathode surfaces. Such counters, with operating voltages of 130 to 250 volts and normal characteristics, have been developed and exhaustively investigated by Simpson [30]. The discharge mechanism of these counters is similar to that described in Sees. 10.1 and 10.2 for ordinary gas mixtures but with one important differ- ence. In conventional gas mixtures or with a single permanent gas, a con- siderable fraction of the energy derived from the electric field during a dis- charge is taken up by atoms that are raised to metastable excited states rather than being ionized. The energy absorbed by these atoms therefore is largely lost since they do not contribute to the total ionization in the dis- charge. With the admixture of a small quantity of a second permanent gas, the metastable states can be rapidly reduced by collisions of the second kind, i.e., by inelastic collisions in which a neutral secondary gas atom is ionized and the metastable atom reduced to the ground state [30,31]; thus, more efficient utilization of the electric field for the formation of ions is possible and the threshold voltage is accordingly reduced. The mechanism described above is possible when the first ionization potential of the secondary gas is less than but near the energy of the meta- stable state of the primary component. In addition, the concentration of the 314 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 secondary gas should be considerably less than 1 per cent of the gas mixture. Combinations of permanent gases suggested by Simpson are given in Table 34. Table 34. Low-voltage Ccwnter Filling Mixtures Primary component Secondary component Gas Metastable state, ev Gas Ionization potential, ev Neon Helium 16.6 20. 16.6 Argon Neon Mercury 15.7 21 47 Neon 10.39 Under most conditions, the minimum threshold voltage is found for primary gas pressures of 5 to 10 cm Hg. The optimum amount of secondary gas depends to some extent on the total pressure and kinds of gases used. For the neon-argon mixture, the most carefully investigated, the minimum threshold of approximately 120 volts is found for a neon pressure of ~5 cm Hg and ~0.01 per cent argon. With argon concentrations up to 0.9 per cent the threshold under the same conditions increases to approximately 160 volts. Construction, evacuation, and purity of the gases require particular con- sideration. The cathode surface should be one that minimizes secondary electron emission from both photoemission and ion bombardment. For this reason a thin coating of cuprous oxide gave the most satisfactory results. Before filling, a counter is thoroughly outgassed by pumping for 4 to 6 hr while its temperature is maintained by a furnace at 300°C. Complete outgassing is further ensured by heating the anode wire to incandescence and by applying high- voltage discharges between anode and cathode. The addition of an organic vapor to make the counter self-quenching raises the threshold to 230 volts or more, but this is still low compared with that of conventional gas mixtures which have thresholds of 800 to 1,500 volts. Specifications for a self-quenching low-voltage counter developed by Simpson [30] are given below. Cathode: Copper, 1.9 cm diameter Anode: 0.01 cm diameter tungsten wire Filling gas: Neon, 5.7 cm Hg; argon 5 to 50 X 10-4 cm Hg; distilled ethyl alcohol, ethyl ether, or amyl acetate, 0.02 to 0.04 cm Hg Threshold: 230 to 270 volts Plateau: 90 to 120 volts Slope: 2 to 5 per cent Sec. 10.8] GEIGER-MULLER COUNTERS 315 10.8. Active Gas -filled Counters. A higher order of sensitivity as com- pared with the thin window counter can be attained in measuring the activity of very low-energy beta-emitting substances by introducing the isotope in some gaseous form into the counter as part of the filling gas. This is par- ticularly useful for measurements of weak activities of Cu (154 kev) and for all activities of H3 (17 kev). In principle, any radioactive isotope that can be put into gaseous form can be measured by this means. If, however, the maximum energy is greater than 0.2 mev or if gamma rays are emitted, a procedure using a thin-window beta counter or a gamma counter is in general faster and more convenient. Beta emitters with maximum energies as low as tritium (17 kev) neces- sarily must be measured under conditions that avoid any absorber including self-absorption. This is possible with counter tubes only by introducing tritium directly into the sensitive region of the tube. Satisfactory pro- cedures of this kind have been developed by Black and Taylor [10], Pace [11], Allen [12], and Cornog [13]. The tritium, is introduced as part of the gas filling mixture in the form of HTO vapor. A conventional design of glass- walled tube is used which has a total volume of 1 liter, a 5-cm-diameter copper-screen cathode, and a 0.010-in. -diameter tungsten anode. The disturbing effects of water vapor in counter tubes are avoided by limiting the HTO vapor pressure in the tube to 2 mm Hg. To this is added a mixture of 2.5 cm Hg of anhydrous ethyl alcohol and 2 cm Hg of argon. A plateau of 300 volts and a threshold of approximately 1,200 volts are reported for this tube by Pace [11]. Memory effects due to absorption of water vapor are considerably more serious than for most other substances, but a procedure suggested by Pace is successful in reducing the counting rate to normal background after each sample measurement. Between samples the tube is alternately evacuated and flushed eight times with inactive water vapor and then followed by an air rinse and finally evacuation to a pressure of 0.3 jj.. A successful type of gas counter for measuring C14 in the form of carbon dioxide has been developed by Miller [14]. A conventional gamma counter tube is constructed of either metal or glass with a 0.006-in.-diameter tungsten anode and, in the glass tubes, a chemically deposited silver cathode coated with aqua dag. Carbon dioxide containing the C14 is introduced at pressures from 10 to 50 cm Hg. Satisfactory Geiger-Muller characteristics are obtained by the addition of 2 cm Hg of carbon disulfide which provides a 200-volt plateau with a 2 per cent slope. The threshold voltage varies from 1,800 to 4,500 depending upon the cathode diameter (1 to 4 cm) and gas pressure. The optimum operating voltage was found to be approximately 160 volts above threshold voltage. Memory effect appears to be negligible for carbon dioxide. 316 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 10.9. Neutron Counters. Counters intended for direct detection of neutrons depend upon either the recoil of light nuclei in the filling gas and from the walls, or on charged particles emitted in nuclear interactions of neutrons with the material of the counter wall or filling gas. The choice between these two mechanisms depends upon the energy range of the neutrons to be detected. Whichever method is used, in most applications neutron counters are operated in the proportional region in order to reduce the less heavily ionizing background of gamma and electron radiation. This is essential for measuring low neutron flux since the efficiency for neutrons is small compared with that for incident charged particles. 10.10. Slow Neutron Counters. Slow neutrons are usually detected by their interaction with B10 nuclei according to the reaction B10(n, a)Li7. The reaction is accompanied by the release of 2.5 mev of which 1.6 mev is contributed to the alpha particle and 0.9 mev to the recoil lithium nucleus. If both particles are stopped in the filling gas, roughly 75,000 ion pairs are formed, assuming an average energy loss of 33 ev per ion pair. Boron can be used in slow neutron counters either as the filling gas in the form of boron trifluoride [15] or as a thin coating of metal on the cathode wall. Boron trifluoride-filled counters are constructed similarly to gamma counters, preferably with materials that do not have large thermal-neutron capture cross sections, as does glass containing boron for example, and filled to pressures of 10 to 760 mm Hg. The maximum pressure that can be used is limited by both the increase in operating voltage and the increased size of electron pulses as the boron trifluoride pressure is raised. The lowest useful pressure is determined by the neutron counting efficiency desired. The efficiency of the counter, defined as the probability that a neutron in traversing an average path length I through the counter is captured, is given [6] by, € = IrpLcr where p = pressure L — Loschmidt's number r = B10 concentration, B10/(B10 + B11) a = B10 capture cross section for neutrons of energy E The neutron capture cross section of B11 is negligible compared with B10 and does not contribute appreciably to the neutron count. Higher counting efficiency therefore can be attained by increasing the enhancement of B10 above its natural fractional concentration of 0.18 [16]. The efficiency also varies with the neutron energy since for boron a ~ E~1/2. Within the experi- mental accuracy, the cross section for energies between 0.01 and 10,000 ev is given by a = — p= — 0.20 barns where E = neutron energy, ev Sec. 10.11] GEIGER-MULLER COUNTERS 317 Neutron counters with boron-coated cathodes are usually filled with con- ventional argon-alcohol mixtures and operated at voltages within the pro- portional region for the particular counter. The thickness of the boron layer on the cathode should not be made greater than the range of the alpha particle ejected from a boron nucleus by a slow neutron capture, i.e., about 0.1 mm. Greater thicknesses will not increase the efficiency but, rather, lead to excessive absorption of neutrons since a larger fraction of ejected alpha particles will not reach the sensitive volume of the counter. The maximum efficiency of such counters is given [6] by the formula paRN 6 ~ A where p = boron density N — Avogadro's number A = atomic weight R = alpha-particle range in boron <7 = boron cross section for neutrons^of energy E In a similar way, a very thin layer of uranium may be used instead of boron. The fission products resulting from the absorption of slow neutrons produce extremely heavy ionization. However if most of the range of a frag- ment lies within the uranium layer, it cannot be distinguished from the alpha particles due to the natural uranium decay and must, therefore, be treated by the usual statistical methods for background counts. The normal fractional concentration of the effective isotope is 0.007 and has a cross section ^550 barns for 0.025 ev neutrons. The use of enhanced U235 mixtures will increase the efficiency correspondingly. 10.11. Fast Neutron Counters. Detection of fast neutrons with counters is accomplished most effectively by the recoil of light nuclei from elastic collisions with neutrons. The maximum energy transferred from the neutron to the struck nucleus is „ AM (M + l)^ = Ea mev where M = mass of nucleus in units of neutron mass E = neutron energy Er = recoil kinetic energy of nucleus and the average energy is approximately E = E 2M (M + 1)= If hydrogen is used for the filling gas, the maximum recoil proton energy, due to a head-on collision, is equal to the full neutron energy. If, for a gas of atomic mass M, the smallest detectable pulse is produced by a recoil energy B0, referred to as the bias energy, the lowest neutron energy 318 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 that can be detected is B = B0/a. For hydrogen, B — BQ, and the scatter- ing cross section for neutron energies above 0.050 mev varies as \/E^~. Therefore, the sensitivity of hydrogen-filled counters varies approximately as [17] JB-H 0-s) The sensitivity rises rapidly for neutrons with greater than the bias energy and then remains relatively constant in the energy interval 1.57 B < E < 9.6B. The existence of a threshold is an important property of the hydrogen-filled proportional counter since it provides a rapid although rough means for determining neutron energies. This is done by altering the bias of a dis- criminator to pass only pulses due to recoil nuclei with energies equal to or greater than B0. An alternative form of proton-recoil counter employs thin hydrogenous radiators mounted within the counter tube [17,18]. Radiators are frequently prepared by evaporation of glycerol tristearate on thin platinum disks in a vacuum. The thickness of the hydrogenous layer is usually of the order of 100 mg per cm2. The same characteristics are observed as for hydrogen- filled counters provided that the filling gas has a sufficiently high stopping power to stop all hydrogen recoils within the gas volume and does not itself recoil with greater than the bias energy B0. Heavy, inert gases such as argon, krypton, and xenon are the most satisfactory filling gases for this reason. The elastic scattering cross section of hydrogen and most other substances for fast neutrons is in the order of 1 barn; hence the efficiency of counters used in this energy range is necessarily low. In addition to counts from recoil nuclei, counts will be registered from competing neutron processes occurring in the counter wall and in the filling gases, liberating protons, deuterons, alpha particles, or gamma rays. The cross sections for these interactions in nearly all substances is also in the order of 1 barn. Thus, if a boron trifluoride counter is used for detecting very fast neutrons, dis- charges are initiated by alpha particles from the reaction B(n, a)lA as well as by recoil boron and fluorine nuclei. 10.12. Accuracy of Counting Measurements. An estimate of the accuracy of counting measurements on the activity of a sample is determined, for the most part, by simple statistical procedures. The methods employed are based upon the fact that each disintegration is a statistically independent event since it is in no way affected by a preceding event or the means by which it is detected. The distribution of disintegrations in time and the Sec. 10.13] GEIGER-MULLER COUNTERS 319 radiation detected is then purely random. In a time interval /, which is small compared to the half-life of the substance, the probability P of observ- ing n particles is given [19] by Poisson's distribution curve for random events. X" P(n) = — e~» nl where N is the true average number of particles detected per unit time. For large numbers of counts the difference between the true average and the com- puted average (the most probable value) is always small, and no significant error is introduced by using the latter value. Random errors accompany all measurements; they are indeterminate and presumably arise from a multitude of unknown factors which influence slightly the measured values. They can, however, be treated by statistical methods which provide a measure of the possible error introduced by random fluctuations. The true value of a quantity, in this instance the counting rate, is seldom known, but in its place the most probable or average value of the set of measurements must be used. Residuals may now be defined as the difference between each measurement %i and the average value n; Xi = n% — n. If the residuals are truly random, there will be about the same number of negative as positive values, and small values will occur with greater frequency than large values. It can be shown that under this con- dition the distribution of the residuals is nearly symmetrical about the average value and follows approximately the Gauss error curve (normal distribution curve) e-xV2 7T V7r -hr-x where a — standard deviation (see below) h = 3^c2 = index of precision If h is large, a greater proportion of the errors are small and hence grouped close to n; if h is small, the spread in data is greater. Aside from the intrinsic form of the distribution of data and errors to be expected, the important facts concerning a set of measurements are estimates of reliability in terms of the variability of the data. Three measures of variability are commonly used for this purpose: average deviation from the mean, standard deviation from the mean, and the probable error. Of these, the probable error is most often used for estimating the statistical error in counting measurements. 10.13. Average Deviation. If n is the average number of counts per unit time for M measurements of the same sample under identical physical conditions, the average deviation of the residuals from the mean value of the set of measurements is (in counts per minute) 320 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 M A.D. = \ \n— tii\ t = i 1 IfM»l, VM(M - 1) h \/^ M cpm A.D. = i= where M Xi = tii — n M cpm n = X ni M cpm and the vertical bars indicate absolute values. These formulas may be applied when counting by predetermined time intervals /,-, or by predeter- mined count number intervals «,-, or by arbitrary choice of both. 10.14. Standard Deviation. The standard deviation a of a measurement is defined as the root mean square of the deviations from the mean value of the counting rate. M Y \n — ni\2 t = lM-l cPm Also a more convenient iorm is generally used when a single measurement of N total counts is taken over a time / 4 cr = \/nt = \/rN counts which is the standard error in terms of numbers of counts. In terms of percentage, 100 Vn % If several sets of measurements are taken, the resulting standard deviation is then the square root of the sum of the squares of the separate o-'s M 2 — V ^2 cr Either this method or the one above may be used for computing cr. The error in any counting measurement must necessarily include the standard Sec. 10.15] GEIGER-MULLER COUNTERS 321 deviation of the background count ab as well as of the sample plus background as and is given by o- = V> % u\ s — Mb) It is seen that, like the standard deviation, the probable error may be calculated from the total number of counts N or from the M sets of measure- ments. The probable error defines limits, ±r, about the mean value, N counts in time t, or n cpm, within which any single measurement of the activity should occur with a probability of 0.5 and with an equal probability for all values outside these limits. When the approximate values of the sample and background counting rates are known, it is frequently more convenient to count samples by time intervals rather than by total events. When the sample plus background and the background are counted separately to give the same relative probable error, the minimum time required to reduce the total statistical error of the sample measurement to a prescribed percentage r is given by 9,100w / = -jrrz rr, mm r-{n — nb)- and for the background, the minimum counting time should be (n — nb)H h = — mm ntii, where n = average counting rate of sample plus background fib = average counting rate of background The true value of h — nb is then calculated with the prescribed accuracy from the total counts N in the time t and background counts Nb in the time tb. When possible, lead shielding should be used to reduce the magnitude of the background counting rate and hence the required counting time. 322 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 10.16. Counter Resolving Time. The shortest interval in which two suc- cessive events can produce in a counter separate discharges of sufficient amplitude to register as counts is referred to as the resolving time t. Since the actual insensitive time of a counter following a discharge varies somewhat, the measured value of t is the average of these intervals. For most counters the resolving time is in the order of 10~4 sec, which is approximately the collection time of the positive ions formed in the discharge. The value of r for any counter can be ascertained by two general methods in use at the present time. The first is an indirect method in which t is calculated from the observed counting loss, and the second is a direct method where the length of the interval is measured with electronic devices such as the synchroscope. The first of these methods is most often used since it requires no special equipment and can be carried out relatively quickly. Two samples, I and II, with nearly equal activities are prepared and measured as follows: Sample I is counted alone giving a counting rate n\\ without disturbing it sample II is placed in counting position and the total counting rate nn of I + II observed; sample I is then removed and the counting rate n2 of sample II obtained. From the three counting rates and that of the background tib, the resolving time is calculated [35] with the formula n\ + «2 — W12 — fib T = z 2 2 mm The total number of counts in each measurement should be sufficiently large and of roughly the same magnitude to ensure a small probable error in the counting rate since r is estimated from small differences between large numbers. The formula given here is one of several that have been suggested for computing the resolving time from a single set of measurements with a paired source. Although the various formulas differ considerably at high counting rates, they lead to nearly the same value for r at low rates where the formula above is valid. It is essential therefore to use test samples whose activities provide counting rates at levels where 100 {ri\ + n2 — n^/n^ is no greater than several per cent. At the same time, however, the activities should be high compared to the background count to ensure accuracy in a reasonable length of time. Normally, samples with counting rates in the order of 1,000 cpm are found most useful. The direct method for evaluating r requires a linear pulse amplifier and an oscilloscope with accurately known sweep frequencies. The width of the pulse in microseconds can be estimated directly from the oscilloscope trace and taken as a first approximation for r. A more useful device is an oscillo- scope equipped with a single sweep circuit and a persistent screen. The Sec. 10.17] GEIGER-MULLER COUNTERS 323 horizontal sweep is triggered by incoming pulses which are then traced at a fixed position on the screen and allow more careful measurement. This provides a better opportunity to observe closely spaced pulses and hence to verify the resolving time. 10.17. Coincidence Corrections for High Counting Rates. Pulse-counting devices such as counter tubes, ionization chambers, and electrical circuits are never linear in their recording rate when the events registered occur in random intervals. As the average counting rate increases, a greater propor- tion of the events producing the counts occurs in intervals shorter than the resolving time of the device, and therefore pairs and triplets of events are more often registered as a single count. This increase in coincidence rate of multiple events causes the response of a counter to deviate markedly from a linear relation to source activity. Unless a coincidence correction is made, the observed counting rates at high levels (> 10,000 cpm) have little signifi- cance and even at levels greater than 1 ,000 cpm may be in serious error. The coincidence correction therefore must determine from the observed counting rate the true rate of events or that rate which would be observed if the resolving time were zero. It is apparent that the true counting rate should be a function of the resolving time and the registered rate, but it also depends on the mechanism of recovery since two distinct alternatives present themselves. The first mechanism leads to a correction formula [35] in the form N = n + thN cpm where N = true counting rate it = recorded counting rate r = counter resolving time At low counting rates where N ~ n, the more convenient approximation N = n + rn2 cpm can be used. This formula and the preceding one are derived on the assump- tion that the insensitive time is more or less independent of events that occur immediately before or after a count is recorded and, in particular, the occur- rence of an unrecorded event during recovery of the device does not extend the insensitive interval. Although this is not strictly true for counters, the influence of this factor is small and the formulas above are the most nearly valid in this case. It is seen from the formula that as the true activity increases to very high levels the recorded counting rate approaches asymp- totically the limiting value 1/r as N — » <=o ; counts are recorded only as fast as the tube can recover. The second correction formula applies less to counters but represents more accurately the counting loss in electronic and mechanical devices. It 324 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 is given by Volz [41] and Schiff [39] as n = Ne~TN cpm It is derived on the assumption that the occurrence of an event while the device is recovering from previous count is not counted but has the effect of prolonging the recovery as though it had been counted. It is evident from this that as the true activity increases without limit the recorded counting rate goes to zero; the device becomes blocked and no counts are passed. At low counting rates, however, the difference between this and the preceding formula is negligible and either one can be validly used. It is tacitly assumed in applying these formulas that the resolving time of the counter tube is longer than that of all components of the circuits which follow, including that of the register divided by the scaling factor. If this were not true, the formulas above would not be valid since the resolving time of such components would also influence the amount of the correction. Fortunately this requirement is met in modern counting circuits, for the exact calculations in this case prove to be impracticable. Nevertheless, at very high counting rates the correction formulas above are not sufficiently accurate to give reliable values for the true counting rate. Consequently it is often necessary to construct a calibration curve with the requisite accuracy extending to very high counting-rate levels. This can be done analytically with any prescribed accuracy by expressing the true counting rate in terms of a power series in n, the recorded rate, of the form N = n + rn2 + vn3 + ju^4 H~ * ' * cpm An arbitrary number of terms may be used, depending upon the desired accuracy, but the labor involved in computing the coefficients of terms beyond the fourth usually makes the inclusion of higher order terms impracticable. The coefficient of the first term is unity because at very low counting rates N c^n. The second coefficient is the counter resolving time. The physical significance of higher order coefficients is less clear other than that they are coefficients of higher order moments which take into account variations from the simple quadratic curve due to second-order effects that influence the counting rate. Kohman [33] has presented in detail a method for evaluating the coeffi- cients from a least-squares solution of measurements on paired sources. Each set of measurements includes the recorded counting rates n\ of source I, »2 of source II, which is approximately equal in activity to I, their com- bined rate n^, and the background count % (see preceding section for experimental procedure). For the greatest accuracy, many sets of measure- ments should be made with paired sources covering the entire counting range. Sec. 10.18] GEIGER-MULLER COUNTERS 325 With data thus obtained the coefficients are calculated which make the quantity (TV! + N2 - N12 - ntf a minimum. This is simply an expression of the principle of least squares stating that the curve which best fits the data is that for which the sum of the squares of the differences between the observed points and the curve is a minimum. When only two terms of the series are used, the single coefficient is cal- culated [33] by the formula 5 (tii + n2 — n\i — nb)(n\ + n\ — n?2) t = — min I — (n\ + n\- n?2Y «12 in which the sum is taken over the 5 sets of measurements of tii, n2, and n\2 When three terms of the series are desired, the two coefficients r and v are calculated from the 5 sets of data [33] by the formulas JK - - EM LM UK - K2 - JL LM - K2 mm min2 where H = / — =■ (»i + n2 — »i2 - nb)(n\ + n\ - n?2) L-l >i{2 s J = / -o («i + th - »i2 - nb)(n\ + n\ - n&) K = y A (»? + < - »A)(*5 + nl - n® s L = y 4 (n\ + nl - n?2y S m = y a (»f + »5 - ^i32)2 Z_Y ^12 10.18. Coincidence Counting Corrections. As is done for single counters, coincidence counting measurements must be corrected for background, in 326 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 this case only for accidental coincidence counts. Such counts may be produced by the simultaneous arrival of several related particles as in cosmic- ray showers or by the chance arrival of two independent particles in a time of the order It due to a high radiation level such as exists near high-energy accelerators. The number of accidental counts per minute to be expected from a twofold coincidence arrangement is m = IfxiUiT cpm where »i, Th = average counts per minute independently from counters 1 and 2 r = resolving time of counters, min For an r-fold coincidence arrangement, assuming the resolving times to be equal, the accidental counting rate is m = rrr_1(wiW2 • • • nr) cpm If the resolving time of each of the counters in an r-fold coincidence set is different, the accidental counting rate is [22] V"l To Tr/ m = 71)112 ■ • ■ nTTiT2 • • Tr\ 1 h ' ■ ■ i — I cpm V"l To Tr/ If the radiation density is not high, the accidental rate can be determined by dispersing the counters and counting the coincidences. Alternatively, the accidental rate can be made negligibly small by increasing the multiplicity of the system and by reducing the counter resolving time. Accidentals may be further reduced by the proper use of anticoincidence counters; however, their use decreases the counting efficiency because of the over-all increase in resolving time of the set. 10.19. Counter Efficiency. Aside from the counting loss due to the finite resolving time, not all particles traversing a counter will produce discharges. The efficiency with which a counter responds to incident particles can be determined with a three- or higher fold coincident arrangement by counting coincidences with and without the counter as a part of the system. The absolute counter efficiency is then given by nr — mr nr-\ — mr-\ where nr = total counts in time / (or counting rate) of r-fold coincidence arrangement, i.e., with tested counter included wr_! = same but with tested counter removed mr = accidental counts in time / (or counting rate) for r-fold coin- cidence arrangement, i.e., with tested counter included wr_i = accidental counts without tested counter Sec. 10.21] GEIGER-MULLER COUNTERS 327 With the efficiency of each counter known, the total efficiency of an r-fold coincidence arrangement is simply the product of the separate efficiencies or et = e\t2 er. c -K- OUTPUT — O NEG. PULSE 10.20. Averaging Effect of Scaling Circuit. The slowest component in a counting circuit is the mechanical register. Even the most efficient registers are slower than the counter tube by several orders of magnitude. In most cases, therefore, scaling circuits are advisable even at moderate counting rates. For a scale factor 5 and a register resolving time T\ no counts are lost or corrections necessary if T\ < st, where r is the counter-tube resolving time, since the counter tube cannot produce two pulses in an interval shorter than the resolving time of the register. On the other hand, it more frequently occurs that Tx > st, indicating that pairs of output pulses from the scaling circuit can occur in intervals shorter than the register can function. A scaling circuit, however, tends to average the intervals between output pulses since it passes only one pulse after receiving 5 random input pulses and the intervals tend to be more uniform. For high scale factors, 32 and greater, the probability that pulse intervals for a counting rate n deviate markedly from s/n is small. Thus, for a scale of 64, the standard deviation of the lengths of intervals from the average is only one- eighth the average interval [36]. For most purposes, register losses are negli- gible when Ti < s/n for scale factors of 32 and greater. At high counting rates, however, it is usually desirable and often necessary to use scale factors of 128 or decade circuits of 1,000. 10.21. Quenching Circuits. Quench- ing circuits serve to extinguish the dis- charge in a counter tube by suddenly lowering the tube potential below the voltage at which a discharge can con- tinue. This action should occur in an interval that is short as compared to the drift time of the positive ions, and the operating voltage should be returned to the tube by the time all positive ions have been swept out. The recovery time of the external circuit should be shorter than that of the counting tube but not so short as to allow continuation of the discharge. Generally it is in the order of 10~5 sec. External quenching circuits are essential to the operation of non-self- quenching counter tubes but usually are not necessary for self-quenching counters. Nevertheless, they are frequently used as the first stage for any + H.V. Fig. 79. Resistance quenching cir- cuit. When the counter tube dis- charges the current that flows through the tube is sufficient to lower the potential across R below the Geiger- Miiller threshold voltage. The time constant of 10~2 — 10~3 sec is too long for most applications. R = 107 — 109 ohms, C = 2 — 10 yu/xf d. 328 1S0T0PIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 o + +H.V. Fig. 80. Neher-Harper quenching circuit. The grid bias voltage is adjusted at R2 so that tube V is normally nonconducting. When the counter tube discharges, the grid is driven positive and the tube conducts, thus producing the necessary voltage drop in resistance R3 to stop the counter discharge. The time constant of the circuit is deter- mined by R3 and C. Approximate values of the constants are Rl = 106 — 107 ohms, R3 = 10,000 ohms and C = 100 wld. [C. E. Wynn-Williams, Brit. Pat., 421 341 (1934); H. V. Neher and W. W. Harper, Phys. Rev., 49, 940 (1936).] H.V. C- Fig. 81. Multivibrator quenching circuit. The high negative bias, — C makes first section of the multivibrator nonconducting while the second section is normally conducting. A negative pulse from the counter tube initiates one cycle of multivibrator during which the first section conducts momentarily and thus applies a high negative voltage pulse to the counter tube anode to extinguish the discharge. The time constant of the circuit depends primarily on the values of R2 and C2. [/. A. Getting, Phys. Rev., 63, 103 (1938).] kind of counter tube since some quenching circuits also serve as a preampli- fier and provide a low-impedance output which permits the use of long con- necting cables to the scaling or the recording circuit. Furthermore it is found in many instances that the quenching circuit can, when properly- adjusted for the counter, improve the pulse shape and duration, particularly Sec. 10.22] GEIGER-MULLER COUNTERS 329 for old counters. If no quenching or preamplifying circuit is used with a self-quenching counter tube, the lead to the counting circuit should be short and well shielded. Lengths up to several meters usually will not seriously impair the pulse characteristics. The most frequently used quenching circuits are shown in Figs. 79 to 82. + 150 v. OUTPUT Fig. 82. Modified Neher-Pickering quenching circuit. This circuit allows operation of the counter tube with the cathode grounded. It further provides one stage of amplification (V2), stabilization by negative feedback and a cathode follower output (V3). Rl, R3 = 1 megohm R2, R6 = 10,000 ohms RA = 240,000 ohms R5 = 5 megohms Rl, R\\ = 20,000 ohms RS = 1.1 megohms R9 = 56,000 ohms RIO = 5 megohms CI == 50 MMfd C2 = 250 MMfd C3 = 100 w*fd VI = 6AK5 V2, V3 = 6J6 10.22. Scaling Circuits. Scaling circuits must be used whenever the counting rate exceeds that which the mechanical register can follow without loss of counts. For the best registers the limiting rate is about 25 to 50 cps. In practice, however, scaling circuits are normally employed for all but the lowest counting rates. Most counter circuits now available are based on the scale of two, with six such sealing circuits in series to provide a total scale factor of 64. The fundamental scale of two circuit consists of a trigger circuit that has two stable states of operation, the first tube conducting and the second nonconducting, or the reverse. The arrival of a pulse flips the trigger cir- 330 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 V2 f-AA/V-*— AAAr^ ' O— * INPUT OUTPUT NEG. PULSE Fig. 83. Scale of two-trigger circuit. The two units of IT form a trigger circuit delivering alternately a positive and negative pulse. Negative pulses are clipped by V3, thus passing one pulse for every two at the input. Scales of 4, 8, 16, 32, etc., are obtained by adding identical units in series. The neon tube V2 serves as an indicator to extrapolate between multiples of the scale factor. Approximate circuit values are 121, R6 = 400,000 ohms VI = 6N7, 6SL7 or pairs of single triads R2, R5 = 500,000 ohms VI = neon, \i watt R3, RA = 40,000 ohms V3 = 6C5 or similar triode CI, CI =40 MMfd -If C4 OUTPUT O P3 R4 B + POS. PULSE Fig. 84. Thyratron scale of two circuit. Higher scale factors are obtained with additional units in series. Approximate circuit values are 121, R2 = 50,000 ohms; R3, R4 = 20,000 ohms; CI, C2, C3, C4 = 0.002 Mf d ; VI, V2 = Thyratron, e.g., 884. Sec. 10.22] GEIGER-MULLER COUNTERS 331 101 r-01.. Oi 1 1 ,~©J ■| i O ..-©J r-AAA^ (, < 5 o< 5-1 z + _ CD 0 AW. ■A/W-* — WV- Ayw 3 0. rAAA^-f — WV — fAAA^ J WV < CD 0 ii XI o d> t+-l u OJ > S3 -a o CD «*H >-. 42 4= CJ a 5J — -a CD 43 to a r2 ^ ra ^ »rt '/j ^ -: a ~ "a « o c o to O on en ^ •- 42 >- -O 3 O O " 4-1 ^~* t-l CD O 43 •O a sj 43 u f 1 ~^ *_ » to - g 2 (J *- D 43 -a H CJ cu -a 8 43 £3 m On ■4— t o o -4-1 c o § £ u o 10 00 .2-3 J* ^e^ 3 c n! o 332 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 V2 REGISTER OB+ Fig. 86. Multivibrator recording circuit. 221 = 1 megohm R2 = 100,000 ohms 223 = 50,000 ohms 224 = 500,000 ohms 226 = 5,000 ohms Approximate values of circuit constants are CI = 0.0001 /ifd C2 = 0.001 /ifd VI = 6SJ7, 6C6 F2 = 6V6, 6F6 O— f C2 R4 n -=- O O ~^" o B+ I B+ Fig. 87. Thyratron recording circuit. Two arrangements of the register circuit are illus- trated to the right of the broken lines. Circuit I is preferred since the recorder is at ground potential and there is less chance of damage to the register due to surges. Approximate circuit values are 221, R3 = 500,000 ohms CI = 0.001 Mfd R2 = 100,000 ohms C2 = 1 - 4 /*fd 224 = 200,000 ohms VI = 6C5 225 = 10,000 ohms V2 = Thyratron; e.g., 884 cuit from one state to the other; hence two input pulses of the same sign are required for a complete cycle. Although two output pulses also appear per cycle, they are opposite in polarity and one pulse can be rejected by a "clipping" circuit immediately following each of the trigger circuits. Nor- mally, the negative pulse, which is the first output pulse in the cycle is Sec. 10.23] GEIGER-M ULLER CO UN TERS 333 rejected. This is usually accomplished either with a multigrid tube with a negative grid bias or with a diode, both of which pass only positive pulses. Typical scale of two circuits are shown in Figs. 83 and 84. Less frequently used in the past, decade counters and "ring" circuits are now finding more frequent application. An example of a highly efficient decade circuit is shown in Fig. 85. TO REGISTER Q Fig. 88. Recording circuit from "Model 200" pulse counter. 71 reshapes the pulse into a rectangular form before it enters the power tube V2. The output pulse length is 0.01 sec and delivers sufficient power to operate any register that requires no more than 40 ma and 300 volts. [W 706(1947).] Rl A. Higinbotham, J. Gallagher, and M. Sands, Rev. Sci. Instruments, 18, 2 megohms R2 = 200,000 ohms R3 = 1 megohm U4 = 1,500 ohms R5 = 10,000 ohms R6 = 20,000 ohms Rl = 30,000 ohms R% = 100,000 ohms CI = 0.05 Mfd CI = 0.005 Mfd C3 = 20pfd C4 = 8 Mfd C5 = 4 Mfd C6 = 0.01 ,ufd VI = 6SL7 V2 = 6V7 10.23. Discriminators. Discriminating circuits are often placed before counter circuits for the purpose of rejecting pulses smaller than a predeter- mined peak voltage. Their function is particularly useful for proportional counters where the pulse size depends upon the intensity of ionization pro- duced by the incident particle. Thus, in counting alpha particles the back- ground is effectively reduced by rejecting the smaller pulses initiated by electrons, gamma rays, and protons. 334 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 With more complicated circuits, pulses lying within a desired voltage range can be passed, whereas pulses smaller and larger are rejected. With several such units, pulses produced by electrons, protons, alpha particles, and fission fragments may be distinguished and recorded separately. 10.24. Recording Circuits. The recording or register-driving circuit is essentially a power output stage delivering sufficient power at each pulse to A OUTPUT Fig. 89. Rossi coincidence circuit. A threefold coincidence arrangement is shown but may be extended to an TV-fold circuit by placing N identical input stages in parallel with the tube plates connected to a common resistance R as shown. All tubes are normally conducting. Any fraction of the coincidence set may be made nonconducting by negative input pulses without altering appreciably the voltage at A provided at least one tube remains conducting. If, however, all N tubes are cut off simultaneously, their combined resistance becomes high and a large pulse is produced at the output A. [B. Rossi, Nature, 125, 636 (1930).] actuate a mechanical register. For most registers available for counter circuits the output pulse should be 200 to 300 volts at 16 to 50 ma. The ideal output pulse shape is rectangular with a width of the order of 0.01 sec. This can usually be achieved by preforming the pulse before it enters the final power output stage. Registers commonly used in counter circuits consist of a light moving armature actuated by the magnetic field of an inductance placed in the plate circuit of the output stage. Through a ratchet mechanism connected to the armature, each pulse is indicated by unit movement on some kind of dial used as an indicating device. The maximum counting rate of a register depends on the inertia of the mechanism and the driving power. Although some registers will indicate as Sec. 10.25] GEIGER-MULLER COUNTERS 335 many as 100 or more uniformly spaced pulses per second, considerable error is introduced in attempting to register random counts at this rate. If the pulse width or the register resolving time is of the order of 0.01 sec, two or more pulses occurring within an interval equal to or less than this are counted OUTPUT o -o V) Ul £0 ft -!(- tt tt OUTPUT Fig. 90. Diode coincidence circuit. [B. Howland, C. A. Schroeder, and V. P. Skipman, Rev. Sci. Instruments, 18, 551 (1947).] as one and therefore result in considerable loss of counts at high rates. Typical recording circuits are shown in Figs. 86, 87, and 88. 10.25. Coincidence Circuits. Coincidence circuits are electronic dis- criminating devices that permit a count to be registered only when a pre- determined number of counter tubes in the circuit discharge simultaneously, or more exactly, within a short time interval, usually of the order of the 336 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 counter-tube resolving time. Typical coincidence circuits are shown in Figs. 89 and 90. If the polarity of the pulses from one or more counter tubes in a circuit is reversed before being mixed with simultaneous pulses from the remainder Fig. 91. Anticoincidence circuit. A pulse at input 3 is reversed in polarity in F4 and will cancel pulses at inputs 1 and 2 if they occur simultaneously with a pulse at input 3. VI, V2, and Vi are normally conducting whereas V\ is normally nonconducting. The resistance R is chosen to give the correct total plate current for VI and 72. [G. Herzog, Rev. Sci. Instru- ments, 11, 85 (1940).] of the tubes, such counter tubes form an anticoincidence set. Simultaneous discharges in the coincidence and anticoincidence sets cancel in the mixing stage and are therefore not registered as a count. Furthermore, independent discharges of the anticoincidence set are clipped at some stage in the counter circuit, thus permitting only independent discharges of the coincidence set to register as counts. Examples of such circuits are shown in Figs. 89, 90, and 91. 10.26. Counting-rate Meter. The counting-rate meter is a circuit devel- oped for the purpose of providing an output, usually a d-c voltage, which is Sec. 10.26] GEIGER-MULLRR COUNTERS 337 proportional to the average rate of incidence of random or periodic pulses [25-28]. A successful counting-rate meter circuit is shown in Fig. 94 and described in principle below [27,28]. INPUT I O OUTPUT O _n_n_ Fig. 92. Pulse-mixing circuit. Fig. 93. Diode pulse-mixing circuit. Rev. Sci. Instruments, 18, 551 (1947).] OUTPUT O n_n_n [B. Rowland, C. A. Schroeder, and V. P. Shipman, Amplified pulses from a counter are fed into a conventional multivibrator which serves as a pulse equalizer by providing an output pulse uniform in size and shape and positive in polarity for each input pulse. The equalized pulses are then impressed on the grid of the vacuum tube of the integrating circuit which contains a resistive-capacitive tank circuit in series with its plate. The d-c voltage developed across the RC circuit is proportional to 338 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 the average pulse rate and, hence, a vacuum-tube voltmeter included in the circuit may be calibrated directly in terms of average counting rate. Alter- natively, automatic recording devices can be inserted when continuous records are desirable. ! ! ! ' ■PULSE EQUALIZER 1 INTEGRATING CIRCUIT VOLTMETER Fig. 94. Typical counting-rate meter. (1947).] Rl, RS, RIO = 100,000 ohms R2, 124 = 250,000 ohms R3, R22 = 300,000 ohms R6, R25 = 2,000 ohms Rl = 500,000 ohms R8 = 3,300 ohms R9 = 30,000 ohms 2211, RU, R13 = 10 megohms RU = 50,000 ohms R15 = 25,000 ohms R\6, R17, #18, R19, R20 = 15,000 ohms [A. Kip, et ah, Rev. Sci. Instruments 117, 323 R21 = 8,500 ohms R23 = 12,000 ohms R2A, R26 = 1,000 ohms CI, C2 = 100 /xMfd C3 =0.5 Mid C4 = 200 MMid C5 = 2 jufd, polystyrene 71, V2, V3 = 6SJ7 74 = 6AC7 - GT/G Ml = D-C Voltmeter /l = Phone jack for recording milliammeter In principle the integrating circuit establishes an equilibrium voltage across the RC tank circuit which is directly proportional to the counting rate. Equilibrium is reached when the charge leakage rate through the high resist- ance of the tank circuit is equal to the rate of charge added by the pulses. In general, equilibrium is established after several decay half-times of the RC circuit. Starting from zero time, equilibrium is reached [27] when t0 = RCm log 2nRC + 0.394) sec where n = number of pulses per unit time Sec. 10.26] GEIGER-MULIER COUNTERS 339 The statistics of this type of counting-rate meter depend on the fact that the reading at any instant is influenced by all previous pulses weighted expo- nentially according to their elapsed time. The absolute probable error of a single reading is given by [27] fey If a continuous recording is made, the probable error may be considerably reduced. From a record taken over a time T the mean value of n is deter- mined by drawing a line through the trace which divides the fluctuations into equal areas on both sides. The probable error of the mean is [27] then (1 + 2T/RQ* r(T) = r (1 + T/RC) REFERENCES FOR CHAP. 10 1. Stever, H. G.-.Phys. Rev., 61, 38 (1942). 2. Wilkemmy, M. H., and W. R. Kanne: Phys. Rev., 62, 534 (1942). 3. Montgomery, C. G., and D. D. Montgomery, Phys. Rev., 57, 1030 (1940). 4. Korff, S. A., and R. D. Present: Phys. Rev., 65, 274 (1944). 5. Ramsey, W. E.: Phys. Rev., 57, 1022 and 1061 (1940). 6. Korff, S. A.: "Electron and Nuclear Counters," D. Van Nostrand Company, Inc., New York, 1946. 7. Olephant, M. L., and P. B. MooN-.Proc. Roy. Soc. {London), A127, 388 (1930). 8. Strajman, E.: Rev. Sci. Instruments, 17, 232 (1946). 9. Montgomery, C. G., and D. D. Montgomery, Rev. Sci. Instruments, 18, 411 (1947). 10. Black, J. F., and H. S. Taylor: /. Chem. Phys., 11, 395 (1943). 11. Pace, N., and L. Kline: Naval Medical Research Institute, National Naval Medical Center, Bethesda, Md., Proj. X-191, No. 5, 1946. 12. Allen, M. G., and S. J. Ruben: /. Am. Chem. Soc., 64, 948 (1942). 13. Cornog, R., and W. F. Llbby: Phys. Rev., 54, 1056 (1941). 14. Miller, W. W.: Science, 105, 123 (1947); Rev. Sci. Instruments, 18, 496 (1947). 15. Korff, S. A., and W. E. Danforth: Phys. Rev., 55, 980 (1939). 16. Watson, W. W., J. O. Buchanan, and F. K. Edder: Phys. Rev.. 71, 887 (1947). 17. Barschall, H. H., and H. A. Bethe: Rev. Sci. Instruments, 18, 147 (1947). 18. Coon, F. H., and R. A. Nobles: Rev. Sci. Instrument, 18, 44 (1947). 19. Bateman, R.-.Phil. Mag., 20, 704 (1910). 20. Ramsey, W. E.: Phys. Rev., 57, 1022 (1940). 21. Kurbatov, V. D., and H. B. Mann: Phys. Rev., 68, 40 (1945). 22. Eckart, Carl, and F. R. Shonka: Phys. Rev., 53, 752 (1938). 23. Curtiss, L. F., and B. W. Brown: Nat. Bur. Standards J. Research, 34, 53 (1945). 24. Curtiss, L. F.: Nat. Bur. Standards J. Research, 23, 137 (1939). 25. Ginrich, N. S., R. D. Evans, and H. E. Edgerton: Rev. Sci. Instruments, 7, 450 (1936). 26. Evans, R. D., and R. L. Alder: Rev. Sci. Instruments, 10, 332 (1939). 27. Kip, A. F., A. Bousquet, R. D. Evans, and W. Tuttle: Rev. Sci. Instruments, 17, 323 (1946). 28. Kip, A. F., and R. D. Evans: Phys. Rev., 59, 920A (1941). 340 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 29. Haines, C. L.: Rev. Set. Instruments, 7, 411 (1936). 30. Simpson, J. A.: Atomic Energy Commission Report MDDC 31. Ruark, A. E., and H. C. Urey: "Atoms, Molecules, and Quanta," McGraw-Hill Book Company, Inc., New York, 1930. 32. Fitch, V. L., and E. W. Tttterton: Rev. Sci. Instruments, 18, 821 (1947). 33. Kohman, T. P.: Atomic Energy Commission Report MDDC 429, 1945. 34. Hull, D. E.: Rev. Sci. Instruments, 11, 404 (1940). 35. Ruark, A. E., and F. E. Brammer: Phys. Rev., 52, 322 (1937). 36. Present, R. D.: Phys. Rev., 72, 243 (1947). See also the following references on counting statistics: 37. Bateman, R.-.Phil. Mag., 20, 704 (1910). 38. Keston, A. S.: Rev. Sci. Instruments, 14, 293 (1943). 39. Schtff, L. I.: Phys. Rev., 50, 88 (1936). 40. Gnedenko, B. V.: 7. Exptl. Theoret. Phys. (U.S.S.R.), 11, 101 (1941). 41. Volz, H.: Z. Phys., 93, 539 (1935). CHAPTER 11 PROPORTIONAL COUNTERS 11.1. General Features and Use. The proportional counter is a variable gas-amplifying diode, in general, similar to a Geiger-Muller discharge tube in construction and materials. The particular usefulness of this form of counter derives from the nearly linear relation between the output pulse size from the counter and the total ionization produced initially in the counter by a charged particle. With appropriate electronic circuits, it is possible to discriminate between kinds of particles traversing the counter and frequently between similar heavy particles of different energies. Thus, in decreasing order of magnitude, definite pulse size for a particular counter can be asso- ciated with fission fragments, alpha particles, protons, and electrons. The property of discrimination can be used to advantage for reducing the observed background from light particles and gamma radiation when low intensities of heavily ionizing particles are measured, by adjusting the counter circuit to amplify and register only pulses larger than a predetermined size. The design of proportional counters depends mainly upon the radiation to be measured. For most applications three forms are commonly used: 1. "Bell" shaped counters with tungsten wire anodes and with thin windows for detecting alpha and beta radiations. 2. Cylindrical glass or metal tubes with coaxial tungsten wire anodes for neutrons and cosmic radiations. 3. Point counters [1] similar to "bell" counters but with a spherical metal anode 1 to 2 mm in diameter supported near the counter window. The sensitive region of these counters lies in only a small volume surrounding the ball anode. In addition a design developed by Zipprich [2], consisting of two parallel plate electrodes and an accelerating grid placed between the plates, is less often used but possesses the advantage of a well-defined sensitive region. Filling gases for proportional counters need not contain polyatomic, or quenching, gases although the inclusion of such gases provides greater stabil- ity, particularly for large pulses. The gases most frequently used are a mixture of argon, 10 to 25 per cent, and methane, 75 to 90 per cent, or various mixtures of nitrogen, methane, ethane, and ether. Pressures commonly used vary from a few centimeters to half an atmosphere. 341 342 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS Chap. 11 The operating voltage for a proportional counter is determined largely by the size pulse required for the particular radiation to be measured. Before the counter can be used, however, it is necessary to determine the proportional region by plotting the counting rate against anode voltage. As shown in Fig. 77, the region for proportional pulse size lies between the starting voltage at which the first counts are detected and the beginning of the transition to the Geiger-Miiller region. 11.2. Theory of Operation. When certain simplifying assumptions are made which appear to be valid for most proportional counters, the formation of a voltage pulse proportional to the initial number of ion pairs is adequately explained in terms of a Townsend avalanche [3,4,5]. It is assumed that (1) the probability of electron photoemission is negligibly small; (2) the probability for secondary electron emission by positive ions collected at the cathode is negligibly small; (3) negative ions such as O-, F~, and Cl~ are not sufficiently numerous to produce an appreciable lag in the counter action; (4) recombination of positive ions and electrons within the gas is negligible. From the N initial ion pairs produced by an incident charged particle, the electrons are collected at the anode in a time of the order of a few micro- seconds while the positive ions formed remain essentially stationary during this time. Within a distance of several mean free paths from the anode, electrons acquire sufficient energy between collisions in the strong electric field to produce additional ion pairs and hence a Townsend avalanche. The avalanche at this point differs from the Geiger-Miiller counter discharge in that the descendants of a single electron multiply to a smaller and, on the average, constant number which is a function of the operating voltage. The factor by which an electron multiplies itself in the avalanche, called the amplification A , may have a value up to a maximum of 104, although generally it is of the order of 103 or less. Within the range from 1 to 104, its value can be chosen arbitrarily by the proper choice of operating voltage, a factor that permits some control over the pulse size which may be desired. When the amplification factor increases beyond 103 or 104 owing to a high operating voltage, the pulse size is no longer strictly proportional and some of the characteristics associated with the Geiger-Miiller discharge make their appearance. Following the completion of the Townsend avalanche the residual positive ion cloud drifts slowly to the cathode. However, during the dead time of roughly 10-4 sec, it still exists as a space charge sufficiently near the anode to reduce the effective electric field and thus prevent a second avalanche which might be initiated by a charged particle arriving within this time. The total charge collected by the anode is approximately Q = eAN, where e is the electronic charge. With a total capacitance of C for the Sec. 11.2] PROPORTIONAL COUNTERS 343 counter and its immediately connected circuit, the peak pulse voltage is then V eAN C REFERENCES FOR CHAP. 11 1. Geiger, H., and O. Klemperer: Z. Pkys., 36, 364 (1926). 2. Zipprich, B.:Z. Pkys., 36, 364 (1926). 3. Rose, M. E., and S. A. Korff: Pkys. Rev., 59, 850 (1941). 4. Loeb, L. B.: "Fundamental Processes of Electrical Discharge in Gases," John Wiley & Sons, Inc., New York, 1939. 5. Korff, S. A.: "Electron and Nuclear Counters," D. Van Nostrand Company, Inc., New York, 1946. CHAPTER 12 IONIZATION CHAMBERS 12.1. Description. The ionization chamber may be described in the most general terms as a gas-filled chamber in which a constant electric field is maintained by a set of electrodes for the collection of ions formed by incident ionizing radiation. In principle, the charge collected should exactly equal the total ionization formed in the sensitive volume of the chamber by the incident radiation. This linear relationship between ionization and collected charge is the most important distinguishing characteristic of the ionization chamber. It is necessary, therefore, that the field strength be high enough to collect the ions formed before appreciable recombination and diffusion of ions has taken place in the gas, yet not so high as to cause the formation of addi- tional ions by multiplicative processes as the charge drifts to the collecting electrodes (see Fig. 78). The useful operating range of potential difference (arbitrary with respect to ground potential) maintained between the elec- trodes can be found by observing the ionization in the chamber as a function of voltage for a constant source of radiation. Starting with zero potential difference, the detected ionization increases with voltage until saturation is attained. The ionization then changes relatively little with further increase in voltage until the field strength becomes sufficiently high to induce ion multiplication by electrons as they drift to the anode. The operating voltage should, of course, lie in the plateau region. In practice, the field strengths used vary from 20 to 500 volts per cm and usually are not critical. Two methods for the detection of the ionization in the chamber may be used: either measurement of the constant voltage produced by the flow of collected charge through a resistance, or measurement of the rate of change of voltage as charge is collected. With a high resistance R connected be- tween the electrodes, the change in potential difference between them after a time t, assuming the rate of ionization is constant, is AV = Vo - V = neR{\ - e~l/RC) volts where V0 = operating voltage n — number of ions formed per second e = electronic charge C = capacitance of electrode system When / >>> RC, the voltage change reaches a constant value AV = neR. The capacitance C can usually be made very small, ~ 10 to 100 pL/^id, so that the 344 Sec. 12.1] IONIZATION CHAMBERS 345 time required to reach the steady state is conveniently short, < 1 sec, even for the high resistances necessary to make AV easily measurable. For ionization chambers in which pulses are detected, it is usually necessary to make RC less than 0.001 sec On the other hand, if R is removed or, more io electrometer Fig. 95. Schematic diagram of the parallel-plate ionization chamber. The essential components of these chambers are A, low-leakage insulators between the electrodes; B, guard ring, maintained at the same potential as the collecting electrode; C, collecting electrode (anode); D, high-voltage electrode for maintaining the charge collecting field (cathode); E, chamber which may be designed to withstand high or low pressures or may- serve merely to shield against external fields. exactly, made very large, ~ 1013 ohms, it is convenient to measure the time rate of change of AV since d(AV) ne dt or in an interval of time / « RC = ^e -t/RC C AT' ^ 4 AT =rl volts sec volts/sec and the linear increase in AV with time is measured. This method is usually used only when the smallest ion currents, ne < 10ru amp, are to be detected. The details of the construction of an ionization chamber depend to some extent on the type of radiation to be detected, but more often its design and 346 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 12 — 2 \\\\V\\\\\\\^ To Detecting Device WWWWWNN^ Fig. 96. Thimble ionization chamber. construction materials are determined by the particular circumstances of the measurements. Despite great variations in design, the chambers are, in most instances, built around two basic forms of collecting electrode geometry. The first is a parallel-plate condenser shown in Fig. 95. The central portion of one plate of the condenser is highly insulated and connected directly to the detecting instrument as well as to some means for charging it to the desired potential, often ground potential, either through a charging (or grounding) switch or a high grid resistance if a vacuum-tube amplifier is used. The remainder of the plate bounding the collecting electrode serves as a guard ring and is maintained at the same potential to define accurately the sensitive volume of the chamber and to prevent leakage of current across the insulator supporting the collect- ing electrode. The opposite plate of the condenser is maintained at the potential necessary to provide the requisite field strength between the electrodes. The second form of chamber frequently used consists of a cylindrical anode (or cathode) within which a highly insulated rod-shaped collecting electrode is coaxially mounted, as shown in Fig. 96. The functions of the guard ring, which is maintained at the same potential as the collecting electrode, are especially important in chambers intended for measurement of weak ionization. The least important of these is to define the sensitive volume. Its more important functions are (1) prevention of leakage currents across the insulator supporting the collecting electrode by maintaining zero potential gradient, (2) prevention of insulator stresses due to potential gradients, since polarization and relaxation of the insulator may induce voltages comparable to those produced by the ions, and (3) elimina- tion of steep potential gradients near any part of the collecting electrode system. All ionizing radiations can be detected with appropriate forms of chambers. Heavily ionizing particles such as protons, alpha particles, and fission frag- ments produce ionization of sufficient intensity to be detected and counted as separate events using the same techniques and external counting circuits as for Geiger-Miiller and proportional counters. Less strongly ionizing radiations such as gamma rays and beta particles cannot be detected and counted as separate events but must be measured by the average charge collected per unit time at the electrodes. Chambers designed for radiation detection by the time rate of accumulation of charge normally will operate satisfactorily when filled with any gas of low molecular weight, including those gases, such as oxygen, water, carbon Sec. 12.2] IONIZATION CHAMBERS 347 monoxide, carbon dioxide, and the halogens, which form negative ions. Air at atmospheric pressure is the most frequently used gas. Chambers operated at high pressures for the purpose of contracting the range of the radiation are often filled with argon or krypton since these gases have greater stopping power and large cross sections for ionization. Pulse chambers, on the other hand, frequently exhibit erratic performance and provide poor pulse shapes when filled with negative ion-forming gases. Usually they are operated with nitrogen, argon, or methane at atmospheric pressure, and in many instances it is convenient to allow the gas to stream through the chamber. This latter method is especially useful when the source of radiation is placed in the chamber and is frequently changed as in measuring radioactive samples. 12.2. Applications. The ionization chamber has found more extensive use and more diverse adaptations than any other device for measuring ionizing radiations. Its simplicity and comparative ruggedness are factors to be considered to its advantage but, most important, the ionization chamber lends itself to measurements of radiation under conditions that cannot be duplicated with other means for detecting ionization. In general, applica- tions of the chamber may be divided into two categories. Although these categories are somewhat superficial, there exists an important physical distinction between them. The first includes measurements of radiations that have ranges comparable to or smaller than the dimensions of the gas volume, and the second applies to penetrating radiations that have ranges very much greater than the dimensions of the chamber. The first category involves measurements on short-range charged particles and slow neutrons. The ionization produced in the chamber can usually be interpreted unequivocally in terms of the number of primary particles or as relative activity of the source of radiation. The design of chambers for this purpose is largely a matter of expediency, consistent with special features of the application and acceptable instrument designing. The source of primary radiation, because of the comparatively short range of charged particles, must be placed within the chamber to permit the greatest possible portion of the range to lie in the sensitive gas volume. In the case of slow neutrons the source may be boron or a fissionable material (see Sec. 10.10). In nearly all cases where the source material is solid, it can be deposited in a thin film on one of the electrodes or on a suitable support that is mounted adjacent to the sensitive volume of the chamber. For the highest efficiency the film thickness should equal approximately the range of the particle in the sub- stance. A somewhat greater ionization efficiency and sensitivity can be achieved when the substance can be introduced as part of the chamber gas since self-absorption is then eliminated and the geometrical efficiency is increased to very nearly 100 per cent. Thus boron tritfuoride is most com- monly used for detecting slow neutrons, and carbon dioxide and hydrogen- 348 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 12 filled chambers are among the most sensitive instruments for measuring C14 and H3, respectively. The second category of applications involves gamma radiation and fast neutrons but may also include charged particles with very high energies such as those encountered in cosmic rays and from high-energy accelerators. The interpretation of the measured ionization in this case is not always obvious since the chamber walls perform an important function in affecting the observed intensity of ionization. When the range, or more correctly the half-value thickness, of the primary radiation in the gas contained in the chamber is very much greater than the chamber dimensions, the ionization produced and measured is, in the most general case, the sum of the ionization produced in the gas volume by the primary radiation plus that produced by recoil and scattered particles from the walls. With chambers of wholly arbitrary dimensions and materials it is difficult to assign values for the energy and flux of primary radiation from the measured values of the ionization because it is nearly impossible to ascer- tain what fraction of the ionization is contributed by secondary corpuscular radiation produced in the walls. Only when the chamber has been calibrated for a specific type of primary radiation and for a particular energy can the indicated ionization be interpreted in terms of dose or as energy flux. The contribution of the walls to the observed ionization depends prin- cipally on the following factors: 1. Atomic number of wall materials. 2. Thickness of the wall relative to the range of secondary corpuscular radiation. 3. Dimensions of the chamber relative to range of secondary corpuscular radiation. 4. Attenuation of primary radiation effected in the walls. 5. In the case of neutrons, possible nuclear reactions. The only simple conclusion that can be drawn concerning these factors is that the maximum wall effect is attained when the wall thickness equals the range of secondary particles produced in it and the material is chosen to give the highest yield of particles; for gamma rays these are materials possessing the highest electron densities such as copper and lead, and for fast neutrons these are hydrogenous substances. In two special cases the foregoing difficulties in evaluating the physical significance of the measured ionization reduces to results that permit simple interpretation. In the first case, consider a collimated beam of primary radiation passing between but not striking the electrodes of a parallel plate chamber. If the walls are placed at large distances compared to the range of the secondary particles in the chamber gas, then the ionization produced in the sensitive volume corresponds exactly to the energy absorbed in the Sec. 12.2] IONIZATION CHAMBERS 349 gas. If the gas is air, the average energy absorbed per ion pair is known for various radiations and the total energy absorbed in the sensitive gas volume is readily calculated. The second special type of ionization chamber provides a means for measuring the amount of energy absorbed from the primary radiation in traversing solid substances and therefore is of the most profound importance to dosimetry and to the absolute measurement of energy flux. For this reason it is described here in somewhat greater detail. It has been shown by Gray [8,9,13] that for a small air-cavity surrounded by a medium M the energy absorbed in M per unit volume per second from the primary radiation is related to the ionization observed in the cavity by the expression E — SJW ergs or mev/cc/sec where E = energy absorbed per unit volume per second in medium M (wall material) S = ratio of stopping power for secondary particles in medium M to stopping power of the gas W = average energy absorbed from secondary particles to form one ion pair in the gas (see Sec. 3.9) / = number of ion pairs formed in the cavity per unit volume per second The quantity S is the ratio of energy loss per unit length of path in the medium M to that in the gas. This may be expressed most conveniently in terms of the atomic stopping powers B and densities p of the two media. Thus, 5 = pmBm/pgBg. In many instances the values of B are not known with certainty, but if the atomic composition of the gas can be made similar to that of M, then Bm = Bg and 5 is given directly as the ratio of only the densities. The simple but important relation above is valid only when the cavity ionization chamber meets the following physical conditions: 1. The dimensions of the cavity must be smaller than the average range of the secondary corpuscular radiation in the gas contained in the cavity. 2. The wall thickness of material M surrounding the cavity must be equal to or greater than the maximum range of the secondary particles in M. 3. The primary radiation should not be appreciably attenuated in trav- ersing the chamber. 4. The relative stopping power must be independent of the velocity of the secondary particles. It is apparent from these conditions that for the equation to be valid the intensity of secondary corpuscular radiation passing through the cavity must exactly equal its intensity within the wall material when it is in radiative equilibrium with the penetrating primary component. 350 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 12 The significant properties of chambers for which the formula and condi- tions above are valid are [9] (1) for sufficiently small chambers the ionization per unit volume is independent of the size of the cavity; (2) the ionization is directly proportional to the gas pressure; (3) for the same primary radiation the ionization in chambers with different wall materials is proportional to the energy absorbed per unit volume of wall material and inversely propor- tional to its stopping power. It is apparent that size is a distinguishing and crucial feature of the cavity chamber, but it is not always clear just how small the dimensions must be since the minimum range of recoil electrons in the case of gamma rays, and recoil protons from neutrons, is essentially zero. In principle the size should be "infinitesimal," but in practice cavity dimensions of the order of millimeters are usually permissible without introducing appreciable error. In any actual application this can be tested with cavities of progressively larger dimensions. The largest cavity that still indicates a constant ioniza- tion per unit volume can be regarded as sufficiently small for that particular wall material and radiation. The exactness of the cavity formula above is also influenced by two factors in addition to finite cavity size. These are (1) the ionization produced in the gas by the primary radiation directly is, in general, not equal to that which would be produced in an equivalent volume of wall material, and (2) the presence of the cavity alters slightly the energy and directional dis- tribution of the secondary corpuscular radiation. These factors are only significant when the constituents of the wall material and gas differ markedly in atomic number, such as in the combination of air and lead. In practice their influence can be ascertained by observing the ionization as a function of pressure. If pressure and ionization are proportional, the cavity formula can be assumed to be valid. The most accurate results are to be expected with wall material and gas of the same atomic composition — a combination that is sometimes difficult to achieve. In applications of the cavity chamber to problems of dosimetry the wall materials usually consists of compositions containing several kinds of atoms in proportions similar to the composition of tissue, and in addition, the primary radiation frequently is heteroenergetic. If these conditions are to be taken into account explicitly, the cavity formula, though still valid, is modified [10] into the form n E = $iV \ fijiyer = Cq mv/sec » = i where v* = values of individual determinations in units of mv per sec This is calculated for NB determinations of the background and A7* deter- Sec. 12.4] IONIZATION CHAMBERS 357 minations of the measured radiation plus background to obtain the total standard deviation from the mean or, where, as before, ot = ( UII. All energies are in units of mev. Level energies are given with respect to the 2.32/3" transition. [From II. Bradt and P. Scherrer, Helv. Phys. Acta., 18, 424 (1945).] will not change its composition for a long time. The sample is sealed per- manently with aluminum foil. b. RaE Standard. In aged rocks containing uranium, the radium and its decay products are in equilibrium and the radium content may be determined, for example, from the radon-producing power. Knowing the radium content, the quantity of RaD can also be calculated and, along with other lead iso- topes, separated quantitatively from the rock sample. Given time, all radioactive lead isotopes except RaD decay completely and equilibrium will be reached between RaD and its daughter substance RaE (see disintegration scheme, Chap. 7, uranium-radium series). The radiations emitted by this sample are then as shown in Table 36. The number of disintegrations from RaD and RaE being known, such a sample may be used for beta-particle standardization by absorbing the radiations of the RaD and Po210. This may be done with an aluminum Sec. 13.6] STANDARDIZATION OF RADIOACTIVE SAMPLES 367 absorber of 10 mg per cm'. Usually the RaD is electrolytically deposited in a very thin surface layer, and if sufficient time is allowed, the alpha dis- integration of polonium may be measured to verify the sample activity. RaE has a single beta particle and no gamma rays, but the beta transition is classified as forbidden so that the spectrum is different from that of beta particles in allowed transitions. There is also one alpha particle emitted for about every million betas. The Bureau of Standards [16] has made a Table 36. Radiations from RaD, RaE, and Po Element Alpha particle, mev Beta particle, mev Gamma ray, mev Half-Life RaD 210 0.025 1.17 0.047 22 years 5 . 0 days 140 days RaE 210 4.87(10-4-10-6 %) 5.298 (100%) Po 210 0.8 (weak) number of standards of this type for distribution among radioisotope workers. These standards can be used to calibrate the approximate efficiency of Geiger counters for beta radiations. However, when this is done a number of rather complex factors have to be considered. These will be discussed in Sec. 13.10. In the method given by Broido et al. [15] for preparation of RaE standards, chemical separation of RaE from RaD and Po210 is utilized. A mixture of RaD, E, and F should be taken up in 10 ml of 0.1 A hydrochloric acid. Add 20 mg powdered nickel, heat the mixture to 80°C, and stir for 3 min. The powdered nickel then takes up the RaE and F. Centrifuge and wash the precipitated nickel three times with 0.1 A hydrochloric acid. Dissolve the nickel with ~1 ml aqua regia and dilute to 10 ml. The nickel may now be separated by addition of 20 mg bismuth carrier and then an excess of ammo- nium hydroxide. Bismuth hydroxide precipitates carrying RaE and fluorine but leaving the nickel in solution. In order to separate the RaF from the RaE an ion exchange column may be used. The bismuth hydroxide is dissolved in hydrochloric acid diluted to an acidity of 0.1 A and passed through a 1-cm diameter column made up of 10 ml 40-60 mesh 1R-1 resin. The bismuth and RaF are absorbed in the column. The bismuth may be eluted with 3A nitric acid (approximately 10 ml.) leaving the RaF in the column. The purity of the RaE preparation may be checked by half-life and absorption measurements and with growth curves of the alpha activity of RaF (Po210). The absolute RaE disintegration rate may be obtained by measuring the absolute RaF activity, // (/), in an alpha-particle chamber and extrapolating back to the amount of RaE at zero time Z«(0), using the equation 368 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 I f(t) (l -KM /.(O) - -\tt p—'kjt where Xe and \/ are the decay constants of RaE and RaF, respectively. The beta disintegration rate of the RaE sample at time / is then hit) = Ie(0)er^ 13.7. Beta-particle Standardization by Direct Measurement of the Charge of the Particles. If a beta emitter is placed on an electrically insulated sup- port in the center of an evacuated metal chamber, the charge due to the beta particles may be observed when these particles are absorbed by the walls. This method has recently been used by Failla [19] and his associates to obtain standardization of some important beta-active isotopes, such as P32. If precautions are followed to avoid secondary effects, the results obtained by this method are within 5 per cent of other independent methods. The value of this method lies in its independence from other methods. For secondary standardization its use would probably not be convenient for routine measurement. 13.8. Indirect Standardization by Calorimetric Measurement of the Total Energy. Zumwalt and his associates [20] employed an isothermal calorim- eter for the determination of the rate of heat evolution from radioactive phosphorus when the beta particles were stopped in the calorimeter. The measurement was carried out with about 25 millicuries of P32 at the tempera- ture of liquid nitrogen, using the rate of evaporation of nitrogen at constant pressure as the measure of the heat output. With measurements of this kind it is necessary to determine certain constants in order to evaluate the absolute disintegration rate. The total energy output is the product of the emission rate and the average energy of the beta particles; hence, it is essen- tial to determine the average energy independently from measurements of the energy distribution of the P32 beta particles. A small fraction of the beta-particle energy is converted into Bremsstrahlung which may not be completely absorbed in the calorimeter. The Bremsstrahlung accounts for about 1.3 per cent of the total energy of P32. A small fraction of the energy lost by ionization in the calorimeter also may be transformed to chemical energy which will not change the temperature of the device. The over-all probable error in calorimetric determinations of the total emission rate is between 2 and 3 per cent. 13.9. Ionization Measurements of Beta and Gamma Rays. Many investi- gators prefer to use ionization chambers for routine determinations of the disintegration rates of various radioactive isotopes. In x-ray dosimetry a number of types of ionization chambers have been in use for a long time, and for special problems in connection with radioactive isotopes highly sensitive chambers and electrometers have been developed (see Chap. 12). Sec. 13.9] STANDARDIZATION OF RADIOACTIVE SAMPLES 369 The ionization produced by a charged particle traversing a gaseous medium is proportional to the energy loss of the particle to the medium. The factor of proportionality appears to be constant over wide limits of particle energy. Thus, ionization measurements become measurements of energy loss in the medium when the factor of proportionality is known. The energy loss per ion pair for beta particles in air is considered to be about 32.5 ev. In practice absolute determination of energy loss by ionization becomes a more complex problem because of the wall effects in the chamber. Both beta particles and gamma rays are scattered back from the walls of the chamber, thus increasing the ionization in the sensitive volume. Secondary electrons produced in the walls by gamma rays also contribute to the ionization, often to an extent that is difficult to estimate. Consequently, considerable caution is necessary in the interpretation of ionization phenomena. In practice, two different ionization-chamber constructions are possible in which these complex conditions may be accurately analyzed. These are chambers in which the wall effect is negligible and chambers in which the wall effect is made the most important contribution to the ionization (see also Sec. 12.2). a. Gas-wall Chambers. These chambers are best suited to standardization of low-energy gamma rays and low-energy beta emitters such as H3 and C14. Such instruments are usually constructed with a central electrode of fine wire and a concentric cylindrical electrode consisting of a coarse mesh made of fine wire. It is important that the solid walls of the chamber be placed farther from the outer electrode than the greatest range of the beta particles being measured or the range of the secondary electrons from the wall when gamma rays are measured. Ionization chambers of this kind often operate at higher than atmospheric pressure in order to reduce the linear dimensions required to meet this condition. For an isotope in gaseous form, emitting beta particles of average energy Ep, the disintegration rate R per unit gas volume may be expressed in terms of the measured ion current / by the simple formula R = WI eVE where e = electronic charge W = average energy required to form one ion pair V = volume of sensitive region For x- and gamma rays the energy flux F may be determined from the expression WI F = (impVe 370 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 where p = density of chamber gas Hm = mass-absorption coefficient for gamma rays in the gas (sum of photoelectric and Compton absorption coefficients) If the gamma rays are monochromatic, with energy Ey, the flux of photons crossing the chamber is then/ = F/Ey. By taking into account the absorp- tion and the solid angle subtended by the instrument with respect to the source, the emission rate of gamma rays from an external source can be determined. b. Solid-wall Ionization Chambers. Gas- wall chambers are not easy to construct and operate, and their usefulness breaks down at energies higher than a few hundred kev. However, ionization chambers with solid walls may be used for x-rays and gamma rays from a few kev to very high energies. Most of the ionization chambers in routine use for radioisotope measurements and dosimetry are of the solid-wall type, a very popular form of which is the so-called "thimble" chamber. The methods for absolute measurement of gamma rays and energy flux with such instruments were elucidated by Gray [21]. To facilitate interpretation, the ionization chambers are constructed in such a way that, for practical purposes, nearly all ionization in the sensitive volume comes from secondaries initiated in the solid electrodes of the instru- ment while the number of secondaries produced in the gas add negligibly small ionization. A simple relationship holds true between the energy Es absorbed per unit mass of the solid medium of the wall and the ionization / produced in a small air-filled cavity of that medium, if the dimensions of the cavity are small compared to the mean distance traveled in the air by the secondary electrons and if the dimensions of the solid are large compared to the distance traveled by the secondary electrons in the solid. This relation- ship, sometimes also called the Bragg-Gray principle, may be written as IW Es eVP S The meanings of W, V, p, and e are the same as above, while S is the relative stopping power per unit mass of the solid medium versus air. With the knowledge of the absorption coefficient p.m of the solid medium of the ioniza- tion chamber the gamma-ray energy flux F at some point near the center of the chamber is then £, IWS P-m HmVep Since gamma rays of a few hundred kev do not lose much energy traversing a few feet of air or through the walls of small ionization chambers, the rate of emission from a point source of monoenergetic gamma rays of energy Ey Sec. 13.9] STANDARDIZATION OF RADIOACTIVE SAMPLES 371 at a distance r from a suitable ionization chamber is approximately ATrr-IWS R = epumVE, Unfortunately, in precision measurements some corrections are again needed. Among these an important one is that due to Compton scattering. Uncertainties come in also in the measurements of various quantities in the above expression, notably in I, W, n,n, and even V, while Ey and 5 may be measured quite accurately. In measurement of /, care must be taken that all ion pairs formed in the sensitive volume are collected without allowing recombination or multiplication. This is best accomplished by the use of an inert gas or dry air and with conveniently shaped ionization chambers which have a well-defined plateau. As long as the collecting potential is held within the limits of the plateau, 100 per cent of the ions are collected. The biggest uncertainty at the present time exists in the value of W, the energy absorbed to form one ion pair, as indicated by the fact that independent methods and investigators have arrived at rather widely differing values for W. One of the best ways to measure this value is by counting the number of droplets produced in cloud-chamber tracks of electrons. The probable error of about 1 per cent for the value quoted above places a limit on the absolute accuracy of gamma-ray disintegration evaluations and also on estimates of the energy absorbed in matter for one roentgen of gamma rays and x-rays. Assuming this value of W to be correct, the conversion factor is 84 + 1 ergs per gm in air. Notwithstanding the experimental difficulties several excellent determina- tions were made of the ionization of weighed amounts of radioisotopes, especially that of radium. One gram of radium, when shielded with % mm of platinum gives, at 1 meter distance, ionization in air equivalent to 0.84 + 0.01 rhm [22 to 25]. Knowing the absorption coefficients, the formula above may be used to calculate the expected energy absorption or the ionization from any radioisotope even with more than one gamma ray present. Marinelli et al. [26] have recently published such data, some of which are reprinted in Table 37. The case of radium is more complex than most other radioactive isotopes because when in equilibrium with its disintegration products a Ra sample emits some 16 gamma rays with different intensities and energies. Never- theless the theoretically calculated value agrees quite well with the experi- mental data [27]. The measuring methods for ionization and energy absorption are constantly being refined. One particularly suitable arrangement for the study of the wall effect and scattering in ionization chambers is that constructed by Failla [28]. This ionization chamber has parallel walls that form the elec- trodes. The gas pressure, the distance of the walls, their material and 372 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 thickness can all be changed and the validity of the Bragg-Gray conditions tested. In spite of the care required for absolute determination of disintegration rates with ionization chambers, their use has much value in routine secondary standardization procedures. They may be made in very rugged form and retain their sensitivity through periods of several years without appreciable change. One form, the Lauritsen electroscope, has been used in biological- tracer studies for many . years. Improved high-sensitivity ionization chambers and electrometers for standardization are available in several laboratories. 13.10. Standardization of Beta-counter Geometry. Much of the beta counting in practice is carried out using end-window type Geiger-Miiller TO AIR TO PUMP Fig. 103. Bell-jar counter and vacuum-chamber assembly used for beta-particle stan- dardization. The principal components of the assembly are A, counter wall (cathode); B, counter anode; C, mica window; D, aluminum vacuum chamber lined with lucite; E, lucite rods for supporting sample; F, sample, point source mounted on thin supporting foil; G, diaphragm, absorbers are placed on top of diaphragm. The vacuum-tight door of the chamber is not shown. [H. Anger and C. A. Tobias, unpublished.] counters with thin mica windows. In principle, the usual procedure con- sists in counting a standard sample which is placed in a standard position underthe counter tube after calibration by one of the independent methods. In this way the efficiency of a particular counter with a fixed geometry is Sec. 13.10] STANDARDIZATION OF RADIOACTIVE SAMPLES 373 readily obtained. However, since the method is not entirely foolproof, it may be useful to consider some of the factors that influence the counting rate, and some of the methods whereby simple and fairly reliable standardiza- tion may be achieved for almost any radioactive isotope. Theoretical considerations as well as actual tests carried out with coin- cidence counters make it fairly certain that each beta particle that passes through the sensitive volume of a counter will be counted. The gas pressure in most counters is made high enough to make certain that each beta particle will make at least one ion pair. Similarly, a gamma ray will be counted if at least one of its secondary particles passes through the sensitive volume. It is generally assumed that the sensitive volume is a well-defined space within the counter. However, this is not strictly true. Measurements of counter efficiency indicate that the apparent sensitive volume changes with beta-particle energy in bell-jar counters [40]. Furthermore, these counters are less sensitive in the region near the end by the window and in the region close to the surface of the cathode (cylindrical electrode) than they are near the anode (wire electrode). In order to avoid using the insensitive regions of the counter a circular aperture about one-half the diameter of the counter is placed in front of the counter window, as shown in Fig. 103. All beta particles within the cone subtended by the aperture from a point source are counted, provided that they have enough energy, penetrate the counter window, and reach the sensitive volume. The aperture may be made in a piece of brass plate thick enough to stop all beta particles. From Fig. 103 it is seen that the solid angle subtended by the aperture at the source is = 0.5(1 — cos a) where tan a = - a The value of <$ is more generally referred to as the geometrical efficiency. In performing measurements on beta particles it is important to keep in mind the effects of multiple scattering. The importance of scattering on beta particles may be emphasized by observing the tracks left by these particles in a cloud chamber. They are observed to be deflected many times, often through large angles. A complete study of the scattering process is not available, but it is known that the beta particles are scattered both by nuclei (Rutherford scattering) and by the atomic electrons. Sometimes the scattering is inelastic, giving rise to x-rays (Bremsstrahlung). The scattering and absorption phenomena are usually superimposed and together modify the distribution and intensity of beta particles. The above "geometrical-efficiency" formula would be correct if the sample were a point source and of negligible mass and if there were no air, window and self-absorption, or scattering by supports. Since these conditions cannot 374 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 be achieved in practice, it is necessary to take them into consideration and make detailed corrections for each factor. Most of the corrections have empirical bases because it would be difficult to make exact calculations of the combined absorption and scattering effects. When absorbers are placed between counter and source and the counting rates are plotted against absorber thickness, the well-known absorption curve is obtained. Near the end of this curve at large absorption thicknesses, the logarithm of the number of transmitted beta particles is, in many instances, 5000 4000 tu 3000 3 Ul a. 52 2000 - z 3 O o 1000 EXTRAPOLATION ■WINDOW AN0 AIR PATH CORRECTION O 12 24 36 48 60 72 2 MG PER CM ALUMINUM Fig. 104. Typical aluminum absorption curve for RaE. The units of abscissa represent only the thickness of aluminum absorber. To this must be added the equivalent aluminum thickness of the counter window and of the mean path of the particles in air. The extra- polation shown is subject to considerable uncertainty. [Redrawn from L. R. Zitmwalt, U.S. Atomic Energy Commission Report MDDC-1346, 1947.] proportional to the thickness. At very small absorber thicknesses this relationship does not hold. In fact, theoretically one would expect the absorption coefficient to be zero at very small absorber thickness because of the shape of the Fermi distribution of beta-particle energies. A typical absorption curve is shown in Fig. 104. Scattering plays an important role in the shape of the absorption curves. Hence there is no well-defined "accepted" absorption curve for any radioactive isotope since the curves vary markedly with the experimental arrangement. It is customary to use extrapolation procedures for correcting the effect of window absorption on the observed beta-particle counting rates [16]. Starting with the counter window as the only absorber additional aluminum absorbers are added in steps; then assuming that the absorption curve is logarithmic, it is extra- Sec. 13.10] STANDARDIZATION OF RADIOACTIVE SAMPLES 375 polated back to zero thickness. Actually such a procedure is only per- missible if the extrapolation is very small. Using soft beta emitters, for example, the absorption curve with the absorber close to the counter window is usually very different from that with the absorber right over the sample [41]. The angular distribution of beta particles from a point source of small mass is isotropic. A sample support of finite thickness, or an extended 130 120 2 UJ o or UJ a. HO p" 1 > Co60 1/ CI < 3 o 1 I 2.8 CM I _ t 100 0 20 40 60 80 100 120 140 160 180 MG PER CM2 of ALUMINUM REFLECTOR Fig. 105. Backscattering of P32 and Co60 beta particles (Ema% = 1.72 and 0.3 mev, respec- tively) as a function of sample support thickness. The counting rate is given in per cent of the rate obtained with a sample support of negligible thickness. The samples were point sources, and the counting geometry is indicated in the diagram showing the position of sample, counter window and sensitive region of counter (broken line). [Unpublished data of H. Anger.] source with finite thickness, changes the isotropic distribution into one preferring a direction perpendicular to the plane of the sample. The first effect is usually called backscattering. The magnitude of this depends on the beta-particle spectrum and the atomic number and thickness of the sample support. Using an aluminum sample support, the effect of different thicknesses on the counting rate of Co60 and P32 is plotted on Fig. 105. It is apparent that if the support thickness is greater than one-half the amount of absorber necessary to stop all beta particles the counting rate does not increase with support thickness. This condition is often called "saturation backscattering." The dependence of saturation backscattering on atomic number of sample support is shown in Figs. 106 and 107. Some beta- particle standards are mounted on supports that give saturation backscatter- 376 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 200 180 160 LU 140 120 100 100 ATOMIC NUMBER Fig. 106. Saturation backscattering as a function of the atomic number of the back- scatterer. The ordinate represents per cent of the counting rate obtained with a sample support of negligible thickness. [Unpublished data of II. Anger.] 180 5 160 U o K Ul Q. 140 120 100 - 1 PLATINUM • / A / C0F >PER / ' / / ALU MINUM 1 1 1 1 1 1 " 1 0.2 0.4 Co' 60 0.6 .131 0.8 1.0 1.2 1.4 1.6 1.8 24 ,32 I'- No MAXIMUM BETA ENERGY IN MEV Fig. 107. Saturation backscattering from aluminum, copper, and platinum for a point source as a function of maximum beta-particle energy. The ordinate represents the count- ing rate with respect to a source with no backscatterer (negligibly thick supporting film). [Unpublished data of H. Anger.] ing, and when these are compared with various beta-particle samples, the variations in backscattering must be taken into account. Absorption curves taken from samples with saturation backscattering are different from those taken with very thin sample supports because the scattered particles increase the relative number of soft beta particles entering the counter. Backscattering can be very nearly eliminated by using extremely thin Sec. 13.10] STANDARDIZATION OF RADIOACTIVE SAMPLES 377 sample supports consisting of films of materials, such as nylon, polyethylene, or aluminum, which have low atomic weights. Scattering by the intervening air and parts of the apparatus can, of course, be greatly reduced by proper design and by placing the entire unit in an evacuated box, as shown in Fig. 103. Routine counting of samples usually necessitates deposition of several milligrams of active material on some kind of standardized sample holder, as described in Chap. 17. For a thin sample the computed and experimental 0.25 0.5 1.75 2.00 0.75 1.00 1.25 1.50 UNITS OF COUNTER DIAMETER Fig. 108. Relative counting efficiency (for P32) as a function of the lateral displacement of the source from the axis of the counter. denotes the geometric efficiency when the sample is on the counter axis. [Unpublished data of H. Anger.] efficiency decreases as a function of the distance the sample is displaced laterally from the axis of the counter in a manner indicated in Fig. 108. Samples with finite thickness introduce an additional effect, a combination of absorption and scattering in the sample material, often called self-absorp- tion. Along with this there is also distortion of the isotropic angular dis- tribution of the beta particles. A counter, however, may be calibrated for measuring samples of any thickness by obtaining first a standard self-absorp- tion curve for a given substance. This may be done in two different ways. A dilution curve is obtained if a sample of known radioactivity and negligible mass is progressively diluted by addition of stable carrier. With samples of identical intensity and sample area the counting rate decreases progressively as the mass of carrier is increased. Another method of measuring self- absorption is by the use of radioactive samples with the same specific activity but different total mass or thickness. Instead of a linear relationship between sample thickness and counting rate, one obtains a typical saturation curve 378 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 reproduced for C14 in Fig. 109. When samples of finite thickness are used, nonuniformity of thickness results in a decreased counting rate as a con- sequence of variable self-absorption. The precise methods for obtaining calibrations for self-absorption have been discussed by Yankwich etal. [31]. / | / 100 / / ^ — > / > 1- o < / / / 1 / 1 /\ ^ OBSERVED 3 5 X < s 50 // // ^EXPECTED u. o // z o 1- o < a u. // _ / °( ' i i i i 1 ) 5 10 15 30 35 SAMPLE THICKNESS, MG PER CM" Fig. 109. Fraction of maximum observable activity of C14in a BaC03 sample as a function of sample thickness. The broken line indicates the activity which would be observed in the absence of self-absorption. [Redrawn from P. E. Yankwich, T. H. N orris, and J. Hus- ton, Anal. Chem., 19, 439 (1947).] 13.11. Secondary Beta-particle and Gamma-ray Standards. The Bureau of Standards has made available a number of secondary standards. Among these are gamma-ray standards of Ra and of Co60 (the latter standardized by the coincidence method) and RaE beta-particle standards. In the near future secondary beta-particle standards of Co60, I131, P32, and C14 will also be added. In the meanwhile further work is going on in the search for a con- venient long-lived beta standard with higher maximum energy than Co.60 Some laboratories and commercial enterprises have also prepared UX2 beta- particle standards. 13.12. Standardization of Neutrons and Protons. Detailed processes for standardization of neutrons are beyond the scope of this chapter, although some of the more important considerations of the problems that arise can be briefly stated. The number of fast neutrons is usually determined by measuring the radioactivity induced in some substance for which the inter- action cross section is known accurately. From the point of view of biology, the ionization produced by fast neutrons is more important than the number of such neutrons. For some purposes, therefore, the ionization is often measured by a thimble ionization chamber. As in the case of gamma-ray Sec. 13.12] STANDARDIZATION OF RADIOACTIVE SAMPLES 379 measurements, it is necessary to achieve the condition in which the ionization in the gas of the chamber is in equilibrium with the ionization within the chamber walls [21,32]. The neutrons exert their biological effects by the ionization produced by the secondary recoil nuclei; hence, it is important that equilibrium is also reached between the primary neutrons and the secondary protons in the material studied. Using 10 mev neutrons, equilib- rium may be reached in'about 3^8 m- °f tissue, whereas with 100-mev neutrons the equilibrium is established only after the neutron beam has crossed some 3 in. of tissue. The measurement of thermal neutrons may be done in several different ways. Among these is the activation of certain elements, e.g., indium, gold, or manganese, which have large thermal-capture cross sections. The neutron flux may be calculated from the observed disintegration rates of the isotopes produced and from the cross sections for the processes. An inde- pendent method utilizes neutron-induced fission of uranium measured with an ionization chamber. Each time the fission occurs a large burst of ioniza- tion appears in the chamber due to fission recoils, and the number of pulses, together with the cross section for fission, yields the absolute number of primary neutrons. If a neutron beam has thermal as well as fast components, separation of the components is possible to some extent by measuring the difference in radioactivity induced in detecting foils with and without cad- mium shielding. The radioactivity induced in the foil shielded with a strong thermal neutron absorber is due only to faster neutrons. Recently protons, deuterons, and alpha particles accelerated in cyclotrons have also been used in biological research. The measurement of a number of particles in such beams may be accomplished by two methods: (1) measure- ment of a total charge carried by the beam by means of a Faraday cage, and (2) by measurement of the ionization produced in air by a fraction of a monoenergetic beam at a given energy. From the known charge carried by each particle and the measured ionization, the number of particles in the beam may be calculated [35,37]. REFERENCES FOR CHAP. 13 1. Curie, I., A. Debierne, A. S. Eve, H. Geiger, O. Hahn, S. C. Lind, St. Meyer, E. Rutherford, and E. Schweidler: Rev. Mod. Phys., 3, 427 (1931). 2. Kohman, T. P., D. P. Ames, and Sedlet: Atomic Energy Commission Report MDDC- 852, Mar. 25, 1947. 3. Condon, E. U., and L. F. Curtiss: Phys. Rev., 69, 672 (1946). 4. Kovarik, A. F., and T. Adams: Phys. Rev., 40, 718 (1932); 64, 413 (1938); /. Applied Phys., 12, 296 (1941). 5. Nier, A. O.-.Phys. Rev., 55, (1939). Values recalculated according to Ref. 4. See also D. Williams, and P. Yuster, Atomic Energy Commission Report. LA-203, January, 1945. 380 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 14 6. Ghiorso, A., B. B. Cunningham, and C. J. Hindemann: Atomic Energy Commission Report. C K 3861, 1944. 7. Rossi, B.: Nature, 125, 636 (1930). 8. Brady, E. L., and M. Deutsch: Phys. Rev., 72, 870 (1947); 74, 1541 (1948). 9. Dunworth, J. V.: Rev. Sci. Instruments, 11, 167 (1940). 10. Wiedenbeck, M. L. : Phys. Rev., 72, 974 (1947). 11. Wiedenbeck, M. L., and Y. Chink: Phys. Rev., 72, 1164 (1947); 72, 1171 (1947). 12. Bay, Z., and G. Papp: Rev. Sci. Instruments, 19, 565 (1948). 13. Schultz, H. L., and R. Beringer: Rev. Sci. Instruments, 19, 424 (1948). 14. Metzger, F., and M. Deutsch: Phys. Rev., 74, 1452 (1948). 15. Broido, A., J. D. Teresi, and P. C. Tompkins: Atomic Energy Commission Report CH-3631-C, November, 1946. 16. Curtiss, L. F.: National Bureau of Standards Circular C473. 17. Broda, E.j J. Gueron, and L., Kowarski: Atomic Energy Commission Report Br 44, 1942. 18. Feather, N.: Br 594 (1944); Br 44 (1943). 19. Failla, G.: Private communication. (Presented at the Chicago meeting of the American Physical Society, November, 1948, by Clark). 20. Zumwalt, L. R., C. V. Cannon, G. H. Jenks, W. C. Peacock, and L. M. Gunning; Atomic Energy Commission Report MDDC-1433, October, 1947. 21. Gray, L. R.:Proc. Roy. Soc. (London), A156, 578 (1936). 22. White, T. N.,L. D. Marinelli, and G. Failla: Am. J. Roentgenol. Radium Therapy, 44, 889 (1940). 23. Taylor, L. S., and G. Singer: Am. J. Roentgenol. Radium Therapy, 44, 428 (1940). 24. Mayneord, M. V., and J. E. Roberts: Brit. J. Radiology, 10, 365 (1937). 25. Gray, L. H.: Brit. J. Radiology, 10, 721, (1937). 26. Marinelli, L. D., E. H. Quimby, and G. J. Hine: Am. J. Roentgenol. Radium Therapy, 59, 260 (1948). 27. Evans, R. D.: "Advances in Biological and Medical Physics," Vol. 1, pp. 189-90, edited by J. H. Lawrence and J. G. Hamilton, Academic Press, 1947. 28. Failla, G., H. H. Rossi, R. K. Clark, and N. Baily: Atomic Energy Commission Report 2142, December, 1947. 29. Zumwalt, L.: Atomic Energy Commission Report MDDC-1346, September, 1947. 30. Grummit, W. E., J. Gueron, and G. Wilkinson: MC-46, National Research Council, Montreal, 1944. 31. Yankwich. P. E., T. H. Norris, and Huston: J. Anal. Chem., 19, 439 (1947). 32. Gray, L. H.: Proc. Roy. Soc, (London), A175, 72 (1943). 33. Aebersold, P. C , and G. A. Anslow: Phys. Rev., 69, 1 (1946). 34. Novey, T. B.: Atomic Energy Commission Report CP 2825 G-X, June, 1945. 35. Tobias, C. A., H. O. Anger, P. P. Weymouth: Atomic Energy Commission Report 2099-A, March, 1948. 36. Kohman, T. P.: Atomic Energy Commission Report MDDC-905, June, 1945. 37. Loevinger, R.: Atomic Energy Commission Report BP 139, October, 1947. 38. Bradt, H., and P. Scherrer: Helv. Phys. Ada, 18, 425 (1945). 39. Wadey, W.: Phys. Rev., 74, 1846 (1948). 40. Englekemeir, D. W., W. R. Rubinson, and N. Elliot: Atomic Energy Commission Report CC-851, August, 1943. 41. Johnston, F., and J. E. Willard: Science, 109, 11 (1949). 42. For details of techniques for handling C14 see also Calvin, M., C. Heidelberger, J. C. Redd, B. M. Tolbert, and P. F. Yankwich: "Isotopic Carbon," pp. 15-127, John Wiley & Sons, Inc., 1949. CHAPTER 14 THE RADIOAUTOGRAPH Patricia P. Weymouth 14.1. Introduction. Established methods for analyses of radioactivity in biological specimens in which the activity of a suitable aliquot of treated tissue is determined will give valuable information concerning gross dis- tribution of the material under study. However, the local distribution of active material in particular parts of an organ and in special cells of a tissue can be studied most effectively by the technique of radioautography. This technique, as the name implies, provides a self-photograph of a radioactive substance as a result of the action of alpha or beta particles on a photographic emulsion (gamma radiation will not be considered since it is of limited importance). The usual photograph, taken with a camera, is the result of activation of silver bromide grains by photons; the energy state of the silver bromide is changed so that at some later time the silver may be easily reduced. Pre- sumably, the action of alpha and beta particles is qualitatively similar to that of photons but quantitatively different because of the physical char- acteristics of the radiations. The alpha particle has a mass about 7,400 times that of the beta particle, and when both particles are of equal energy the beta particle will travel at a much greater speed than the alpha particle. When the alpha particle passes through an emulsion containing silver bromide grains, it proceeds in a straight line giving up energy to the grains along its path until it is brought to rest and neutralized. A radioautograph produced from an alpha source will show distinct tracks of closely spaced grains. The tracks, each produced by a single alpha particle, proceed in a straight line, lie in random directions, and end abruptly. In a picture from a beta source the situation is somewhat different, for in this case the velocity of the beta particle compared with that of an alpha particle of equal energy is much greater; the grains affected by a single particle are more widely spaced since the beta particle passes many grains too rapidly to induce an image on them. Furthermore, because of the small mass of the beta particle, it is easily deflected by atoms in its path and will not travel in a straight line. From this discussion, it will be recognized that with a beta source the picture obtained will consist of a random distribution of developed grains, no two of which can be ascribed to any one beta particle. In addition, the length of path of the beta particle through material is much greater than that of an 381 382 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 14 alpha particle since the former loses energy more slowly. As a result, an image produced by a point source of a beta emitter will be quite large; for example, from a point source of beta particles with an average path length of 2,000 n, a symmetrical image approximately 4 mm in diameter is produced. These circumstances are unfortunate for they limit the resolution of beta autographs and decrease the possibility of determining with certainty the origin of beta radiation from tissue samples. It is especially unfortunate since many of the isotopes most useful in biological studies, such as carbon, sulfur, sodium, and iodine, are beta emitters. The alpha emitters are heavy metals, and their present importance falls primarily in the realm of health protection of workers in atomic-energy plants and in the effects of the atomic bomb on plant and animal life. 14.2. Techniques for Preparing Radioautographs. A radioautograph of a large sample of tissues containing radioactive material, such as half a kidney or a smooth bone surface, is relatively simple to produce. The block of tissue is held in firm contact with the film for the desired length of time, and the film is then developed, after which, areas of blackening are easily cor- related with regions of the tissue block. The problem of more accurate localization to particular structures in the tissue is more complex. In this type of radioautograph the following factors are of particular importance: the resolution or separation of darkened areas and their restriction to an area the same as that of the source should be as great as possible in order that localization may be accurate; the sensitivity must be adequate to detect even small amounts of radioactive material; and, for the purpose of com- paring concentrations of material in various areas, it is necessary that the range of response be as great as possible. These factors may be controlled, in so far as they are independent of the type of radiation, by manipulation of the various conditions discussed below. The most important aspects to be considered are contact between emulsion and specimen during exposure and alignment of radioautograph and specimen after development. Contact and alignment may be secured (1) by mounting the section and emulsion on separate supports such as microscope slides, (2) by spreading liquid emulsion or stripping film over the section, or (3) by mounting the section on the emulsion. In the first method (1) the tissue is prepared by the usual histological techniques, and one or more sections are mounted on a microscope slide or cover slip. Factors such as solubility of the radioactive material and section thickness, discussed in detail below, must be carefully controlled for best results. The slide holding the unstained section is then placed over the proper type of film, section and emulsion together, and firm, even pressure is applied for the duration of the exposure. After developing the film and staining the section the two may be easily compared for evidence of gross Sec. 14.2] THE RADIOAUTOGRAPII 383 distribution of active material, but microscopic examination is more difficult A frame designed to fix the slide or cover slip with respect to the film is of some value for this purpose. The film and slide are fixed in their respective frames and held together by alignment pins or angles during exposure. After separate development and staining they may again be aligned and the tissue slide fixed to the film in the original position. Both components may then be removed from their frames. This procedure will yield a fairly satisfactory preparation for microscopic examination under low power and, depending on the thickness of the tissue preparation, perhaps under high power. The use of the oil-immersion objective, which is necessary for cellular localization of the radiation source, is impossible with this type of preparation. A microscope comparator may be used whereby tissue section and film may be aligned by a reference mark, such as a spot shadow of a small piece of gold leaf, and picture and tissue examined simultaneously. Alignment in this instance is not accurate enough to yield definite information concerning cellular origin of radiation. The problems of realignment are solved by either of the last two methods (2 or 3) listed above. In the second method, the section is placed on a slide or cover slip, stained or not depending on the radioactive material being studied, and covered with emulsion. If the section is stained prior to exposure, it may be held on the slide by a very thin coating of collodion. Liquid emulsion, prepared by formulas given in the literature or melted from a plate or film, is then spread over the tissue. Preparation and handling of liquid emulsions is an art, and great care must be taken to avoid excessive grain size and high background fog. In addition, it is often difficult to obtain a uniform and thin film necessary for preparation of good radioautographs. However, a more satisfactory procedure is the use of an emulsion obtainable in the form of stripping film, which is prepared so that the emulsion may be removed from its backing and cemented over the section. After the proper exposure and development of the film, the section is stained if this has not already been done. Here and in the procedure outlined below, the usual histological stains are of limited use because of the strong affinity of the gelatin of the emulsion for the dyes. A completely satisfactory staining technique that gives excellent tissue differentiation and does not stain the emulsion has not yet been described. Another drawback in using liquid emulsion or stripping film is distortion of the emulsion through handling. This distortion is, of course, most serious in the case of liquid emulsions but also occurs to some extent with the stripping film, which frequently during the course of developing and staining becomes detached from the supporting slide. Although separation may be unavoidable, the radioautograph is still of value if developing and staining are finished carefully and the film with section attached is dried between blotting papers. 384 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 14 The last method (3) to be discussed eliminates the possibility of film dis- tortion due to handling. Here, the cut sections are spread on water and (in the darkroom) are floated onto the emulsion supported on a microscope slide or other film backing cut to convenient size. The preparation is then air dried and stored in a lighttight container until the desired exposure time has elapsed. The emulsion acts as a fixative to hold the section to the slide. The collodion or paraffin is then removed, the picture developed, and the tissue section stained. The resultant preparation consists of the stained section lying on the emulsion. Tissue and radioautograph when examined microscopically under low magnification will appear to lie in the same plane. Under high magnification, they may be examined separately, since the tissue will appear at the uppermost level of focusing while the radioautograph will be brought into focus at a lower level. Whatever method is used for assuring contact and alignment, several addi- tional conditions should be examined and regulated to give the most effective results. During preparation of the tissues for sectioning, and through the staining procedure when the radioautograph is to be made after staining, it is important that the radioactive material not be dissolved from the tissue by any of the reagents used. For instance, I131 in organic molecules may be treated in the usual way without loss of material, whereas P32 is lost rapidly in acid fixatives. In the case of tissues containing the latter isotope, all solutions used in histological preparation prior to exposure for radioautog- raphy must be neutral. The question of solubility of radioactive material in the histological reagents may be answered only by checking all such reagents used prior to exposure of the film to the section. If the half-life of the radioactive substance under study is short, as with Na24, or if the half-life is longer and the amount of material is small, it will be essential to reduce the time of histological preparation. By using small pieces, gentle heat, and agitation during fixing and embedding, the time required for preparing the tissue may be decreased markedly. The time may also be shortened and the problem of solubility eliminated as well by using frozen sections without fixing, although this introduces certain difficulties with regard to both his- tology and radioautography. The thickness of the tissue sections used will influence the resolution greatly. Sections of 5 and 10 /x are preferable, since resolution is inversely proportional to section thickness provided that the latter is less than a limiting value, depending on the type of radiation. If the path length of the radiation is short, thickness of section is not critical with regard to resolution since particles from within the tissue will be absorbed. When radiation intensity is low, thicker sections may be necessary to obtain sufficient expo- sure in the requisite length of time. It is difficult to prepare frozen sections as thin as 5 to 10 /x- Sec. 14.3] THE RADIO AUTOGRAPH 385 14.3. Radioautographic Emulsions. Photographic emulsions available for radioautography may be divided into four general groups according to the application for which they are intended: those used with visible light, x-ray, spectroscopic, and special particle plates. For alpha irradiation the very fine-grained emulsions of the last two groups are most useful, especially the "alpha-particle" film. For beta radiation, however, these plates are not sensitive enough. X-ray or dental film is very sensitive to beta particles, but the grains are large and irregular and hence definition is poor. The somewhat finer grained lantern-slide plates are a suitable compromise. In general, with a small grain size, the probability of a relatively slow and heavy alpha particle hitting and imposing a latent image on a grain is greater than that of a faster beta particle. The probability of a hit with a beta particle, and therefore the sensitivity, increases with increasing grain size, but the resolution diminishes. As charged particles pass through the emulsion they will be scattered by the atoms of the emulsion. Hence with thicker emulsions, the scattering will be greater and the resolution consequently, diminished. The backing or film support also contributes to this effect especially in the case of beta particles of high energy. The usual thickness of x-ray film and lantern-slide plates is approximately 100 fx, and alpha-particle plates have an emulsion thickness of about 40 p.. A thinner film may be obtained by using liquid emulsion or by the use of plates recently developed by the Eastman Kodak Company which have emulsion thicknesses of 5 to 10 ;u, which are available under the designation NTP. The use of liquid emulsion or stripping film eliminates scattering due to film backing. On the other hand, if the number of grains is increased by increasing the emulsion thickness, the probability of a beta particle imposing a latent image increases. Therefore when sen- sitivity and range of response are the desiderata, a thick emulsion should be used. Exposure and development are the remaining conditions to be considered in the preparation of a radioautograph. The time of exposure will depend to a great extent on the amount of radiation present in the samples to be analyzed. This may be determined prior to preparation of the radioauto- graph by determining the activity of one or of a few sections by a suitable counter. In general, a satisfactory beta autograph may be obtained with about 107 particles per square centimeter, whereas 2 X 106 alpha particles will be sufficient. However, less total radiation is often sufficient if local concentrations are high. This is also true in the case of alpha autographs made for the study of tracks rather than film blackening. When possible, a number of plates should be exposed and developed at various intervals to enable selection of the most suitable exposure time. In the case of beta autographs made on lantern-slide emulsions, a prior run with the more 386 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 14 sensitive and faster x-ray film will indicate the proper exposure time. Where other factors permit, exposure time should be less than 2 to 3 half-lives of the radioisotope since the latent image fades with time, a phenomenon that may be slowed by storing the setup at low temperature. Although a longer exposure time increases the range, of response, the resolution is thereby decreased and the possibility of background fog from stray radiation is increased. Background fog is a serious problem in cases of low-intensity radiation and in attempting to estimate the quantity of radioactive material by numbers of developed grains. It may be controlled to some extent by careful selection of emulsion and, in some cases, by overexposure and underdevelop- ment. A permanganate wash during development also diminishes back- ground, but care must be taken since it also decreases image intensity. In summary, the conditions affecting the three desirable factors are as follows: (1) Sensitivity is increased by use of a thick emulsion of large grain size, by prolonged exposure, and by reduction of preparation time to a minimum. (2) Resolution is improved by careful selection of the proper emulsion for a particular type of irradiation, by use of a thin emulsion with small grain size, by keeping exposure time to a minimum, by decreasing back- ground fog by overexposure and underdevelopment, and through the use of proper chemicals. (3) Adequate range of response is dependent on use of thick emulsions, complete development, and comparison of radioautographs made with various exposure times. Other conditions that are of general value in obtaining good radioautographs include the following: the distance between the sample to be studied and the emulsion must be reduced to a minimum; the radioactive material must not be appreciably soluble in any of the reagents used prior to exposure of emulsion to section; the stain used for the tissue must yield good differentiation, i.e., if applied after develop- ment it should not obscure or fade the image, and if applied before exposure it should not be washed out by any of the reagents used for development. References 1, 2, and 3 are excellent reviews with extensive bibliographies, but a number of the more recent references dealing with the general subject of radioautography will be given here. The physical principles are dis- cussed in papers 4 and 5. The technique of making radioautographs with section and emulsion supported individually and realigned after separate staining and developing is described in 4 and 6. Articles 7 and 8 deal with preparation of liquid emulsions and methods of spreading these on sections. The method of floating section onto emulsion is detailed in references 9 and 10. REFERENCES FOR CHAP. 14 1. Axelrod, D. J., and J. G. Hamilton: University of California Radiation Laboratory Report BP 111. Chap. 14] THE RADIO AUTOGRAPH 387 2. Evans, T. C: Nucleonics, 1, 58 (1947). 3. Gross, J., and C. P. Leblond: McGill Med. J., 15, 399 (1946). 4. Boyd, G. A.: /. Biol. Phot. Assoc., 16, 65 (1947). 5. Marinelli, L. D., and R. F. Hill: Am. J. Roentgenol, ami Radium Therapy, in press. 6. Axelrod, D. J., and J. G. Hamilton: Am. J. Path., 23, 2S9 (1947). 7. Belanger, L. F., and C. P. Leblond: Endocrinology, 39, 8 (1946). 8. Demers, P.: Am. J. Research, A25, 223 (1947). 9. Evans, T. C.: Proc. Soc. Exptl. Biol. Med., 64, 313 (1947). 10. Endicott, K. M., and H. Yagoda : Proc. Soc. Exptl. Biol. Med., 64, 170 (1947). CHAPTER 15 THEORY OF TRACER METHODS 15.1. Introduction. The multitude and diversity of applications to which tracers have been put make a detailed description of tracer methods imprac- ticable in the present volume. The discussion here will be confined, there- fore, to some of the principles of tracer methods which have found the most frequent use. On the other hand, an exhaustive treatment of the possible mathematical descriptions of biological, chemical, and physical systems in which tracers could be utilized would in any case perhaps not be warranted since it would present nothing essentially new. A tagging agent is assumed to be chemically and physically indistinguishable to the system and hence will follow, in most instances, processes already described in great detail in standard references on physics, chemistry, and especially thermodynamics. Labeling agents are most commonly radioactive isotopes and rare stable isotopes, but they include, as well, substances such as dyes. It is required only that the tracer be chemically and physically exactly equivalent to the substance it represents or displaces and that it in no appreciable way affect the system differently from its normal counterpart. Although distinguish- able to the observer, the labeled substance cannot be discriminated by the system so that tagged and untagged molecules enter each process with equal probability. In certain instances this condition is not altogether satisfied. Thus, in dynamic systems in which H2 or H3 is introduced as a tracer for hydrogen, or C13 or C14 for C12, it is known that some discrimination occurs because of the large mass differences in the isotopes. Particularly in tracer experiments with hydrogen isotopes it is necessary to give special attention to possible differential diffusion and reaction rates. Such isotope effects are less pronounced with carbon and are probably entirely negligible for isotopic tracers of greater mass. Very often the tracer must be present in minute quantities to satisfy the condition of indistinguishability. This is especially important with radioactive tracers. A high radiation density produced by excessive amounts of a radioactive tracer may have a profound effect on the character and dynamics of the system into which it is intro- duced. In order to guard against the influence of excessive radiation it is sometimes desirable to estimate, if possible, the maximum doses to be expected in various parts of the system for a given quantity of radioactive tracer. A third possibility of disturbing the system is encountered when 388 Sec. 15.1] THEORY OF TRACER METHODS 389 the substance to be traced occurs normally in minute amounts. It is some- times found, particularly in biological systems, that the addition of labeled substance considerably in excess of the normal amount present leads to processes that are not characteristic of the normal system. The possibility that a labeling agent may not behave strictly as a tracer should always be kept in mind in any novel application of tracers; caution should be exercised in interpreting experimental results until it has been ascertained that the tracer itself does not appreciably influence the system. The choice between stable and radioactive isotopic tracers is usually not difficult to make; if a radioactive isotope of the element to be traced is avail- able, it should be used. Radioactive isotopes are, from the technical point of view, by far the easier to detect. A great variety of radiation measuring instruments are available at reasonable cost. Samples are relatively easily prepared, and measurements of specific activity are rapidly made. On the other hand, with the exception of deuterium, stable isotopic tracers can be measured only with the mass spectrometer. The preparation of samples is tedious and in many instances extremely difficult. Both the sample prepa- ration and actual measurement are, in addition, time-consuming and often subject to many uncertainties. Perhaps equally important is the relative sensitivity of stable and radio- active tracers. The dilution of a stable isotopic tracer in a system is limited by the normal abundance of the isotope and inherent accuracy of the measure- ments. Mass spectrometers usually have an accuracy of about 1 per cent, or somewhat better under favorable conditions. If, for example, the normal isotopic abundance is 1 per cent, as in the case of C13, the greatest possible dilution factor is 10,000 and in practice is likely to be more nearly 1,000. For radioactive isotopes, however, dilution factors greater than 106 are not uncommon in routine practice. Quantities as large as 1 millicurie can some- times be used in tracer experiments, and quantities as small as 10-4 micro- curies are always measurable. There remain finally the absolute quantities of the two types of tracers which must be used. Whereas the mass of a tracer quantity of radioactive isotope is negligible by ordinary standards, the mass of a stable isotope necessary to label a substance is a considerable fraction of the total amount of the element present. In several notable instances it is necessary to resort to stable isotopes. In biological investigations the most important of these are, of course, oxygen and nitrogen. There are no useful radioactive isotopes of these elements, and the stable forms N15 and O18 must be used. In general, tracer applications are as extensive as the processes and systems they are used to investigate. In the broadest sense, their applications can, however, be divided into three categories: (1) quantitative determinations of substances in complex systems, primarily by the method of isotope dilu- 390 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 tion; (2) identification of substances in various parts of complex systems and of the routes that the tagged substances undertake and the processes they undergo; and (3) determination of the rates of transfer and the quantities of labeled substances in various processes and phases of a system. A partial description of some of the methods that can be employed in these applications is given in the following sections. Many species of radioactive and stable isotopes are available to qualified persons and institutions from the United States Atomic Energy Commission for research, medical, and industrial use. Some of the isotopes are available in a variety of chemical and physical forms and at a moderate price based on the cost of manufacturing and handling. All inquiries relevant to the pro- curement of isotopes should be addressed to Isotopes Division, United States Atomic Energy Commission, P. O Box E, Oak Ridge, Tenn. The available radioisotopes are listed in the Radioisotopes Catalog and Price List which may be obtained from the Isotopes Division. Application for any of the listed radioisotopes is made by filing with the Isotopes Division, three copies of Application for Radioisotope Procurement, A. E. C.form 313. When the proposed use of the isotope is approved, a purchase order may be sent on receipt of A uthorization for Radioisotope Procurement, A. E. C. form 374. Form 313 may also be used for procurement of certain organic com- pounds labeled with the radioisotopes C14, P32, S35, I131, and Au195. Inquiries concerning specifications other than those listed in the catalog, and pile- irradiation of substances supplied by the applicant should be addressed to the Isotopes Division prior to preparation of the final form. Stable isotopes that are available from the United States Atomic Energy Commission are listed in the catalog Stable Isotopes or in circular E-13. These isotopes are obtained by preparing the set of forms Stable Isotope Request form 100. The isotopes D (and D20), B10, and O18 are available for direct purchase, whereas all other stable species, which are separated electro- magnetically, can be obtained only on loan. All isotopes now being sold are also being distributed without charge to qualified physicians and research workers in the United States for use in cancer research, diagnosis, and treatment. The physician who is planning to use the isotopes must have had clinical experience with radiations and must be associated with an institution that is properly equipped to handle radio- isotopes. Further details on the conditions under which free isotopes are allocated are contained in circulars E-35 and D-4 issued by the Isotopes Division. 15.2. Isotope Dilution. The method of isotope dilution provides a power- ful but simple means of quantitative analysis in many applications where all other methods fail or may be extremely difficult. Although it has its own limitations and in many instances is not so convenient as standard analytical Sec. 15.2] THEORY OF TRACER METHODS 391 procedures, its particular usefulness is to be found in problems where the total quantity of a substance must be ascertained without at the same time disturbing the system in which it occurs, such as determinations of total body water, or of certain amino acids in humans in vivo, or in problems where quantitative recovery together with a high order of purity is otherwise impossible. In principle the method consists in adding to the system containing the substance to be analyzed a small quantity of the same substance that has been tagged with a radioactive or rare stable isotope. After complete mixing has taken place, a sample of the substance is isolated with the requisite purity and analyzed for its content of the tracer isotope. The dilution of the isotope is then directly related to the total quantity of the substance with which mixing can occur. In practice the major difficulty sometimes lies in syn- thesizing with a labeling agent the compound to be used. Furthermore, for measurements in vivo it is necessary that the substance is neither eliminated nor produced in appreciable quantity during the course of the experiment; i.e., the system must be in static or quasi-statie equilibrium during the experi- ment. In simple solutions and mixtures this difficulty usually does not exist, but in metabolizing systems some caution must be exercised. When the labeling agent is a radioactive isotope, computation of the total initial quantity of substance in the system from the observed dilution is simple. Denoting the specific activity of the material introduced by X\ and that of the sample afterward taken from the system by X2, the total quantity of diluent [1,2] is 6H Q = q [— — 1) gm or cc where q is the quantity of labeled material added. The situation with regard to stable isotopic tracers is somewhat more involved so far as measuring the isotopic concentrations is concerned. Both diluent and labeled material contain the two isotopic species; the former contains both isotopes in their normal abundance, and in the latter the rare isotope is enriched by an arbitrary but accurately known amount. For this reason it is more convenient to express isotopic concentrations in atom per cent excess (per cent in excess of normal abundance) rather than atom per cent. In most applications of the dilution method there is only a single dilu- ent and carrier (labeled substance), and only two isotopes to consider. The total quantity of diluent [1,2] is then (a - ■) <2 = <7^M^-1) gmorcc 392 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 where q = grams of labeled substance added M x = molecular weight of added substance with enriched rarer isotopes M B — » C — > . . . , radioactive decay, absorption of gamma rays, and combinations of these and other processes. For the sake of generality, therefore, a labeling agent introduced into a system in one form or another will be considered to be present in certain "phases" with the under- standing that a phase may refer to a particular chemical or physical form, an organ or certain tissue, or a specified volume with or without well-defined geometrical form. The precise meaning and units of phase will, consequently, depend upon the type of system and process under consideration. Expressed in general terms, tracer techniques provide the means for identifying the phases involved in the processes under consideration, determination of the amounts of substance present in each phase, and the determination of the rates of change of a substance from one phase to another. For a steady-state system containing only irreversible first-order reactions, the concentration of a labeled substance as a function of time in any one phase of the system can be represented by the polynomial x = aieklt + a%ek2t -}-••■ + aneknt The parameters a,- and kj can be determined only from measurements of the tagged molecules in the phase. The coefficients a;- may take any positive and negative values or may be zero. They represent the amplitude of the separate terms when extrapolated back to zero time. For phases other than the one in which the labeled substance is initially introduced, the coefficients usually have the property that ai -f- a2 + ■ • ■ + an = 0. The unit of dj may be microcuries or microcuries per gram when radioactive isotopes are used, and atom per cent or atom per cent excess for stable isotopes. The parameters kj are negative or zero but not positive, since positive values indicate a concentration increasing without limit. They represent the fractional amounts of labeled substances entering (for dj positive) and leaving (for a, negative) the phase per unit time. In practice the experimental data, consisting of periodic measurements of 394 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 the tracer concentration, are plotted on semilog paper with a linear time axis. The separate exponential component of the resulting curve may then be subtracted out as straight lines. From the analyzed curve the coefficients dj are obtained by extrapolating each component back to zero time. The parameters kj are also obtained from the component curves by their relation to the half-times, kj = 0.693/Tj. For most purposes the half-times Tj are determined with sufficient accuracy by inspection. However, unless the 1000 TIME Fig. 110. Reduction of elimination curves of the type x = aie~*i' + atf-**1 + • • • into separate components. Three components are shown in the diagram together with the curve from which they are'reduced. The longest component is taken out first by approxi- mating the straight line to which the curve is asymptotic. The remaining components are obtained by successive subtractions. parameters kj differ in magnitude by a factor of two or more, it is often diffi- cult to evaluate them, and also a,-, with accuracy or even to assign uniquely the number of components that appear to be present. This becomes espe- cially difficult when the number of terms exceeds three or four. In any event, whether one or several components are present the physical and physiological significance of the constants may not always be obvious until other phases of the system are also investigated. A number of simple processes frequently encountered in tracer studies of biological systems are described in greater detail below. It must be kept in mind, however, that the expressions are valid only for systems possessing the following physical characteristics: (1) only first-order reactions occur; (2) the system cannot distinguish between labeled and unlabeled substance of the same chemical and physical form; (3) the system, except for the tagged molecules, remains in a steady state; (4) the mixing time of tagged molecules Sec. 15.3] THEORY OF TRACER METHODS 395 with untagged molecules of the same substance in any phase is short com- pared to the time in which the concentration changes appreciably after equilibrium. a. Simple Elimination from One Phase. The total quantity M of substance in the phase is assumed to remain constant; the rates, in either grams or cubic centimeters per unit time, of appearance and disappearance are equal and constant. If labeled material of the same form is added to make the specific activity in the phase at t = 0 equal to X microcurie per gm, the specific activity subsequently decreases as x = Xe -kt The parameter k, obtained from the plotted measurements, is referred to as the turnover rate for the substance being traced. Physically, it is the frac- tion r/M of the total amount of the substance (labeled plus unlabeled) replaced per unit time. Its reciprocal 1/k = M/r, called the turnover time, is the time required for the replacement of an amount equal to M. The quantity r is then the actual rate, in grams or- cubic centimeters per unit time, at which the substance (tagged plus untagged) enters and leaves the phase. The turnover time 1/k is readily determined by inspection from the experi- mental data plotted on semilog paper since 1/k = T/0.693, where T is the half-time for disappearance of the tagged molecules. Thus far only the ratio r/M has been found. The actual value of M, and hence of r, can however be determined, as described in Sec. 15.2, by the dilution of the administered active material (at / = 0). It is apparent that more than one route may be taken by the substance when it leaves the phase, for the turnover rate may be written also as the sum of rates of transfer to several different phases; e.g., r (fi + 7*2 + r% + ' ' * ) M ~~ ~M~ As measured in the one phase, the dilution with time still follows the single exponential expression above since only the sum of the rates is apparent. The separate rates can be determined only if the labeled substance can be traced to the phases that follow. b. Labeled Substance Accumulated in One Phase. Accumulation of sub- stances normally found in a system usually does not occur over extended periods when the system is in a steady state. The important exceptions to this are substances eliminated from the system, usually in expired gases, feces, and urine. In practice excreta are either accumulated over a suitable length of time and the total content of excreted tracer is measured, or the excreta may be sampled periodically for the concentration of the tracer. It is usually not reasonable in such measurements to speak of specific activity, 396 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 but rather to consider the actual amount u of the eliminated (or accumulated) tracer. The rate of elimination (or of accumulation) can sometimes be represented by Am ,. . , , _,... . . . ,, • microcuries/day At = —a,\e ktt — • + bxe-^ + The total amount eliminated during the interval of time 0 to t is then u = —kidi(l — e~klt) — ' • • + b\hi(l — erhlt) -+-••■ microcuries A second example of accumulation sometimes occurs when an essentially 100 o < o o UJ Q. 10 V TIME TIME PHASE A k PHASE B \ \ \ \ < \ \ \ \ \ \ (i -e"k,)= x(t) e TIME Fig. 111. Simple uptake curve. The uptake curve x(t) is subtracted from the constant a to obtain c~ki from which the parameter k can be determined by inspection. This method presumes only one component to be present and that measurements are continued long enough to enable a reasonable value of a to be estimated. foreign substance is introduced into the system. If it is introduced into phase A from which it is transfered to phase B by a first-order reaction, the amount accumulated and fixed in B is Mb = m0(1 — e kt) microcuries while the amount remaining in A is ua = u0e~kt. The specific activity of the substance does not change; the substance is not normal to the system, and the ratio of tagged to untagged molecules remains constant in any process. c. Constant Uptake Rate and Exponential Elimination. When the rate of uptake of labeled molecules is maintained at a constant value of p micro- Sec. 15.3] THEORY OF TRACER METHODS 397 curies per sec, but the rate of disappearance from the phase is proportional to the concentration, the specific activity, assuming it is zero initially, is * = m <» " **> microcuries/gm PHASE A K! PHASE B ">* As before, k is the turnover rate or k = r/M, where M is the total constant quantity of substance in the phase and r is the constant rate of disappearance. After a long time compared to 1/k, the specific activity approaches the constant value of p/kM. d. Transfer between Two Phases. One of the most common rate problems investigated with tracer techniques is the transfer of a labeled substance or of the labeling agent itself from phase A, into which it is introduced, to one or more phases B, C, D, . . . where the activity is measured. It is assumed as before that the system is in a steady state, the amount M of the substance (labeled plus unlabeled) in each phase is constant, and the rates r, of appearance and disappear- ance of the untagged substances are constant. Consider A to be the precursor of several phases B, C, D, . . . which receive material directly from A. If the specific activity in phase A is raised initially to X microcuries per gm of labeled substance, its subsequent specific activity is x\ = Xe~klt, where k\ = ri/Mi is the turnover rate, Mi is the total quantity, and rx is the rate of disappearance from A. The specific activity in any one of the phases B, C, or D, for which the turnover rate is M% PHASE B tmo. TIME Fig. 112. Specific activities in separate phases A and B in a simple two-phase system as a function of time. is initially zero but after a time / it is X2 k2XMi (k2 - ki)M2 (g-*i< _ e-k,t) microcuries/gm The activity in this phase increases from zero to a maximum in the time . 1 T h max ~ kx - k2 g h Afterward the concentration of the tagged molecules decreases at a rate equal 398 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 to the smaller of ki and k2. The expression above for x2 is equally valid when A is the precursor of only B and all the material that leaves A reappears, usually as a different chemical form, in B. It is apparent from inspection of the formula above that when kx = k2 it is no longer valid. In this special case it takes the indeterminate form 0/0 and must, therefore, be used in its limiting form when ki — > k2 which is x2 kXMi M2 tc -kt microcuries/gm e. Series of Three-phase Changes. However complex a system may be, it is often possible to investigate a specific phase of it by introducing labeled PHASE K| > PHASE K2 PHASE S A i B 1 c i T 1 T > i- PHASE A > i- ^PHASE 8 < o PHASE C u. o 111 a. CO TIME Fig. 113. Uptake and elimination of tagged material in three phases. The curves indi- cate the time variation of specific activity in each phase when the labeled material, intro- duced at phase A, passes directly through all three phases. It is possible in certain instances for the labeled material to leave also by other routes as indicated by the broken lines. The areas under the curves will then be somewhat smaller, each by a different factor, than if all the material were to pass from A to C. material directly into the phase or into the immediately preceding phase. If it is necessary to go back two or more phases, the reactions, particularly in biological systems, tend to become exceedingly complex. When, however, a substance in phase A passes successively through a series of phases A-*B^>C-> ■ • • and only A can be tagged, the concentration of the tagged molecules in C can be described by an expression similar to those above. After introducing into A an amount of labeled substance to raise the specific activity to X microcuries per gm, the material, possibly in different chemical forms, passes from A to B, B to C, and from C it is eliminated or otherwise metabolized. X A " Sec. 15.4] THEORY OF TRACER METHODS 399 The activity in C at any time / is then k,k2X Mi (k2 -kx){kz - k1)(k3-k2)M3 [(&3 — k2)e~klt — (&3 — ki)e~kit — (ki — k2)e~k3t] microcuries/gm where ku k2, £3 = turnover rates of phases A, B and C Mi, Ms — total amounts of traced substances in phases A and C, respectively It is seen that this formula is a form of the general expression consisting of a polynomial with exponential terms. In this case the explicit expressions for the coefficient ai are rather complicated because of their interdependence on the turnover rates ki, k2, and k3. A classic example of the usefulness of the formulas outlined above for describing one-, two-, and three-phase systems is provided by the experi- ments of Zilversmit and his associates [6,7]. Radioactive phosphorus (P32) was used in these experiments to determine the turnover rate of phos- pholipids in the plasma of dogs. Measurements of the specific activity of the phospholipids and of their immediate precursor gave the necessary curves representing the uptake and disappearance of tagged molecules from which, by analysis similar to that above, the turnover rate of phospholipids could be determined. 15.4. A More General Theory of Tracer Methods. While the descriptions of processes given by the simple expressions for first-order reactions are probably the most widely useful, they are by no means adequate for systems in which higher order reactions are involved. When it is found advantageous to describe such processes in terms of mathematical expressions, it may be possible, as in the case of first-order reactions, to formulate the requisite differential equation and to solve for a particular solution in terms of suitable initial and boundary conditions. This procedure, however, is possible only when the nature of the process is already known in some detail. On the other hand, general equations may be found that are valid for large classes of phenomena. Thus, in first-order reactions the concentration of a tracer n as a function of time is given by the general formula x = > (nekit. A more ? = o general equation has been pointed out by Branson [3] who showed its useful- ness and great power when applied to tracer investigations of metabolizing systems. In view of the importance of tracer applications to biological systems, the equation and a few of its uses described by Branson are given below. A generalized metabolizing system may be regarded as a single complex phase in the sense described in the last section. The phase may be a physical 400 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 or chemical state, or it may be a specific tissue or a region, with or without well-defined boundaries, in which the substance under consideration is consumed, produced, transferred, modified, or stored. Despite a great variety of processes that may conceivably occur, these systems can be described by an integral equation already familiar to mathematicians [4,5]. In order to clarify the meaning of the equation, consider a single phase in which the total amount of metabolite present initially (/ = 0) is M0. Since it is being metabolized- there remains of this original amount after a time t the quantity MoF(t), where F(t) is some metabolizing function appropriate to the system and a function only of time. Simultaneously, additional molecules of metabolite are accumulated at the rate R(t), and in any interval of time 8 to 6 + dd an amount R(d) dd is added. The accumulating metab- olite also undergoes metabolism, and of the amount R dd added at time 6, there remains at time / the amount R(d)F(t — 6) dd. The total quantity of metabolite in the phase at time / is then the sum of MgF plus what remains of the amount added during 0 to t, giving the general integral equation M (/) = MoF(t) + J' R(d)F(t - d) dd The method of solving the equation depends on which of the functions M (/), M0, F(t), and R(t) are known or can be determined empirically. When M0, R(t), and F(t) are known, M{t) can, of course, be obtained by direct or numerical integration. If M(t), M0, and F(t) can be found, the unknown function R(t) appears only in the integral and the equation becomes a Volterra integral equation of the first kind in R. Finally, when all the functions but F(t) are known, it becomes a Volterra integral equation of the second kind in F(t). In certain cases the metabolizing system will permit simplifications to be made in the equation above. Thus, if the system is in dynamic equi- librium, the total amount M(t) of metabolite present remains constant, or M(t) = M0, and the integral equation then becomes M0{\ - F{t)) = £ R(6)F(t - 6) dd In some instances, also, the rate R is known to be constant or, if not, it may sometimes be held constant during the course of the experiment. When simplifications such as these are possible, the work of determining the unknown functions and solving the integral equation is greatly facilitated. Empirical determination of the functions depends upon which quantities are accessible to measurement without seriously disturbing the system. For this purpose tracer methods are perhaps the most powerful. While the labeled homologue of the normal metabolite will also be described by the integral equations above, the functions M(t) and M0 will not, in general, be Sec. 15.4] THEORY OF TRACER METHODS 401 the same for the tagged and untagged fractions. However, if it can be assumed that the system does not discriminate between tagged and untagged molecules, the functions R and F will be the same for both; thus, measure- ment of the change in concentration of tagged molecules in the phase enables a choice of functions R and F to be made which will, therefore, describe the kinematic behavior of the normal metabolite. The procedure to be followed may be illustrated by two applications described by Branson. The first method assumes that the metabolite can be labeled and introduced as a single dose at / = 0. The equation for the tagged metabolite then reduces to the simple form M*(t) = M*F(t), where * denotes the labeled metabolite. F(f) is determined directly from measurements of M*(t) and M*, and when substituted in the integral equation M(t) = MoF + f* RF dd M{t) can be found by integration if M0 and R are known, or the equation may be solved for R if M(t) and M0 can be determined empirically. Usually, M(t) = M0 = constant which can be determined by the method of dilution. The second case is a considerably more complex problem that arises when two or more phases must be considered, as when the precursor A of the met- abolite B is labeled. If a single dose of labeled A is added, the steady state system A — > B — ■> is described by the equations A*(t) = A%FX A(\ -Fx) = fi RiFtdO B*(t) = V R2F2 dd B(l - F») = Jlg R2F2 dd = B*(t) An additional relation B*(t) = B*F can be used if the metabolite can be tagged and introduced into phase B in the same or a similar system but in a separate experiment when B* from the precursor is not present. Alter- natively a second labeling agent, e.g., a stable isotope, or a different species of radioactive isotope distinguishable from the first, may be used to determine the relation B(i) = BJFi, where the bar indicates the metabolite tagged with the second isotope. Although technically the latter procedure may be, and usually is, considerably more difficult, it provides a distinct advantage in that all the quantities required may be measured simultaneously and in the same system. The general procedure to be followed in applying the integral equation to complex systems of several interrelated phases is found as an extension of the example above. The metabolite AU in any phase i is described by the 402 1SOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 general integral equation given above, with n equations for the n related phases. To these are added the equations for the labeled substances. The form of these equations can be simplified to some extent by proper choice of the experimental conditions. Thus, if the substance Mi is labeled with an isotope, designated by the subscript j, and introduced into phase i, relations of the form M%{t) = MfjFi are obtained, where F{ is the metabolizing function of the phase and is not influenced by the particular isotopic label. In addition, if the precursor of Mi is labeled with the isotopic tracer k, a set of relations are obtained in the form MUt) = j* RiFi dd In each such phase (M0)*k is zero since initially no labeled metabolite is present and none appears until it is provided by the precursor through normal processes. For most of the elements of biological interest, there are now available several species of isotopes, e.g., H2 and H3, C13 and C14, and the several useful isotopes of iron. While the technical difficulties often increase rapidly with the multiplicity of tracers used in a single experiment, the more extended field of applications open to multiple-tracer techniques in complex systems should not be overlooked. The technique is still relatively undeveloped, but already many instances are found where systems are accessible to detailed investigation only through such techniques and, per- haps as well, through more advanced mathematical treatment such as that outlined above. REFERENCES FOR CHAP. 15 1. Gest, H., M. D. Kamen, and J. R. Reiner: Arch. Biochem., 12, 273 (1947). 2. Kamen, M. D.: "Radioactive Tracers in Biology," Academic Press, New York, 1947. 3. Branson, K.:Bull. Math. Biophys., 8, 159 (1946); 9, 93 (1947). 4. Margenau, H., and G. M. Murphy: "The Mathematics of Physics and Chemistry," p. 506, D. Van Nostrand Company, Inc., New York, 1943. 5. Webster, A. G.: "Partial Differential Equations of Mathematical Physics," p. 379, G. E. Stechert & Company, New York, 1933. 6. Zilversmit, D. B., C. Enteman, and M. C. Fishler: /. Gen. Physiol, 26, 325 (1943). 7. Zilversmit, D. B., C. Enteman, M. C. Fishler, and I. L. Chaikoff: /. Gen. Physiol., 26, 333 (1943). CHAPTER 16 INTERNAL DOSIMETRY 16.1. Physical Principles of Dosimetry. The essential purpose of dosim- etry is the quantitative evaluation of some effect produced in tissue by a given quantity and type of radiation. The radiations with which internal dosimetry is chiefly concerned are those emitted by radioactive materials distributed in or near tissue. The principles and methods outlined in the following sections, however, apply equally well to other kinds and sources of radiation including x-rays and neutrons, protons, deuterons, and alpha particles obtained from high-energy accelerators. The first requirement of dosimetry is an index on which a unit of dose can be established. In the most general terms the index may be a biological indicator, some physical or chemical effect produced by the radiation, or some property of the radiation itself. The ultimate information desired is, in nearly all cases, the biological or clinical effects produced by a given radiation or source of radiation. As yet, however, no biological indicator has proved satisfactory as a unit of dose. Factors such as mean lethal dose, chromosomal changes, and mitotic activity may be taken as biological indi- cators but are useless as units of dose. They do not lend themselves to convenient measurement and not at all to calculation. Different tissues and organs as well as different species of animals vary widely in their resist- ance to radiation so far as observable biological or clinical results manifest themselves. Moreover, for any one tissue exposed to a given energy flux of radiation (mev or ergs per square centimeter per second), observable biological effects are strongly dependent on both the type and the energy of the radiation. For these reasons an index based on any one biological effect would in practice be difficult to correlate with other effects and with similar processes in different tissues. This applies equally well to chemical effects induced by radiation since they are subject to the same shortcomings. There remain, consequently, only physical properties of either the radiation itself or its interaction with tissue. From a physical point of view the ideal unit of dose is either the energy absorbed from the radiation per unit mass of tissue or the ionization formed per unit mass. Both these quantities can be measured with reasonable accuracy and may be expressed in absolute units. Since units of energy 403 404 1SOTOP1C TRACERS AND NUCLEAR RADIATIONS [Chap. 16 absorbed and of ionization may be denned so that they are more or less inde- pendent of the type of radiation and absorbing medium, dose expressed in such physical units may be accurately reproduced in different tissue and can be correlated with any biological or clinical effects that occur. Units of energy absorbed per unit mass or volume of medium have, at the present time, found universal although informal acceptance for expressing dose delivered by corpuscular radiations. The important features of such units are their evaluation in terms of fundamental physical units, the accuracy and convenience with which they are measured, at least in principle, and the fact that they are amenable to calculation when the source of radiation is given. On the other hand, the ionization produced per unit mass of tissue possesses essentially the same qualifications as energy for a unit of dose in addition to the important physical distinction of being the immediate and only directly observable product of radiation interaction with tissue. Ioniza- tion as such is in effect the only measurable precursor of the biological, clinical, and chemical effects that occur. From the standpoint of dose measurement, some advantage is to be found in units based on the number of ion pairs formed per unit mass since the dose is then given in terms of the quantity directly measured with the ionization chamber. The units of energy absorbed which have found the most widespread use include the roentgen-equivalent-physical (U. S.), the gram-roentgen (British), and the energy-unit (British). The only unit of ionization is the J, proposed by the British Committee for Radiological Units. The roentgen, which applies only to x- and gamma radiation, is actually a partial description of the radiation at any specified point (not necessarily in an absorbing medium) , but it is regarded by some as essentially a unit of energy absorbed in air, i.e., 83 ergs per gm of air — a meaning that is not strictly correct. Whichever unit of dose is employed, the physical quantity actually measured is, in all instances, the ionization produced per unit volume per unit time. In the case of dose expressed in roentgens, the ionization meas- ured must, by the definition of the roentgen, be that produced in air at the point under consideration. In order to make use of conveniently small ionization chambers and yet measure true air ionization, it is necessary to use "air-wall" chambers, i.e., chambers with solid wall material consisting of airlike atomic composition, in determining dose in roentgens. Dose expressed in the various energy units requires conversion of the detected ionization to ergs or mev of energy absorbed. This can be done only when the average energy W required to form one ion pair in the medium is known. For ions produced in air by electrons, W = 32.5 ev. In the absence of con- clusive experimental data on tissue, this value is sometimes adapted to tissue dose assuming air and tissue to be nearly the same in atomic stopping power for electrons. Sec. 16.1] INTERNAL DOSIMETRY 405 Tissue dose obtained by calculation is most conveniently stated in terms of one of the units of energy absorbed (ergs, mev, rep, or gram roentgens) since calculations are based directly on the energy released by disintegration of a radioactive isotope or on the energy flux (ergs or mev per square centimeter per second) of beams of neutrons, protons, or other radiations. Conversion of energy absorbed to ionization units, and also to roentgens in the case of gamma radiation, again requires that the value of W be known for the medium. A distinction, sometimes overlooked, should be made in the terms dose, dosage rate, total dose, integral dose, and the various combinations of these terms that are frequently used in connection with radioactive isotopes. The term dose refers to roentgens (for gamma rays only), to energy absorbed per gram of tissue, or to ionization produced per gram of tissue at a specified point. These quantities usually vary throughout the volume of an organ or animal in some complicated manner depending upon the source and type of radiation. Since dose is a point function it can often be represented, as in x-ray dosimetry, by a family of isodose surfaces, each surface containing all points in the medium at which the dose has a particular constant value. A statement of dose should, in general, always be qualified by a precise description of the point at which the dose was measured or computed. It must be assumed otherwise that the dose was uniform throughout the organ or entire animal involved. The interval of time in which a specified dose was given is not involved explicitly since all dose units are independent of time. Time is introduced explicitly only in the term dosage rate, which, depending upon the units chosen, is the roentgens exposure, energy absorbed, or ioniza- tion produced per unit time at the point under consideration. For radio- active isotopes the dosage rate usually is not constant but depends in some more or less complicated way on metabolic activity and radioactive decay. It is then convenient to speak of total dose, which is the dose received at a point in the tissue during the whole interval of time the isotope remains in the tissue, or during complete decay of the isotope if the isotope remains fixed in the body. The terms above refer only to points within the tissue or other medium, and the dose units are roentgens for gamma rays, rep, energy units, or gram roentgens per gram, or J units for any ionizing radiation. Integral dose alone refers to the total energy absorbed or total ionization produced in an entire organ or in a given mass of tissue. The single unit of integral dose is the gram roentgen, and in particular, the roentgen, rep, energy unit and J cannot be used as a unit of integral dose. Combinations of terms, such as total integral dose and integral dosage rate, are also frequently used. 406 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 It was in effect stated above that energy absorbed and ionization produced per unit volume are absolute measures of tissue dose. While this is strictly true within the limits of the definitions of the various dose units, there still remain important uncertainties in the actual measurement of ionization under certain conditions and in both the physical and biological significance of the energy absorbed. The first difficulty is encountered only in measurements of ionization produced by heavily ionizing particles such as alpha particles and fission fragments. The ionization produced by these particles is extremely intense since their entire energy is spent in ionizing the relatively small volume of tissue enclosing the short path of each particle. The resulting high ion density presents a difficulty in measuring dose with an ionization chamber in that partial recombination tends to take place among ions of opposite charge before they have been separated and swept out of the gas volume of the ionization chamber by the electrostatic collecting field. It is likely that something less than the total ionization produced by multiply-charged particles is actually detected, whereas, for beta particles whose ionization is more dispersed, this is not the case except at very high pressure (> 10 atm). The local high density of ionization caused by these radiations also leads to more profound biological and clinical effects than are observed for the same energy absorption or ionization produced per cubic centimeter of tissue exposed to beta particles and gamma rays. Greater biological effectiveness of a similar magnitude is also found for protons, deuterons, and for fast and slow neutrons. Indeed, there is reason to believe that for the same dose the biological effectiveness of beta particles varies with energy, although to a lesser extent than the difference between beta particles and protons or alpha particles. It is also well known that even for electromagnetic radiation clinical effects vary with the energy composition of x-ray beam. At the present time these effects can only be lumped under the term relative biologi- cal effectiveness (R.B.E.) which expresses the ratio of gamma-ray dose to the dose that is required to produce the same biological effect by the radiation in question. The evaluation of this factor for various radiations is not easy nor can it be extrapolated with certainty from one tissue to another. This is due primarily to the difficulty in evaluating biological effects quantitatively and because of the striking variation in the magnitude of the effects produced in different tissues and animals. The R.B.E. of protons, deuterons, alpha particles, and neutrons has, however, been extensively investigated in certain species of animals, notably the mouse and rat. For these mammals, and possibly also for man, the R.B.E. of protons, deuterons, and neutrons is about 4, while for alpha particles it has a value of about 10, i.e., 0.1 rep of alpha particles produces about the same biological effect as 1 r of x-rays (x-rays not photoelectrically converted). Considerable caution must be Sec. 16.1] INTERNAL DOSIMETRY 407 exercised in extrapolating these values to other animals or to specific tissue since, as has been illustrated by extensive experiments with neutrons, values of R.B.E. varying from 0.8 to as much as 30, depending upon the neutron energy and substance irradiated, have been reported by various investigators. The precise physical significance of the absorbed energy is not as yet entirely clear. The greater part of the energy absorbed from incident radia- tion is perhaps utilized in the production of ions in the medium, but there is also reason to believe that an appreciable fraction of the absorbed energy is taken up by processes in which no ions are formed, such as excitation of atoms and molecules, decomposition of complex molecules, and the formation of certain substances as in water exposed to x-rays. Although the influence of these processes is not yet well known, they do not directly affect the practical problems of dosimetry since the term dose as used in radiobiology means essentially a measure of the energy absorbed without regard to the manner in which it is absorbed. Ionization, therefore, serves as an empirical measure of energy absorbed. The empirical determination of dose received by tissue exposed to radiation requires some means for ascertaining the density of ionization within the tissue. This is made possible by measurement of the ionization produced in the gas of a small cavity ionization chamber placed at the point under consideration. A discussion of the principles of the cavity chamber is given in Sec. 12.2, based on the detailed description of the theory and application of such chambers to gamma rays and neutrons reported by Gray [12,18]. In brief, it consists of a small gas-filled cavity with linear dimensions that are small compared to the range of the secondary beta particles in the gas. If the cavity walls are tissuelike in atomic composition or, if differing from tissue, they are made extremely thin and surrounded with tissue, the energy absorbed in the tissue per cubic centimeter of tissue at the point where the cavity is placed is related to the observed gas ionization by the simple relation E = JWS ergs/cc/sec where / = number of ion pairs formed in gas per cc per sec II" = average energy absorbed to form one ion pair in gas (about 32.5 ev for electrons in air) 5 = stopping power of wall material (tissue) relative to the gas The factor S is given by the ratio NtBt/NuBg, where Bt and Bu are the stop- ping numbers of tissue and gas, respectively, computed from Bethe's stopping formula, and ATf and Ary are the respective numbers of atoms per unit volume of tissue and chamber gas. If the atomic composition of the chamber gas is made similar to that of tissue, then Bt = Bfl and the factor S is simply the ratio of the number of atoms per unit volume of tissue to the number per unit 408 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 volume of gas. For many purposes air is sufficiently similar to tissue to use the simple ratio S — Nt/N&iT; in more accurate measurements, gas mix- tures with approximately the same atomic composition as tissue can be prepared. The average percentages of the principal atomic constituents by weight in lean tissue, for example, are hydrogen, 9.9 per cent; carbon, 13.4 per cent; nitrogen, 4.1 per cent; oxygen, 70.11 per cent; and light minerals, about 1 per cent. Chambers based on the. cavity principle are applicable to all types of radia- tion and absorbing media. They provide an accurate means for determining dose in terms of absolute quantities, either ionization produced or the energy absorbed expressed in fundamental physical units. When one is measuring the dose in roentgens, the chamber gas and wall material, as pointed out above, cannot be chosen arbitrarily but must consist of air and airlike substances. Calculations of dose delivered to tissue by a uniformly distributed source of charged corpuscular radiation (beta particles, alpha particles, and fission fragments) may be expected under favorable circumstances to yield results in reasonable agreement with the actual dose. Under less favorable con- ditions and in most instances where x- or gamma radiation is involved, calculations of dose by the methods available at present can be relied upon to give only the order of magnitude of the true dose. The uncertainties accompanying such calculations are due chiefly to the lack of sufficiently detailed information concerning the exact disposition and concentration of the radioactive isotope throughout a tissue and to the difficulty in evaluating that fraction of the energy made available by radioactive decay which is actually absorbed in the tissue under consideration. The importance of metabolism as a factor in internal dosimetry is obvious. The dose delivered to specific tissues by an administered radioactive isotope depends upon the amount taken up in the tissue and the length of time it remains there. The metabolic paths and rates of turnover are not unique for a given isotope but often depend on the chemical substance in which the isotope is incorporated. These factors are known in some detail for certain organic molecules that can be labeled with active isotopes, and the metabolic fate of a few isotopes such as iodine, phosphorus, and sodium in inorganic salts is reasonably well understood. For a few other substances it is sometimes possible to determine the concentration in a specific tissue either from biopsy or from previous tracer investigations. In most instances the concentration does not remain constant in any one tissue, but, depending upon the com- plexity of the chemical reactions the administered active substance under- goes, it is regulated by the metabolic rates of uptake and elimination. From the clinical standpoint, estimates of dose are further complicated by the considerable variation among different individuals in the tissue mass of Sec. 16.2] INTERNAL DOSIMETRY 409 organs and in the metabolic rates of uptake and elimination. The simplest problem, for example, is encountered when the isotope is rapidly accumulated and fixed in one or more organs, but instances of this are few, and calculations based on this assumption usually do not serve even as a first approximation for most of the problems met with in practice. The rate at which energy is made available by the decay of a known con- centration or total quantity of administered isotope is easily calculated if the decay scheme for the isotope is known. The distinction between available energy and actual decay energy released per disintegration should, however, always be kept in mind. For example, in simple beta decay the available energy per disintegration is not the beta maximum energy given in isotope tables but an average value which is often about one-third of Em^. The remainder of the decay energy is carried off by neutrinos which do not con- tribute to the tissue dose. Also in the process of pair production the gamma- ray energy transferred to kinetic energy of secondary electrons is not Ey but Ey — 2m0c2, where 2m0c2 is twice the rest energy of the electron. Although the total available energy is easily determined, the fraction of this energy actually absorbed within a specific mass of tissue (usually the tissue containing the active material) and, therefore, contributing to the dose is often subject to considerable uncertainty. Gamma rays, except possibly those in the soft x-ray region, are never completely absorbed in the organ from which they originate since the absorption (aside from a geometrical factor of 1/V2) is exponential with a half-value thickness greater than the linear dimensions of large organs. The same difficulty affects beta emitters as well. When the dimensions of the organ containing the isotope are comparable to or smaller than the range of beta particles emitted, a con- siderable fraction of the radiation is only partially absorbed and, con- sequently, cannot contribute its entire energy to the organ under considera- tion. Even in very large organs some loss of energy may be sustained due to escape of radiation from active material lying near the surface. At the present time the fraction of available energy contributing to the dose received by a specified mass of tissue can be calculated for only those cases involving the simplest physical and geometrical considerations. In other instances estimates of the dose received can often be made by graphical methods- They may also be made empirically with the aid of phantoms and ionization chamber probes. 16.2. Units of Dose. Many units of dose have been proposed in order to circumvent the limitations of the roentgen. Thus far, however, only the roentgen has been accepted by international agreement, while the various proposed units have met with varying degrees of success through common usage. Those units which have found the most frequent use in the United States and Great Britain are described below. 410 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 a. Roentgen. A dose of one roentgen, received at any point, means 1 esu of ion pairs produced per cc air 2.083 X 109 ion pairs produced per cc air 1.61 X 1012 ion pairs produced per gm air 6.77 X 104 mev absorbed per cc air 5.2 X 107 mev absorbed per gm air 83 ergs absorbed per gm air Air refers to dry air at 0°C, 760 mm Hg. Values of energy absorbed are based on 32.5 ev absorbed to form one ion pair by an electron in air [9,12]. Definition: The roentgen is "that quantity of x- or gamma radiation such that the associated corpuscular emission per 0.001293 gm of air, dry, 0°C, 760 mm Hg produces, in air, ions carrying 1 electrostatic unit of quantity of electricity of either sign" [1]. The roentgen, by its definition, is a partial description of the electro- magnetic radiation at a point measured in terms of the ionization produced in air. It is a unit not of intensity, energy, or flux but rather of the time integral of the flux density evaluated according to its ability to ionize air. The relationship that does exist between the energy absorbed in air exposed to one roentgen and energy flux (number of photons per square centimeter X energy, hv, per photon) shows a complicated dependence on gamma-ray energy. As shown in Fig. 114, x- or gamma rays of very low energy, corre- sponding to the energy range in which the photoelectric effect is the principal absorption process, produce the greatest ionization or dose for a given energy flux. Only in the range from 0.08 to about 1.2 mev, where Compton scatter- ing is the principal interaction process, is the roentgen nearly independent of gamma-ray energy for constant flux. In this region 1 r corresponds to approximately 2,800 ergs per cm2. In general, however, for a given energy flux the dose in roentgens decreases with increasing gamma-ray energy, at least for energies less than about 30 mev. An important feature of the definition of the roentgen is its reference to air. One roentgen of gamma rays is the quantity of radiation such that about 83 ergs are absorbed per gram of air, but in substances of different atomic number and density the amount of energy absorbed for this same quantity of radiation will be different. Thus, in soft tissue the energy absorbed per gram per roentgen is about 93 ergs, and in bone it may be several hundred ergs. Despite the great variation in the relative amounts of energy absorbed in different substances, the dose is still 1 r if the same quantity of radiation produces 1 esu of charge of either sign per cubic centimeter of air at the point under consideration. The dose expressed in roentgens is totally inde- pendent of the absorbing medium that is exposed and of the amount of energy that the particular medium absorbs. Sec. 16.2] INTERNAL DOSIMETRY 411 LU ,- o O o o o o (0 IO o o o <* o O o O o O ro C\J o o o N30JLN30W/ W0/S9H3 Nl XfTU A9H3N3 412 1S0T0P1C TRACERS AND NUCLEAR RADIATIONS [Chap. 16 The roentgen is in some respects a measure of virtual energy absorbed, i.e., the time integral of the energy absorbed if the medium were replaced with air. A dose of 1 r is delivered only when 1 esu of charge is formed per cubic centimeter of air, but this amount of ionization may be produced in any arbitrary interval of time. The time is introduced only in reference to dosage rate expressed in roentgens per unit time. For any given gamma-ray energy the dosage rate is directly proportional to the intensity of radiation. b. Roentgen Equivalent Physical {proposed by H. M. Parker [19]). A dose of one roentgen-equivalent-physical means 83 ergs absorbed per cc tissue 5.2 X 107 ev absorbed per cc of tissue Definition: "That dose of any ionizing radiation which produces energy absorption of 83 ergs per cubic centimeter of tissue is 1 rep" [19]. The rep is a dose unit applicable to all corpuscular radiations such as beta and alpha particles, protons, and deuterons and is a measure of energy absorbed in tissue exposed to these radiations. Its value is established on the basis of the energy absorbed in air exposed to 1 r, but the rep is not, in general, equal to the energy absorbed per gram of tissue exposed to 1 r. The energy absorbed in tissue exposed to gamma-radiation depends on the atomic com- position and density of the tissue as well as on the energy of the radiation, whereas, the rep is always 83 ergs per gram of tissue, independent of tissue composition, type of corpuscular radiation, and energy. In soft tissue, for example, a dose of 1 r corresponds to the absorption of about 93 ergs per gram, whereas this amount of energy absorbed from corpuscular radiation corresponds to a dose of 1.1 rep. If it is known either from computation or experiment that Ei ergs or E2 mev of energy are absorbed per gram of tissue, the dose delivered expressed in rep is Ei/83 or E2/5.2 X 107, respectively. The rep is essentially the same unit as the equivalent roentgen (er), used by Marinelli, et al. [13], and such units as tissue roentgen and roentgen equivalent proposed by others. c. Grain Roentgen (proposed by W. V. Mayneord [12]). A dose of one gram roentgen means 83 ergs energy absorbed 5.2 X 107 ev energy absorbed Definition: the gram-roentgen is that amount of gamma-ray energy con- verted into kinetic energy of secondary electrons which is equal to the energy absorbed by 1 gm of air exposed to 1 roentgen. The gram roentgen is a unit of energy conversion but without regard to the quantity of tissue in which this amount of energy is absorbed. It is, there- fore, a unit of integral dose and should be clearly distinguished from other Sec. 16.2] INTERNAL DOSIMETRY 413 dose units as such. It can, however, be expressed as a dose unit (energy absorbed per gram of tissue at a point) by writing it as a gram roentgen per gram of tissue. From its definition, 1 gm r = 83 ergs, assuming that the energy required to form one ion pair in air by a secondary electron is 32.5 ev. Like the rep, the gram roentgen represents an amount of energy absorbed independent of tissue composition and is not equal to the energy absorbed per gram of tissue exposed to 1 r. On the other hand, the relation between gram roentgen and rep is exactly 1 rep = 1 gm r per gram of tissue. d. Energy Unit {proposed by L. II. Gray [11]). A dose of one energy unit means 93 ergs absorbed per gm water (soft tissue) Definition: The energy unit is that dose delivered to tissue by ionizing radiation such that the energy absorbed per gram of tissue is equal to the energy absorbed per gram of water exposed to 1 r of gamma radiation. The energy unit is a unit of energy delivered to tissue by any kind of radiation, and its magnitude is chosen so that the energy absorbed in soft tissue is the same whether it is expressed in roentgens or energy units. This equality is not valid however for hard tissue and other substances differing from water (soft tissue) in atomic composition and density. The relations between eu, rep, and gm r per gm are approximately 1 eu = 1.1 rep = 1.1 gm r per gm e. J Unit [10]. Definition: "One J has been received at any point in a medium when the ionization which would have been observed in an infinitesimal cavity contain- ing the point is 1.58 X 1012 ion pairs per gram or air enclosed in the cavity." The J is a unit of dose proposed by the British Committee for Radiological Units (1948) and intended to replace existing dose units. It defines dose in terms of a quantity that is measured directly, namely, the ionization pro- duced in the gas of a cavity ionization chamber (see Sec. 16.1). Because of the properties of the cavity chamber, the J is applicable to all ionizing radia- tions, electromagnetic and corpuscular, and is valid for all energies of the primary radiation. The numerical value of the J in terms of ion pairs is chosen to correspond to the number of ion pairs formed in water or soft tissue exposed to 1 r. Consequently, 1 J (1.58 X 1012 ion pairs per gram of air) corresponds to 93 ergs absorbed per gram of air, or alternatively, air exposed to 1 r (1.61 ion pairs per gram of air) of gamma rays not appreciably absorbed photoelectrically corresponds to a dose of 1.02 J. /. Roentgen Equivalent Man {Mammal) {proposed by H. M.Parker [19]). A dose of one roentgen equivalent man has approximately the following significance: 414 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 1 rem ~ 1 rep for beta particles ~ 0.25 rep for protons, deuterons, and neutrons ~ 0.1 rep for alpha particles Definition: The rem is that dose which, delivered to man (or mammal) exposed to any ionizing radiation, is biologically equivalent to the dose of 1 r of x- or gamma radiation (not photoelectrically converted). The rem was proposed as a practical unit of dose to circumvent the diffi- culties imposed on other units by the discrepancies in the relative biological effectiveness of various radiations. Hence, the rem is not a measure of energy absorbed or of the ionization produced in tissue; rather, it is a measure of the quantity of radiation that produces certain observable biological effects. The magnitude of the rem in terms of other units is not known with certainty because of the difficulties in evaluating biological effects quanti- tatively. As yet no wholly satisfactory biological indicator is known since different tissues and organs as well as different species of animals exhibit marked variation in radiation resistance. For this reason the relative biologi- cal effectiveness of the same ionization produced, for example, by fast neu- trons and gamma rays has been found experimentally to vary from 2 to about 10 in mammals. An approximate value of 4 for the relative effective- ness of neutrons to gamma rays in this instance was derived from the mean lethal neutron dose for rats [5], assuming that the radiation resistance of rats is not significantly different from man. g. n-Unit {proposed by R. S. Strong). A dose of 1 n is approximately 1 n ~ 2.5 rep ~ 200 ergs absorbed per gm of tissue Definition: A dose of 1 n is delivered to tissue by fast neutrons when the ionization produced in the Victoreen 100 r thimble chamber equals the ionization produced by 1 r of gamma radiation. The n-unit provides a convenient means for measuring fast neutron dose with the standard air-wall thimble chamber used in x-ray dosimetry. It does not, however, represent accurately the ionization produced by neutrons in tissue. The dose measured with the thimble chamber represents ionization produced by recoil nuclei in air and from the wall which is airlike in com- position, but in tissue the greater percentage of hydrogen increases the con- version of neutron kinetic energy. On the average protons recoil with a greater fraction of the incident neutron's energy than do oxygen and nitrogen atoms. This effect results in tissue ionization 2 to 2.5 times greater than that measured with the air-wall chamber. 16.3. Calculation of Beta-particle Dose. The dose delivered to tissue by beta particles (negatrons or positrons) emitted from radioactive isotopes can Sec. 16.3] INTERNAL DOSIMETRY 415 usually be estimated by relatively simple methods when the concentration and disposition of the isotope are known. The fact that the range of beta particles in soft tissue is usually only a few millimeters means that the exposed tissue is confined largely to the same regions that contain the active material. For this reason calculations of tissue dose from beta particles, and other low-energy (< 15 mev) corpuscular radiations as well, are essen- tially estimates of the energy made available by the decay of a certain quantity of active isotope per gram of tissue; the result divided by an appro- priate constant permits direct conversion to the desired units of dose. An important factor concerning beta-particle dose should, however, be kept in mind. Although the relatively short range and the consequent localized absorption of beta particles provide a considerable advantage over gamma rays in calculating dose, it cannot be assumed in every instance that a reason- able estimate of dose will be obtained by considering the entire beta energy to be absorbed solely in the tissue or organ containing the isotope. This assumption is valid only when the linear dimensions of the organ are large compared to the range of the particles. If thcactive material is concentrated near the surface of a large organ or in tissues whose linear dimensions are only a few millimeters, a considerable fraction of the more energetic particles is not completely stopped in the tissue but expends part of its energy outside the region. This is especially true when energetic beta emitters such as P32 (1.7 mev) are taken up in the organs of mice and similar small animals. The computed dose, assuming complete absorption of beta radiation in the organ under consideration, may be in error by a considerable amount. This factor is less important for soft beta emitters, such as H3, C14, and S35, since the ranges in tissue are much less than a millimeter and few organs are this small. The range of beta particles expressed in milligrams per square centimeter is very nearly constant among elements of low atomic weight. It can be assumed, therefore, within the accuracy with which dose calculations are possible, that the range in tissue is essentially the same as in water and aluminum for which the range-energy relations are well established. Note, however, that if the range in a medium is to be expressed in centimeters, the range in water expressed in milligrams per square centimeter must be divided by the density of the medium. Beta particles in the range of energies encountered from radioactive isotopes (0 to 3 mev) lose energy primarily by ionization. Nevertheless, some energy is also lost by radiation {Bremsstrahlung) which in turn is absorbed only in large thicknesses of tissue in the same manner as con- tinuous x-rays. The amount of this radiation is difficult to estimate, but because it is usually small compared to energy loss by ionization, it is disregarded in dosimetry. Positrons present a special problem. Each 416 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 ~-3i*~?- - '="->- jIe'eOI?" "7*~.\ X --.y- i--lL 1^====? - >^ ^44||t^-4---=-=S||=i=||ij :tf ,--->"t"^z;=pE^=^~?^r~. [^ ' •" — r — fc=-=-====z:=====^£==:===geB lli|llllllllliiiiiii=|illiiiiHllllllHUlllllllllllllll|llH=lll=lB = E^ = = ^ = = = = - = ------r? = zzzzz-zzz = = z = = = = z = EP=:r-z = = z = = = ^2? = = = = = E|±: = = rr zz:=zziz=iiiz=z===-?!i=====zzzEzziz :z=ri:iii-??i__ii-ii=__rr:rrii: iiii[iiiiiiiKi|ili jg jIeW |i i ; .^g -SPi. y B- -S mnHrriri^^ ilHt f 1 Tlffff^ffl 1 1 1 1 ii 1 1 J/fi ft "H'ftff litif 1 TTTT1 1 / ^ _ f~ ? m, ^ ~1 ./^ V- - / J *** J > —K*"*'' 0 i /l / c **** -.:- --■■£:. y -- _r ^ = = = = = - - -_ J* j | | £ -^-~ ---=,= -?-.---:■:- _ z^ "■_ - ^ ^ - ■ = --=,: mjIlJlmiiiiijijiliiiiim :i:: — ^ ^ \j ^ — f— zzzzzfz = = zzzzzz;z^ = zzz = zzzzzzzzzzzzzz = zz.?z'z3zzzzzzzzzzzz = zzzzzz3E = zzz = : yj ;:;: : = jj-; izzz^zzzjzzzzzzzzzzzzzzzzzEzzzzzzzzzzzz: 1 iiiuliiHiiteHiuniiMHij Z :==: = = z = ^=z ==zzzzzizz?= = === = = = = zzzizzz = zzz = izz==^-===zzzz = zzEEEEzzE: E? j ? i i 3 ^ ***^ IAJ f f - ^ CD r ** Z * j / <** ^ / / ^r o^ 001 / *^ ipiiKiiiiiiK :"p::::p:z::^:::::"::::::"::::::::: = = :=:::"-"::":::::::::::: If $ liiiifilli! llfl'l :|=z = = zzz = ==== ==z = z=zz = ===zz: = = = = = = z|=== = = = = = = = ====zz = zz = z== = = = zzzz: 0.001 100 200 300 400 500 600 700 ELECTRON VOLTS Fig. 115. Range of beta particles in tissue of density-1. [E. J. Williams, Proc. Roy. Soc. (London), A130, 310 (1930).] Sec. 16.3] INTERNAL DOSIMETRY 417 particle, after losing its kinetic energy to the absorbing medium, undergoes annihilation, producing in the process two gamma rays, each of 0.511 mev (m0c2). This amount of available energy sometimes cannot be disregarded, and the positron-active isotope may then also be treated as a gamma-ray emitter. The energy made available per gram of tissue per second by the decay of a beta emitter is given by the product of the number of disintegrations per second per microcurie, the concentration u of the isotope in microcuries per gram of tissue, and the average energy E$ of the beta particles. Ed = 3.7 X WuEf, ev/sec/gm Similarly, the total energy made available per gram of tissue in the interval of time 0 to / following administration of active material is ED = 3.7 X 104£e T u dt = 3.7 X W'EpU ev/gm in which 3.7 X 104£/ is the number of disintegrations that have occurred in the tissue per gram of tissue during the interval. The quantities u and U depend on the rates of metabolic accumulation and elimination as well as on the rate of radioactive decay. In general, therefore, u and U are functions of time and are given in Sec. 16.6 for various cases of biological interest. The simplest possible case may be noted as an illustration. If u0 microcuries of isotope of long half-life remain fixed in an organ, u is a constant equal to u0. The quantity U for the interval of time 0 to / is then ii T U ' 0.693 U e ' where T = decay half-life The average beta-particle energy Ep is not to be confused with maximum energies given in tables of radioactive isotopes. The particles emitted by any isotope vary continuously in energy from zero up to the maximum Em&x. If the beta spectrum is simple and no conversion electrons are present, the average energy in many instances is about E = £max/3. In general, however, beta spectra are complex; each nucleus decays with emission of one of several possible beta particles for which the maximum energies are different. Fur- thermore, the presence of strongly converted gamma rays greatly influences the average energy. Under either of these conditions reliable values of E$ can be determined only from the observed energy distribution obtained with the beta spectrograph. Values of E$ determined by this method for some of the commonly used isotopes are given in Table 6. With the available energy calculated from the formulas above the dose 418 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 received by the tissue in terms of conventional units is easily found as follows: a. Dosage rate in rep per sec or in gm r per gm per sec , Ed 3.7 X 104 p rep/sec " 52.5 X 1012 == 52.5 X 1012 3 or gm r/gm/sec where 52.5 X 1012 is the factor for conversion of ev of energy absorbed to rep. b. Accumulated and total dose in rep n Ed 3.7 X 104 np rep " 52.5 X 1012 == 52.5 X 1012 " or gm r/gm c. Integral dosage rate in gm r per sec Ld- = 52.5 X 10'2 gm r/sec where m is the weight of the tissue containing active material. d. Accumulated and total integral dose t n mE° LD- = 52.5 X 10>2 gm r e. Dosage rate in ionization units 1.58 X 1012W J/ /. Accumulated and total dose in ionization units Ed D = 1.58 X WW the factor 1.58 X 1012 is the number of ion pairs per J, and W is the average energy required to form one ion pair in the gas of a cavity ionization chamber placed in the medium. For air, W — 32.5 ev per ion pair formed by an electron. In principle, d, D, Id., and I.D. should be multiplied by a fraction / (< 1) to take into account the available energy that is not absorbed in the tissue under consideration. If, judging from the linear dimensions of the tissue mass relative to the beta-particle range, it can be assumed that the available decay energy is absorbed almost entirely within the tissue, then / ~ 1. If the dimensions of the tissue mass are relatively small, then/ < 1 and can be evaluated only by graphical methods [16] or, if the beta-particle absorption coefficient for the substance is known, the beta particles may be treated by the same method used for computing gamma-ray dose (see Sec. 16.5). Sec. 16.4] INTERNAL DOSIMETRY 419 The method for calculating beta-particle dose may be illustrated by a simple example. Assume that a colloidal suspension of chromic phosphate containing 2 millicuries of P32 is administered to a dog and that 75 per cent is rapidly accumulated and fixed in the liver which weighs 300 grams. The only factor affecting the dosage rate is then the reduction in u resulting from radioactive decay. It is assumed that all beta particles are stopped in the liver and that the isotope is uniformly distributed. The initial (/ = 0) dosage rate is , (3.7 X 107)(2 X 0.75H6.95 X 105)(60) n . .„ d = (300) (52.5 X 10") = °"147 rep/min After 10 days the dosage rate has diminished to d = O.147e-°-693xl0/14-5 = 0.0913 rep/min The accumulated dose delivered to the liver during the first ten days is D _ (0.147)(14.5)(60 X 24) (J _ ^„]X10/1„) _ ^ rep Similarly, the total dose (complete decay of the isotope) is n (0.147)(14.5)(60 X 24) D = — = 4,400 rep The integral dosage rate and accumulated integral dose are obtained in units of gram roentgens by multiplying through by the weight of the liver (300 gm). 16.4. Absorption of Gamma Rays in Tissue. From the point of view of dosimetry the absorption of gamma radiation is concerned primarily with conversion of gamma-ray energy to kinetic energy of secondary electrons. While it is true that the energy given to a single secondary electron is not absorbed in the tissue at the point where the photon interacts with the elec- tron, i.e., the electron causes ionization along a path which at high energies may extend a considerable distance, nevertheless, when radiative equilibrium exists between the primary and secondary radiation, the amount of gamma- ray energy converted to kinetic energy determines directly the density of ionization produced at each point in the tissue. Transfer of energy takes place by three distinct physical processes: the photoelectric effect, Compton scattering, and pair formation. Each of these processes depends in a differ- ent and complicated way on the gamma-ray energy, and the photoelectric effect and pair formation are, in addition, strongly influenced by the atomic composition of the absorber. A more detailed description of the interaction of gamma rays with matter is given in Chap. 2, and only those properties important to dosimetry, 420 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 essentially the problem of gamma-ray absorption in light elements, are discussed below. The photoelectric effect is important only at relatively low energies, < 0.1 mev, and in the energy range of soft x-rays (< 25,000 ev) it is almost Ei a> .5 "5 o o o in a < o .05 .01 1 ■ r ; , , ! r- 1 - - : ■ : lif'-;: :,;£ .::;)... ■ .i i i .■•:;; L; : 1 : - 4 • : • ; 1 : : . !" H~ ■ A - : : ■; :. „= ( ': ':'■[ illlvi': ■y.-\-:r. ■:.. ; -j— hi": ;■:: ::":: — t- — ■ — ~~ir \~ | :::: ::::;:::: :r:: : ----- - - - 1 ■ } ■ ' 1 .:.: ,;, :.!.. .p..p.j..y| X 1 h-- - - f rfrrf ■■■■!-in--! \ -rt- topLfc — \ ::;4:;:;i~f"-i 'Pit j^Frl"" ■ .... p_: S ■:;: E = = V;: i .... jit TtWF ittH 1 t_ _i_ - iiiii::iii| ;,. r: ^ :;-=!"- : : : -i : ■.-. H-. :;: = -:■■-- — - ' ': ^ ;. ' : h.r" r;:: 4 4 -. ! ;,; ; • -- =:;;(: -- -. •)-" - \ : :: . j ;- . ' ;;4i=<-i- - - :-:; .;;; --- i - p i • : : - Y . .:; ■-4-— ... rtt (_. :::: s — | — — - p fegH — i . r:-; - .-=J~- : :;£};:- ~ =S3 ; is : ] ;:T^r --H ~- ;": 35 35: _ , — p - 1 Y '■'■ :; :.:===5 ■~J|i :.•- - ... 14-4- -- :::; ::: .... = 2j = §1 1 tIP tlf| r~-r :::::::±im m iiiiiiiilffe m k pi |p:::: :::::::ii r Ei mr — ~-- H-.r- " 1 _ • _- : .z: j ._ ": . ■HH Hi i li • -i ~Ar-l - '-^ I ::. . : --'- ! i - ;;]; :;||j; ■: V '[.. • ;■-- i 1 1 i - . i ^:-"j'.:- .- ■■■;.--; H f : :H:!. :-_:_! • ■_; - ti : i- :": ; ;--;-"-|-H — ■;• ~)n. ::^- :. :!:::: - 1 " ' !'.:■' ■ '-.'——, "^3ftft~ - -:=: =J= = --it-}Si::a iiL -7 j^hjj .... -±3r- ; — r " --: - ; :;r;n;lv: l. ■ --• "j-i^- — T" -::::: 1" ..:. — H — iHlBIi .:. m ::.: tllli "ilj Ug § m - ~~£ II' : : ::: fffff I | ... I iH Z .01 .05 .1 .5 1 5 Gamma Ray Energy in mev Fig. 116. Linear-absorption coefficient ixe of water as a function of gamma-ray energy in mev. The absorption coefficient includes the photoelectric effect, scattering absorption, and pair production but does not include the contribution from Compton scattering. [From L. D. Marinelli, E. H. Quimby, and G. J. Hine, Am. J. Roentgenol. Radium Therapy, 59, 260 (1948).] wholly responsible for absorption of electromagnetic radiation in tissue. It involves the complete absorption of a gamma photon by an atomic electron that recoils from the atom with a kinetic energy Ee = Ey — I, where / is the ionization potential of the shell, K, L or M, from which the electron is ejected. In light elements composing tissue, / is usually small compared to Ey, and for the purposes of dosimetry is neglected. The photoelectric Sec. 16.4] INTERNAL DOSIMETRY 421 cross section per electron and per atom and the linear- and mass-absorption coefficients are designated by re, r0, ri, and rm, respectively. Compton scattering is usually the most important absorption process for gamma- ray energies 0.1 < Ey < 3 mev associated with radioactive isotopes. Each photon that collides with an electron undergoes a deflection from its initial direction and a partial loss of energy, the amount of which is con- tributed to kinetic energy of the recoil electron. The absorption coeffi- cient ae, di and D = > Di. i i In practice, evaluation of the dose integral above is possible only after the most extreme geometrical and physical simplifications are introduced. The volume V can take only the most elementary geometrical forms such as spheres, cylinders, disks, and ellip- soids. These shapes may, however, often be used to approximate a given organ or animal. Formulas for dose calculations with these forms are given in Sec. 16.7. The density u(R,t) of radiative material, in microcuries per gram of tissue, may sometimes be regarded as a point source, as in the case of radium needles, but usually it is assumed to be constant throughout the tissue within a certain region or organ; nevertheless, because of metabolic processes and radioactive decay, the activity density is, in general, dependent on time. Only in the single instance of a long-lived isotope that remains fixed in the tissue can u be considered a constant. In other cases, when the rates of accumulation and elimination are known, u may be estimated with formulas given in Sec. 16.6. Assuming the active material to be distributed uniformly in a particular region, organ, or entire animal that is essentially constant in tissue density and composition, the dosage rate and total dose at one point due to gamma rays of a particular energy can be computed from the somewhat simpler formulas d = IAu{t)g r/sec D = I A U(t)g r Fig. 117 424 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 where g is the geometrical factor taking into account the volume distribution of active material in some appropriate simple shape which approximates the actual organ. The constants / and A are described below. Integral gamma-ray dose presents a somewhat more difficult problem for which it is necessary to evaluate a double integral or else establish the isodose curves throughout the organ. In units of gram-roentgens the integral dosage rate and total integral dose delivered to a specified volume of tissue are ue~ llR dV dV1 gm r/sec I.D. ---- 83 IAP j J ^-dVdV1 gmr or I.d. = 83 IAuG gm r/sec I.D. = 83 I A UG gm r where 83 is a conversion factor (83 ergs absorbed per gram per roentgen) for conversion of energy in ergs to gram roentgens, and G is the integral geometri- cal factor (see Sec. 16.7) and p is the tissue density. If the isodose curves have been determined empirically, the integral dosage rate is I.d. = \ S3pdiAVi gm r/sec i where p = tissue density di — dosage rate in r per unit time in volume AVi AVi = volume of tissue between isodose surfaces The number A of gamma rays of a particular energy emitted per second per microcurie of radioactive isotope depends upon the complexity of the decay scheme of the radioactive isotope. If there is no branching or inter- nal conversion, each isomeric transition occurs once per disintegration or A — 3.7 X 104 gamma rays per second per microcurie of isotope. When decay schemes are complex, branching alone will often make A < 3.7 X 104. Since gamma radiation may be emitted in isomeric transitions in the nucleus, from annihilation of positrons and as x-rays accompanying K capture and internal conversion, the value of A must be determined for each component on the basis of the decay scheme. Isomeric transitions (I.T.) are usually the principal source of gamma rays in most isotopes of biological interest. Assuming that branching and internal conversion £I.C.) occur, the number of gamma quanta emitted per second per microcurie is then Alt. = 3.7 X 104(1 — })v 7/microcurie/sec Sec. 16.5] INTERNAL DOSIMETRY 425 where v = fraction of disintegrations in which the particular isomeric transition occurs / = conversion coefficient (defined by Ne/{Ny + Ne), where Ne, Ny are numbers of conversion electrons and gamma rays per transition The value of A for annihilation follows in a similar way Aan = 2 X 3.7 X 10% where vp is the fraction of disintegrations in which a positron is emitted. Each positron on annihilation produces two gamma rays, each of 0.511 mev (m0c2). Nuclei that undergo K capture in a fraction v% of disintegrations cause the emission of K x-radiation. The number of such x-rays is AK = 3.7 X 10 V The estimation of x-rays associated with internal conversion is often less certain. If only one gamma ray is strongly converted, the value of Ai.c. for all x-rays (K, L, . . . ) is ,4 i.e. = 3.7 X 104j/i.t./, where vi.r. is the fraction of disintegrations in which the isomeric transition occurs. If several gamma ray are converted, A = SA», summed over all isomeric transitions. The values of the constants v and / are given when known in the decay schemes for various isotopes. Unfortunately, accurate values of these quantities are known for only a few isotopes of biological and clinical interest. The factor /, as used in the formulas above, is the dose in roentgens received at the surface of a sphere of unit radius due to a single gamma quantum of energy Ey emitted from the center. For the purpose of its evaluation, consider a single unstable atom placed at the center of a spherical shell of medium with a radius of 1 cm. When the single gamma ray is emitted, the gamma energy converted to kinetic energy of secondary elec- trons per gram of medium at any point on the unit sphere is EjU£. = T [Ey(Tm "J" a f!l $S E 03 c iLl o ac o E E o o ■*•> — ' c "o rt fci 3 c> o o CVJ uio I jo jq-ouu /j in CJ Q '-i. o C/i H> M > 0) £ ~ 00 o pj f-H '** W) _ o >- Q tn OJ vO m o O OJ o Z10 00 imma-r herapy, bb t-. 428 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 The product A I in the dosage-rate formula has the following important physical significance: it is the dose in roentgens per second at a point 1 cm distant from a point source of 1 microcurie of radioactive isotope for a particular gamma ray (or x-ray) emitted by the isotope. Its value in air calculated by Marinelli, et al. [13], as a function of energy is plotted in Fig. 118, assuming one gamma ray per disintegration and a 1-millicurie point source. If the decay scheme is complex or if strong internal conversion occurs, the value of roentgens per millicurie at 1 cm taken from the graph should be multiplied by the factor A/3.7 X 107, which is the fraction of the disintegrations in which the gamma ray appears. Experimental values of I A for air are given in Table 37, but it should be remembered that they represent the dose per hour per millicurie at 1 cm due to all gamma and x-radiation emitted by the substance. In making gamma-ray dose calculations for any isotope the values of I A given in Table 37 or the graph may be used, or they can be calculated as indicated above. The foregoing discussion may at first glance appear to place dose calcu- lations generally beyond the scope of anyone but the physicist or radiologist who is thoroughly familiar with the subject. For the most exacting calcu- lations involving complicated distributions of active material and inhomogen- eous absorbing material this may perhaps be true, but in many kinds of problems of practical importance even relatively complicated dose calcu- lations can be carried out quickly and with the exercise of nothing more difficult than ordinary arithmetic. Furthermore it is usually unnecessary to consult elaborate tables and charts in order to compute a reasonable approximation of the radiation dose resulting from internal irradiation. The only really essential physical data for this purpose are the energies and per- centages of the radiations emitted by the isotope, and the absorption coeffi- cient of tissue for the gamma rays in question. The energies and per- centages are given in the table of isotopes (Sec. 7.12) and by the decay scheme (Sec. 7.10) if it is known for the isotope. The absorption coefficient of soft tissue has a value of about 0.03 per cm (or cm2 per gm), which is sufficiently accurate for most calculations involving gamma rays with energies from 0.08 to 2.0 mev. The remaining information that is required is more or less physiological and anatomical; at the very least, this must include some information concerning the amount of the isotope taken up in various tissues and the changes in concentration with time. The comparative simplicity of most dose calculations, as well as the gen- eral procedure to follow, is best demonstrated by a typical, although ele- mentary, gamma-ray dose problem worked out in detail. The method described below is easily extended to more involved problems with the aid of formulas discussed in Sees. 16.6 and 16.7. The example to be considered here is the calculation of the gamma-ray dosage rate and the accumulated Sec. 16.5] INTERNAL DOSIMETRY 429 dose at the center of the trunk of an average man to whom 0.1 mc of Na24 is administered. Tracer investigations have shown [20] that Na24 given intravenously comes to equilibrium in the interstitial fluids throughout the body within the first 10 min. Following the initial 10-min mixing period, about 27 per cent of the original Na24 is accumulated in the bones at two different rates for which the corresponding half-times are 10 to 15 min and 1 to 3 hr. Finally, elimination of the Na24 from the body is found to occur exponentially with a half-time of 12 to 14 days. The uptake in the bone structure of 27 per cent of the Na24 does not appre- ciably alter the gamma-ray dose at various points in the body. The dose may therefore be calculated on the basis of a fixed, uniform distribution of the Na24. The justification for this is evident from the fact that the half- value thickness of tissue for the gamma rays from Na24 is about 25 cm, and consequently within distances of this magnitude the bone structure can also be regarded as uniformly distributed. It should be borne in mind, however, that calculations of the dose delivered by the beta particles to bone and to soft tissue must take into account the uptake of Na24 in bone. Finally, the data and approximations required for computing the gamma- ray dosage rate and accumulated dose in this example may be listed in detail: 1. Point in the body for which the dose is to be determined. The trunk may be approximated geometrically by a cylinder of tissue 60 cm long and 40 cm in diameter. The point under consideration then lies on the axis midway between the ends of the cylinder and represents the region in the body receiving the maximum gamma-ray dose. The total body weight is assumed to be 60,000 gm. 2. Effective half-time of Na24. The elimination half-time of Na24 is long compared to the decay half-life of 14.8 hr, hence only the latter need be considered in the accumulated dose calculation. 3. Gamma rays. Two gamma rays are emitted with energies of 1.38 and 2.76 mev in each disintegration (see Sec. 7.10). 4. Absorption coefficient. The absorption coefficients for the 1.38 and 2.76 mev gamma rays are about 0.03 and 0.024 cm2 per gm respectively. 5. Distribution of Na24. The total quantity of 0.1 mc Na24 is assumed to be uniformly distributed throughout the cylindrical volume. The dosage rate at the center of the trunk may now be calculated from the formula d = I Aug for each gamma-ray component and for any time following administration of Na24. For the 1.38-mev gamma ray, the factors in the formula takes the following form and values: 1 = 4tt (Samma-ray energy) (absorption coefficient) ( ^) ye™™ tissue) 430 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 = ^X 1.38 X 10fi X 0.03 X 1.6 X 10~12 X ^ = 5.67 X lO"11 47r 9o A _ /disintegrations^ /gamma rays \ /sec\ = ^ ^ Q ^ \ milhcune-sec / \disintegration/ \hr/ = 1.33 X 1011 (millicuries \ , . . . 0.1 n fiQ„/7, j-, ) (decay factor) = ^7^ e-°-G93t/T gm of tissue/ J 60,000 = 1.67 X 10-6 X e-°-693"r g = geometrical factor for cylinder (Sec. 16.7) = 200 Thus, the dosage rate for the 1.38-mev gamma ray is dx = I Aug = 2.5 X 10"3 X e-°-69WT r per hr. Repeating the calculation above for the 2.76-mev component yields d2 = 4.0 X 10-3 X e-°-™st/T r per hr. Finally the actual gamma-ray dosage rate at the center of the trunk for any time t following injection of Na24 is d = dx + d2 = 6.5 X 10"3 X e-°-69SI/T r per hr. Neglecting the initial mixing period because it is short compared to the half-time of Na24 in tissue, the dosage rate immediately after injection is just 6.5 X 10~3 r per hr, and after five days it is 2.4 X 10-5 r per hr. It may be noted that the dosage rate produced by the beta particles from Na24 immediately after injection is 2.3 X 10~2 rep per hr. The change in dosage rate with time is somewhat more complicated for the beta particles because of the accumulation of sodium in bone. Calculations of the accumulated gamma-ray dose during any prescribed interval of time presents no added difficulty in this simple case since elimina- tion of sodium depends almost entirely on the decay half-life. Integrating the expression for d above (see Sec. 16.6) the accumulated dose at any time following injection of Na24 is 6 5 V 10~3T U ~ 0.693 " U e } At the end of the first day, for example, the gamma-ray dose received at the center of the trunk is D — 9.4 X 10-2 r, and at the end of the fifth day it becomes D = 0.14 r. The precise significance of a dose calculation such as the example worked out above should always be borne clearly in mind. In this instance the meaning of the computed values is quite evident. The dose was calculated for only one point in the body, the point at the center of the trunk where Sec. 16.6] I X TERN A L DOSIMETRY 431 presumably the maximum gamma-ray dose is received. If the body were actually a cylinder filled with soft tissue of unit density, the calculated dose would be very nearly correct, but since the body contains large cavities and an extensive bone structure consisting largely of minerals, it can be said only that the computed values should be in the correct order of magnitude. The dose received at any other point in the body should be less than at the center, but it is difficult to make such calculations; at the surface of the skin, for example, the gamma-ray dose may be from one-fourth to nearly one-half that at the center. The necessity for uniform distribution of active material is in this case entirely satisfied, at least initially, but in many other instances it is not so certain. Finally, the contribution to the dose made by the beta particles emitted by the isotope must, of course, also be computed. In most cases, especially where small organs are involved, the beta-particle dose will be many times greater than that produced by the gamma rays. 16.6. Calculation of Radioactivity Density in Tissue. The dose delivered to tissue or an organ that has taken up radioactive material in one form or another depends directly on the number of atoms that disintegrate while still within the tissue. The estimate of this number is, with a few notable exceptions, complicated by the involved and often uncertain metabolism of the radioactive isotope itself or the substance in which it is incorporated. In most instances metabolic uptake and elimination of active material exhibit rates that are comparable to and often very much smaller than the rate of radioactive decay. Consequently, the number of atoms that decay while in the particular organ under consideration usually is not equal to the number of unstable atoms that pass through it; some atoms decay before entering and many decay after leaving the organ. An estimate can be made, however, when the metabolism of the isotope is known at least superficially, i.e., the gross rates of uptake and elimination regardless of the chemical changes that the isotope undergoes. To do this it is necessary to determine either empirically or by calculation the activity density u expressed in microcuries per gram of tissue at any instant, and the function 3.7 X 104Z7, the number of disintegration per gram of tissue in a given interval of time. It is to be expected that a mathematical description of metabolic processes will often be impossible or else lead to inconveniently complicated expressions, particularly where second- or higher order chemical reactions are involved. If it is assumed, however, that uptake and elimination can be described by a linear or exponential function of time, the calculations are reasonably tractable and the results are valid for many biological processes and may serve as a first approximation in more involved cases. In addition, it must be assumed that the density of active material is uniform throughout the organ 432 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 for which the dose is to be calculated, the total amount of active material in the organ is then just mu where m is the tissue mass. The activity density u is calculated from the representative, though not general, equation ■jj = f(u,t) - h(u,t) which states that the rate of change of activity equals the rate of uptake minus the rate of elimination. The functions f(u,t) and h(u,t) are arbitrary in that they are chosen to describe each case in accordance with appropriate physical and chemical conditions. The function U is obtained by integration of u over the interval of time 0 to /. U = I udt microcurie sec/gm a. The simplest and also a common dose problem is that in which a given quantity u0 microcuries of isotope is rapidly fixed in a tissue and subsequently is neither accumulated nor eliminated. The activity density after a time / is u = — e~°-693t/T microcuries/gm m where m = mass of tissue, gm T = decay half-life of isotope the function U for the interval of time o to / is then u T U = k JL-, ■ (1 — e-0-69S'/r) microcurie sec/gm 0.693m b When the entire quantity of isotope decays, U = uoT/0.693m. It may be recalled that 3.7 X 104£/ was the number of radioactive atoms originally present (at time t = 0) per gram of tissue. b. Initially no active material is present in the tissue, but for t > 0 it is taken up and fixed in the tissue under consideration at a constant rate of b microcuries per gm of tissue per second. This represents the behavior, for instance, when active substances are ingested or breathed at constant rates or when taken up from blood or other reservoirs maintained at a constant level of activity. The activity density at any time / > 0 is then u — _ ,_, (1 — e~°-G9Zt/T) microcuries/gm 0.693 where T = decay half-life The activity in the tissue increases exponentially and approaches after a long time, / » T, the constant level bT/0.693 microcurie per gm. The disintegration function U for the interval 0 to / is Sec. 16.6] INTERNAL DOSIMETRY 433 bT U = 0.693 1 0.693 U C microcurie sec/gm After a long interval compared to T the number of atoms that disintegrate in the tissue, and hence the total dose, increases linearly with time. If instead of being fixed in the tissue the active material is eliminated exponentially with a half-time T%, the formulas above are still valid when T is replaced by TiT2/(Ti + T2), where Tx is now the radioactive decay half-life. c. In many cases the active material is taken up and fixed in an organ or certain kinds of tissue at a rate proportional to the activity remaining in a reservoir such as blood when the material is given intravenously or perhaps when given orally. Assuming that no activity is present initially in the organ and no elimination occurs, the activity density at time t following administration of n0 microcuries is u * = n*n? g-°-693'/r>(l - g-°-693'^) microcuries/gm 0.693m to where T\ = decay half-life To — uptake half-time The accumulated activity reaches a maximum value when . Jj_, _Tj_ ''max " f. /iCil o T" I T SeC U.OVO 1 i ~\- 1 2 The disintegration function U for the interval 0 to / following administration is " r L_ a _ e-o,,m) Ln _ -a^(<*±*>v .693 K ' 0.693(7! - T2) \ microcurie sec/gm When the entire quantity u0 decays, the disintegration function becomes U = — m U = Jn 0.6931^+ T%) m^rocurie sec/gm This formula, aside from the factor 3.7 X 104, represents the number of dis- integrations that actually occur in the organ during a long time compared to Tx. d. A more involved case is encountered when part of the administered active substance is taken up in the tissue under consideration at one rate and removed at another rate. Part of the administered substance may also be taken up in other tissues or eliminated directly. All such processes tend to decrease the concentration in the reservoir, and if the removal is exponential 434 JS0T0P1C TRACERS AND NUCLEAR RADIATIONS [Chap. 16 the tissues that take up most activity are those with the shortest uptake half-times. In any one tissue the activity density following administration of u0 microcuries of substance is u = — _ ZlTz n, v 0-°-693'/r' - g-o.693 - 1) rr, 0.693 (T+Tz) 1 S ->] (e TTl — 1) microcurie sec/gm Tz + T as before, if T y> Ti,T2,Tz, then U = - o f.QxJ(TZ ^m [Ti{e~™™'T* - 1) - Tz(e-0-™»T> - 1)] m 0.693r2(i i — Tz) microcurie sec/gm 16.7. Geometrical Factor. The dosage rate in roentgens per second at a certain point in an organ or animal due to a known volume distribution of u microcuries of active material per gram of tissue was shown in Sec. 16.5 to be given by the expression d = IAu(i)g The geometrical factor g gives the contributions of all parts of the volume distribution of active material to the dose at the point under consideration. Assuming a uniform distribution of radioisotope and a constant tissue density and composition within the volume V, then g = / e~wdV cm Sec. 16.7] INTERNAL DOSIMETRY 435 where n = linear-absorption coefficient, cm R = distance of point from volume element dV In practice the integral leads to excessively complicated expressions for all but the simplest geometrical shapes of the volume. For the same reason the point in the organ or animal for which the dosage rate is computed cannot always be chosen arbitrarily. Furthermore, it is sometimes convenient to neglect absorption in order to simplify the calculations. This is usually justified when the dimensions of the organ are very much smaller than \/n, where fx is the linear-absorption coefficient of tissue for a gamma ray of energy Ey. Formulas for g are given below for various geometries that can be used to approximate organs and tissue masses. It is assumed that both the tissue and radioactive substance are uniform in density and composition throughout the volume. a. Geometrical Factor for the Center of Sphere. For a sphere of radius a, the value of g at the center is Air < g = — (1 — e-"a) cm M ~ 4ra cm b. Arbitrary Point in Sphere. Neglecting absorption, the value of g for any point at a distance c cm from the center of a sphere of radius a cm is [14] x ( 2c H log — — '■ I \ c a — c) g = t [ 2a H log I cm \ c a — cf It is seen that at the surface c = a, and g is just one-half its value at the center. c. Disk. Considering the disk to be flat with radius a and thickness /, then neglecting absorption, the value of g at any point located a distance c from the plane of the disk and a distance b from its axis is [15] , . a- - b- + c? + V(a2 -b* + c2)2 + 4a-b2 g = *t log ^ cm d. Cylinder. The value of g at the mid-point of the axis of a cylinder of length 2L and radius R is approximately [13] 8 = 2tt (l log (l + ??\ + 2R tan-1 (^ - M{ L V& + U - U- + R- [log (Z + VR- + L~) - log A'] | J c m e. Graphical evaluation of g is possible for any arbitrary point whether inside or outside the tissue mass containing active material and may be 436 IS0T0P1C TRACERS AND NUCLEAR RADIATIONS [Chap. 16 applied as well to irregularly shaped masses. The entire tissue volume is divided (graphically) into small volume elements AVi whose dimensions are very small compared to l//x. For an arbitrarily chosen point P at which the dose is to be determined, the value of g is computed by a summation of the contributions from all AVi] thus 5 I e-"RiAVi -^— cm where Ri is the distance from the center of AVi to the point P. The calculations are facilitated by taking as the first term of the sum the largest sphere with P as its center which lies entirely within the tissue; then s t-- e-"RifiARi cm The fraction /j is, of course, determined by estimating the surface area of the shell bounded by the organ and dividing by 4tR2{, where Ri is the radius to the mid-thickness of the shell. The determination of integral dose or total energy absorbed by the tissue presents a more difficult problem in that the geometrical factor G which must be calculated is given by a double integral G = I ~dVdV' cm4 where V is the volume containing uniformly distributed activity, V is the volume for which the integral dose is to be determined, and R is the distance between the volume elements dV and dV. The volumes V and V need not be identical. Although V is determined, in principle, uniquely by the distribution of the active isotope, the volume V may be chosen arbitrarily provided that the factor e_Mii is retained. This integral does not reduce to Sec. 16.7] INTERNAL DOSIMETRY 437 simple integrable form except for the sphere when absorption is disregarded ; then G = Air-aA, where a is the radius of the sphere containing the radio- active material and for which the integral dose is determined. In most other cases the evaluation of G is possible only by numerical integration. In principle, G can be evaluated by a double summation similar to that for g Rh G = lu j = 1 / = 1 in which the sum i = 1 to 5 is taken over all volume elements AVi into which the exposed volume is divided and the sum j = 1 to r is taken over volume elements AV'j containing active material. R^ is the distance from AVi to AVj. It is apparent that the labor involved in evaluating this double sum will often be prohibitive. REFERENCES FOR CHAP. 16 1. Curie, M:, A. Debierne, A. S. Eve, H. Greigfr, O. Hahn, S. C. Lund, St. Meyer, E. Rutherford, and E. Schweidler: Rev. Mod. Phys., 3, 427 (1931). 2. Speers, F. W.: Brit. J. Radiology, 19, 52 (1946). 3. Lea, D. E. : "Actions of Radiations on Living Cells," The Macmillan Company, New York, 1947. 4. Condon, E. U., and L. F. Curtiss: Science, 103, 712 (1946); Phys. Rev., 69, 672 (1946). 5. Taylor, L. S., and G. Singer: Am. J. Roentgenol. Radium Therapy, 44, 28, (1940). 6. Gray, L. H.: Brit. J. Radiology, 10, 721 (1932). 7. Mayneord, W. V., and J. E. Roberts: Brit. J. Radiology, 10, 365 (1937). 8. White, T. M., L. D. Marinelli, and G. Failla: Am. J. Roentgenol. Radium Therapy, 44, 889 (1940). 9. Gray, L. U.:Proc. Roy. Soc. {London), A122, 648 (1928). 10. Memorandum on Measurement of Ionizing Radiations for Medical and Biological Purposes, British Committee for Radiological Units, 1948. 11. Gray, L. H.: Nature, CXLIV, 439 (1939). 12. Gray, L. H.: Proc. Cambridge Phil. Soc, 40, 72 (1944). 13. Marinelli, L. D., E. H. Quimby, and G. J. Hine: Am. J. Radiology Radium Therapy., 59, 260 (1948). 14. Mayneord, W. V. : Brit. J. Radiology, to be published. 15. Mayneord, W. V.: Brit. J. Radiology, 18, 12 (1945). 16. Jones, H. B., C. J. Wrobel, and W. R. Lyons: /. Clin. Invest., 23, 783 (1944). 17. Mayneord, W. V.: Brit. J. Radiology, 13, 235 (1940). 18. Gray, L. K.: Proc. Roy. Soc. (London), A156, 578 (1936). 19. Parker, H. M.: "Advances in Biological and Medical Physics," Vol. 1, p. 243, Aca- demic Press, New York, 1948. 20. Pace, N., and E. Strajman: Private communication. CHAPTER 17 THE PREPARATION OF THIN FILMS OF RADIOACTIVE ELEMENTS BY ELECTROLYSIS Rayburn W. Dunn 17.1. General Considerations. Although many methods have been pro- posed for the preparation of thin films that may be used for radioactivity measurements, probably the most convenient and satisfactory is the elec- trolytic. Under properly controlled conditions it is possible either to elec- troplate or to electrodeposit many of the elements quantitatively from solu- tions of their salts, and the resulting film can be made quite uniform in thickness. If the apparatus is correctly designed, the area that this film covers will be both accurately fixed and reproducible. With certain minor modifications, the electrolytic methods generally employed for quantitative chemical analysis are readily applied to radio- assay. For the most part, these methods are for electroplating rather than electrodepositing. The term "electroplating" is usually taken to mean the formation, by electrolysis, of a closely adhering metallic film. "Electro- deposition," on the other hand, may have this same meaning, or it may refer to the electrolytic formation of a nonmetallic layer, closely adherent or not, on the electrode. It is in the latter sense that it is employed here. Among the elements that have been successfully electroplated from aqueous solution are copper, silver, gold, zinc, cadmium, mercury, tin, lead, anti- mony, bismuth, chromium, iron, cobalt, nickel, and platinum. Aluminum and several other metals that are not reducible in aqueous solution may be plated from organic solvents. In the group of electrodeposited elements are, among others, uranium, oxygen, and fluorine as U02 and UF4, and thorium, iron, carbon, and nitrogen, as ThFe(CN)6. Quantitative proce- dures for electrolyzing most of these elements are well known, although only a few have as yet found use in radiochemistry. In general the methods for commercial electroplating cannot be suc- cessfully applied in analytical work, although the chemical principles and reactions of both procedures may be identical. This is essentially true because the conditions of temperature, ionic species and concentration, current and voltage required for quality plating do not necessarily satisfy the requirements for quantitative recovery. It is advantageous, however, to obtain a smooth, shiny film whenever possible. Rough films are likely to be porous and may occlude extraneous salts from the electrolysis solution. 438 Sec. 17.3] PREPARATION OF THIN FILMS BY ELECTROLYSIS 439 Colloids are frequently used to improve the electroplate, but no specific rules can be given to govern their use. 17.2. Apparatus. Many types of electrolysis cells and stirrers have been designed and used by the various groups that are investigating the field of radioassay. Unfortunately, many of these developments, like those of the chemical procedures, have not found their way into the published literature. The simplest electrolysis apparatus will have a rotating anode of platinum or platinum-10 per cent iridium wire. The wire is usually coiled in a flat spiral and serves both as a conductor and a stirrer. A platinum dish con- tains the electrolysis solution and serves as the cathode. Alternatively, cathodes consisting of thin disks are probably the most convenient for both gravimetric and radiometric measurements. Cathodes of 1 or l}^ in. in diameter are most frequently employed. These vary in thickness from 0.0005 to 0.005 in. depending upon the cost of material, the ease of handling, and the effect of background scattering on the counting rate. A glass cylinder and gasket, each having the same inside diameter and an outside diameter of either 1 or 1}^ in., generally constitute the body of the cell. The base is constructed so that either it serves for the cathode con- nection itself, or a separate connection is incorporated in it. Finally some means must be provided to hold the glass tightly against the base with the gasket and cathode in between. 17.3. Anodes. Platinum wire or gauze anodes have been almost univer- sally used for laboratory electrochemical reactions, principally because they are very passive. Platinum has some limitations, however, of which cost is not the least. Electrolysis of acid chloride solutions produces free chlorine at the anode, and in the presence of this gas, platinum loses its passivity to some extent and small but appreciable amounts are dissolved. This reaction increases with hydrochloric acid concentration, temperature, and current density but is minimized if the platinum is alloyed with 10 per cent iridium. Similar attack occurs if electrolysis takes place in an alkaline solution containing free ammonia. This attack will not be very great if the current density and ammonium hydroxide concentration can be kept low; however, it may account for cathode deposits of 0.1 to 0.2 mg if lengthy electrolyses are carried out. Substitutes for platinum have not proved too satisfactory for quanti- tative analytical work since most are attacked in either acid or alkaline solution. If the cathode film need not be weighed, alloys of the 18-8 variety of stainless steel sometimes may be used; carbon or graphite may be employed if anodic oxygen is not formed and if the rods are not appreciably porous. Tantalum cannot be used because it forms an oxide coating that prevents the flow of current from solution to anode, although the reverse process occurs with ease. 440 1SOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 17 17.4. Cathodes. The selection of a satisfactory metal for electroplating or electrodeposition depends largely upon whether gravimetric as well as radio- metric assay determinations are to be made. If the cathode film is to be weighed, it is best to employ platinum disks; if not, copper, iron, etc., may be used. Furthermore if the film is to be ignited or calcined, platinum is to be preferred; it must be used if both heating and weighing are necessary or if the film is later to be recovered quantitatively in a pure state. In most cases gold may be substituted for platinum. It is generally assumed that cathodes of gold or platinum will be cleaned and reused. Under some conditions it may be impossible to remove com- pletely the radioactive film, in which case the disks must be discarded, or the activity of each recleaned disk must be recorded before the next use. When these alternatives are either impractical or uneconomical, gold-plated copper disks may be substituted. A commercial plate 0.0001 in. is usually sufficiently thick and is relatively inexpensive. After use, the plated gold may be reclaimed, although it is safer to discard the disks rather than to reuse the recovered gold since it may contain contaminating radioactivities. Although most of the elements that can be electroplated will plate out on and adhere to copper, platinum, and gold, there is no hard and fast rule that can be used to determine exactly what results may be obtained with each element and each cathode. Both electroplating and electrodeposition are greatly influenced by the character of the cathode surface, as well as by the composition of the electrolysis solution. Cathodes of the same material will vary from lot to lot and even from front to back. For these reasons, duplicate determinations will frequently produce films greatly different in appearance and possibly in composition or crystal structure. Presumably identical electrolysis solutions and cathodes will frequently show wide varia- tion in gas production, even though the currents and anode potentials are the same. The formation of satisfactory films by electrodeposition is more critically influenced by the character of the cathode surface and solution composition than is such formation by electroplating. The greatest problem in electro- deposition is to obtain a film that will adhere to the electrode, and it is for this reason that etching of the surface may be advantageous. Inasmuch as no definite instructions can be given in every case regarding the selection of a satisfactory cathode, it is often necessary to try each metal in turn, starting with platinum or copper. Since the cathode surface is so important to satisfactory film formation, thorough cleaning of disks cannot be overemphasized. Surface impurities result from rolling, handling, dust, oxidation, and attack by moist air con- taining small amounts of such gases as sulfur dioxide, hydrogen sulfide, hydrochloric acid, and nitric acid which are not usually excluded from the Sec. 17.5] PREPARATION OF THIN FILMS BY ELECTROLYSIS 441 air in the laboratory. The greasy coating due to handling should be removed before the oxide and salt coating, unless removal of both can be accomplished at the same time. The noble metals, gold and platinum, are readily cleaned by immersion in warm concentrated sulfuric acid-dichromate cleaning solu- tion, and, if desired, this treatment may be followed by boiling in either con- centrated nitric or hydrochloric acid. Copper and iron may be degreased with organic solvents, or by immersing for a very short period in the dichromate cleaning solution, followed by washing with hot water, or they may be cleaned with fine sandpaper. After any of these procedures, immersing in cold dilute hydrochloric or nitric acid will complete the cleaning. Nitric acid will attack and etch the copper surface faster than hydrochloric, while the reverse is true with iron, and advantage may be taken of these rate differences to effect cleaning with or without appreciable etching. As pointed out above, it may sometimes be advantageous to etch the cathode during cleaning, using aqua regia or sand- blasting if necessary. Rinsing the disks in acetone before drying is particu- larly recommended for cathodes that are easily oxidized. 17.5. Electrodeposition. The electrodeposition process involves not one but two different chemical reactions; namely, oxidation or reduction and, concurrently, precipitation of an insoluble salt on the electrode. Electro- deposition, unlike electroplating, can occur on either the anode or the cathode. Anodic depositions, although reported in the literature, have not as yet been successfully applied to the problems of radiometry. Anodic films of lead sulfate and oxide, and of manganese oxides, for example, have been produced, but procedures for quantitative recovery by this means have not been worked out. The underlying principle upon which electrodeposition is based can be explained as follows: A cation A, which can exist in solution in either of two or more valence states, is oxidized at the anode and reduced at the cathode. An anion B, also in solution, but neither electrolytically oxidizable nor reduci- ble, forms an insoluble compound either with the reduced cation but not the oxidized, or with the oxidized but not the reduced. If the reduced cation deposits with B, then cathodic deposition is obtained, and by the converse process, anodic deposition may be obtained. These may be represented as follows: Anode Cathode which are the cation electrode reactions, where x has a value between 1 and 3 and the quantity (x + y) has a value between 2 and 5. If the anion B has a valence of — z, it will form two salts with A , namely, AZBX and A zB{x+y). For electrode film formation, one of these must be insoluble in the electrolysis 442 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 17 solution. Of necessity the cation must be introduced into the electrolysis solution in such a valence state that it will not form this precipitate in the solution itself. Neglecting valences and electrolysis reactions for the moment, one other consideration is important, namely, the independent role that B plays in forming and maintaining the precipitated film. The reaction that occurs may be represented as A (ion) plus B (ion) +±AB (precipitate) The equilibrium constant for this reaction, Kab, equals the product of the concentrations of A and B; the value of each of the latter is squared or cubed, etc., depending upon whether one, two, or more ions are concerned in forming the precipitated molecule. Therefore the greater the concentration of B in solution, the smaller will be the concentration of A when equilibrium is reached and, thus, the more quantitative the recovery. The electrodeposited film, however, is not only slightly soluble in water, but is also usually dissolved by acid or base, or by complex ion formation. If the rate of solution by any one reaction or combination of these reactions is faster than the rate of valence change and precipitation, no electrode film will form. A rather delicate balance of these reaction rates is usually necessary if quantitative results are to be achieved and such side reactions must be eliminated or minimized. 17.6. The Electrolysis Current and Voltage. A convenient power supply for electrochemical reactions is the ordinary 6-volt storage battery. Voltages above 12 are not usually necessary, and a parallel or series-parallel arrange- ment of two or four batteries will supply as much power as will, in general, be needed for routine analytical work. Electrolyses from nonaqueous solution, however, may require much higher voltages, in which case a vacuum-tube d-c power supply will be much more convenient than either batteries or a generator. In addition to the voltage, three other independent variables will influence the electrolysis current, namely, the distance between anode and cathode, the resistance of the electrolysis solution, and the electrode-solution boundary resistances. The electrolysis-solution resistance, in turn, is dependent upon the ion concentration and upon the temperature of the solution; increasing either one decreases the resistance. The desired electrochemical reactions occur only at the boundaries joining the electrodes and the electrolysis solution; therefore the potential drop across each of these boundaries is of considerable importance. These electrode voltage drops determine which reactions will occur, and the current that flows determines the reaction rates. If either of the boundary resist- Sec. 17.6] PREPARATION OF THIN FILMS BY ELECTROLYSIS 443 ances or the resistance of the solution is too high, little or no current will pass through the cell, and consequently the reaction rates will be negligible. The minimum electrode reaction potentials are determined by (1) the back emf , which is the potential with which the particular reactions tend to reverse themselves; (2) the "passivity" of the electrodes; and (3) the "polari- zation" within the boundary. The last-named phenomenon results, pri- marily, from localized concentration changes of the electrolysis solution; passivity is due to electrode surface conditions for which discussions will be found in standard texts. An electrode becomes polarized owing to the progressive removal of one or more ions, by reduction or oxidation, within the boundary; equilibrium is regained or maintained by rapid stirring of the solution. The net result of the above three factors is to establish a minimum potential below which little or no current will flow and no reactions will occur and above which a rapid increase in current is obtained. The polarization of an electrode, which is required to produce a given irreversible reaction under given conditions, is known as the overvoltage of this reaction. Overvoltage values for the same reaction vary considerably, depending upon the electrode material and surface condition. Thus the hydrogen overvoltage for a platinized-platinum cathode is lower than for smooth platinum, which, in turn, is lower than for mercury, etc. The importance of hydrogen production at the cathode may be illustrated by the following example: If the electrode emf for the reaction or reduction of A is 0.5 volt and the hydrogen overvoltage is 1.0 volt, reaction A will begin when the potential slightly exceeds 0.5 volt and will continue with little or no hydrogen evolution until the potential reaches 1.0 volt. At this point hydrogen gas begins to form and, as the voltage increases, both hydrogen formation and reduction of A occur together. The reduction of hydrogen at the cathode is accompanied by the formation of hydroxyl ions. These in turn may exercise considerable influence on the reduction of A or upon the character of the reduced film. If this influence is deleterious, then voltages below the hydrogen overvoltage should be employed. On the other hand, increased alkalinity may be helpful; furthermore the presence of hydrogen gas within the body of the solution may cause reductions that will aid in the quantitative recovery of A. When the hydrogen overvoltage is much lower than the voltage necessary for the reaction A and the applied voltage is between the two, then no reduc- tion of A will occur and only hydrogen gas will be formed. To overcome this, a different cathode material with a higher overvoltage may be used or the voltage may be increased to the point where reaction A begins to occur, whereupon the cathode becomes coated and the hydrogen overvoltage increases to a value that is characteristic of a cathode made of metal .4 . Of 444 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 17 course, if the hydrogen overvoltage of the latter metal is lower than the voltage necessary for its plating, then the reduction rate may be very slow and may not occur quantitatively within a finite time. Oxygen overvoltages and the formation or lack of formation of oxygen gas and hydrogen ions should be considered in exactly the same relation, but with respect to the anode. However, since most of the electrolysis work with radioactive materials will be concerned with cathodic film formation, anodes with low oxygen overvoltages should be employed; this condition is adequately met in platinum. CHAPTER 18 TREATMENT OF BIOLOGICAL TISSUES FOR RECOVERY OF RADIOACTIVE ELEMENTS Rayburn W. Dunn 18.1. Introduction. Methods for ashing plant and animal tissues have been described by many workers. Descriptions of satisfactory ashing methods are usually included with the corresponding analytical procedures, frequently with only slight variations from previously reported work. There are, therefore, very nearly as many ashing techniques in biological work as there are methods for the estimation of inorganic elements. Since it is doubtful whether any one procedure can be said to be superior to the rest, only a general description of ashing techniques will be given. It should be possible to devise, from the information given, a method that will meet the specific requirements of a particular problem. A glance at the two tables copied from Hawk will show the relative amounts of inorganic elements that are to be found in human-tissue ash [1] and in blood [2]. Table 38. Inorganic Constituents of Human Blood Normal range, Constituent mg 100 ml Chlorides, as NaCl 450-500 Sulfates, inorganic, as S (serum) 0.9-1.1 Phosphorus, inorganic, as P (plasma) 3-4 Iron, as Fe 52 Copper 0 . 05-0 . 25 Calcium (serum) 9.0-11.5 Magnesium (serum) 1-3 Sodium (serum) 330 Potassium (serum) 16-22 Iodine (micrograms per 100 ml) 8-15 In selecting ashing and purification procedures, the normal presence of these elements must be taken into consideration. The concentrations of calcium, magnesium, sodium, potassium, phosphorus, chlorine, sulfur, etc., in the ash will greatly influence their own recovery and that of other elements present in trace amounts. These concentrations will also dictate the course to be followed in the subsequent analytical procedures. 445 446 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS Chap. 18 Table 39. Inorganic Constituents of Human Tissue Element Per cent Approximate amount, in grams, in a 70-kg Man Oxygen 65.0 18.0 10.0 3.0 1.5 1.0 0.35 0.25 0.15 0.15 0.05 0.004 0.0003 0.0002 0.00004 45,500 12,600 7,000 2,100 Carbon Hydrogen Nitrogen Calcium 1,050 700 Phosphorus Potassium 245 Sulfur 175 Sodium 105 Chlorine 105 Magnesium 35 Iron 3 Manganese 0 2 Copper 0 1 Iodine 0 03 18.2. Dry Ashing. Ashing at 500 to 800°C is generally carried out in platinum, porcelain, Vycor, or nickel crucibles, although in general, platinum is to be preferred. It cannot be employed, however, if fluxes are used that contain such materials as potassium acid sulfate, sodium peroxide or hydrox- ide, excessive amounts of potassium nitrate, or any compounds likely to liberate free chlorine. Such fluxes are not usually encountered in biological work, but if they are needed, it is advisable to use porcelain or Vycor, pro- vided that etching by the alkali is not objectionable. Admixtures of such materials as magnesium acetate and calcium hydroxide will not result in attack on platinum. If the dissolution of ash requires the use of aqua regia, porcelain or Vycor must be used, whereas platinum is indicated when hydrofluoric acid is employed. One of the most difficult problems encountered when porcelain is used is the fusion of the inorganic material with the crucible; this is a particularly undesirable characteristic of some animal tissues. Although the loss of a small portion of the sample due to crucible fusion may not appreciably affect the analytical results, it may preclude the subsequent use of this crucible. The danger of cross contamination due to residual activity in laboratory glassware must be kept in mind at all times; crucibles showing unremovable residual activity should, therefore, be discarded. Further- more, if fusion occurs, recovery of the ashed material is not only difficult but time-consuming. Vycor and platinum are more satisfactory under these conditions, although from an economic standpoint it may be less expensive to Sec. 18.2] TREATMENT OF TISSU E FOR RECOV ERY OF RADIOISOTOPES 447 use porcelain and to discard the crucibles if appreciable activity remains in them. For dry ashing the muffle furnace which has heating elements at the sides as well as top and bottom is much to be preferred to gas burners. Not only is the ignition more convenient, but it is also more uniform. The muffle furnace has the disadvantage, however, that when completely filled the available oxygen inside is rapidly exhausted. When this condition is reached, the combustible gases produced will leave the furnace as a tarry and soot- laden smoke; the latter must usually be removed by forced ventilation. To avoid this and to aid in combustion, oxygen may be introduced into the furnace through the thermocouple housing, using a quartz tube. When this procedure is followed, the heating units must be reversed if possible so that the coils do not face toward the inside of the furnace, and furthermore the stream of oxygen must not be directed onto the thermocouple itself. The general ashing procedure consists of air-drying the weighed sample at a temperature of 100°C or slightly less followed by ignition at 500 to 800°C for a minimum of 2 hr. Samples that'have been ground or macerated may be dried at reduced pressures; 100 mm or less is recommended for grain and stock feeds, meat meal, plant tissues, etc. [3]. Caution must be exercised in drying whole tissues, such as liver, since they tend to swell at elevated temperatures or reduced pressures or both. Temperatures above 100°C are permissible for removing the last portions of water and volatile oils. Drying by means of overhead radiant heating has been found to be particularly useful with nearly all types of biological tissues as well as with solutions of both organic and inorganic compounds. In many cases the material to be ashed is already dry enough to place in the muffle furnace. Ground grains, bone, and the woody portions of plants, for instance, seldom need to be dried before ignition. When possible cross contamination or contamination of the muffle furnace is likely to influence the results, it is best to place the samples in a cold fur- nace and to allow the temperature to rise gradually to the value desired. Rapid ashing produces volatile gases at rates that are sufficient to carry small amounts of the material out of the crucible. Thus radioactive deposits will collect on the walls and floor of the furnace as well as in the adjacent crucibles. The duration of ashing and the temperature must be considered in relation to the volatility of certain compounds. For example, some iron generally will be lost as ferric chloride, phosphorus as phosphoric acid, sulfur as sulfur di- and trioxide, fluorine as hydrogen fluoride or silicon tetrafluoride, and chlorine as hydrogen chloride. Because of the difficulty of completely mixing samples with additives that are designed to prevent these losses, 100 per cent recovery of some elements is impossible. From a quantitative standpoint these losses may be inconsequential, but they must be considered 448 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 18 in light of the possibility of serious radioactive contamination. Wherever feasible, therefore, wet ashing should be considered if the radioactive element is likely to be volatilized at muffle-furnace temperatures. For radioactive tracer studies, ashing to constant weight is not important. The aim is solely to decompose the tissue to the point where organic com- pounds, which are likely to interfere in the subsequent analysis, are com- pletely decomposed. Ashing beyond this point, to oxidize the last traces of carbon, is unnecessary and time-wasting. The use of perchloric acid after such incomplete ashing should not only be safe but should also facilitate the dissolution of the inorganic salts. The loss of important elements from the tissue ash might very well be eliminated by this less vigorous procedure; com- pounds difficult to dissolve should not be produced so frequently. Aids to ashing have been employed with considerable success. Calcium nitrate, magnesium acetate, and mixtures of calcium and aluminum nitrates may be advantageously used. These salts act not only to supply oxygen, but they also increase the bulk of the ash and render it more amenable to dissolu- tion. The use of these aids is indicated with samples producing little or no ash of their own, e.g., fatty tissues and carbohydrates. Magnesium acetate in alcohol is particularly recommended for use with such finely ground mate- rial as flour [4]. Fusion of material with the crucible is practically eliminated when ash aids are employed. Etching of the glaze on porcelain is not com- pletely prevented, however, and chlorine attack on platinum, due to oxida- tion of chloride by nitrate, is likely to occur. 18.3. Wet Ashing. Less drastic than furnace ignition but more satis- factory in many respects are the procedures for oxidation of organic mate- rial in solution. Wet digestion may require more attention and will fre- quently be slower than dry ashing, but on the whole these disadvantages are more than offset by the superior results obtained when the quantitative recovery of certain elements is desired. The choice between wet and dry ashing is based, therefore, upon consideration of the likelihood of loss by volatilization at higher temperatures versus the inconvenience in increased time and labor of digestion at lower temperatures. Maximum wet digestion temperatures are governed by the boiling point of the solution in which this digesting occurs, provided that the samples are not taken to dryness, and are roughly 400 to 500°C lower than the usual minimum dry-ashing temperatures. The Kjeldahl procedure, with modifications, utilizes concentrated sulfuric acid as an oxidizing agent and has been by far the most widely used method for digesting plant and animal tissues. In addition, potassium sulfate or persulfate together with a catalyst such as copper, mercury, or selenium are generally employed. Perchloric acid may be used to great advantage with sulfuric acid as a modification of the original Kjeldahl method. Nitric acid and mixtures of nitric acid with hydrochloric acid, hydrogen Sec. 18.3] TREATMENT OF T1SSUEF0R RECOVERY OF RADIOISOTOPES 449 peroxide, or perchloric acid have been successfully applied in wet-ashing procedures and are to be preferred whenever the introduction of excess sulfuric acid or sulfates is disadvantageous. Extensive work has been carried out by Smith [5] and by Kahane [6] on the use of perchloric acid for the digestion of organic material. The former author's publication includes a review of the literature through 1940 and a compilation of some of the more important procedures employing this reagent in conjunction with sulfuric and with nitric acid. REFERENCES FOR CHAP. 18 1. Hawk, P. B., B. L. Oser, and W. H. Summerson: "Practical Physiological Chemistry," 12th ed., p. 987, The Blakiston Company, Philadelphia, 1947. 2. Hawk, P. B., B. L. Oser, and W. H. Summerson: "Practical Physiological Chemistry," 12th ed., p. 451, The Blakiston Company, Philadelphia, 1947. 3. "Methods of Analysis," 6th ed., p. 237, Association of Official Agricultural Chemists, Washington, D. C, 1945. 4. "Methods of Analysis," 6th ed., p. 238, Association of Official Agricultural Chemists, Washington, D. C, 1945. 5. Smith, G. F.: "Mixed Perchloric, Sulfuric and Phosphoric Acids and Their Application in Analysis," 2d ed., G. Frederick Smith Chemical Co., Columbus, Ohio, 1942. 6. Kahane, E.: "L'Action de l'acide perchlorique sur les matieres organiques," Vols. I and II," Herman et Cie, Paris, 1934. CHAPTER 19 THE SAFE HANDLING OF RADIOACTIVE MATERIALS 19.1. Introduction. The manipulation of radioactive materials presents two major problems with which a laboratory must be adequately prepared to cope in so far as they affect laboratory design, operative procedures, and personnel. These are, in the broadest terms, the health hazard of radiations to which personnel may be exposed and contamination of the laboratory and its equipment. Contamination represents a relatively uncontrolled source of radiation and in this sense must always be regarded as a potential health hazard in addition to the constant danger it poses for confusing experimental results. It demands, almost without exception when active materials are handled in appreciable quantities, that measures be taken to detect and eliminate it. So far as radiation is concerned, little differentiation can be made in the procedures taken to preclude any possibility of excessive per- sonnel exposure, whether the radiation is from contamination or from care- fully handled quantities of active material. Fortunately, in most private institutions using radioactive materials in research and for therapy these problems are less complex than in the isotope processing laboratories of the Atomic Energy Commission because the quanti- ties of active material handled are comparatively small. Laboratory design, equipment, and monitoring procedures for this reason often can be made quite simple. Usually the quantity of material will not exceed 100 milli- curies, and rarely is it as great as a curie. Hot cyclotron targets in most instances are likely to be the most active sources to be dealt with and may at times approach the curie level. Almost without exception, however, when active material is handled in amounts greater than tracer quantities (~ microcuries) suitable protective measures must be instituted. In addition to the quantity, the species of isotopes that will be handled in a laboratory affects the extent to which precautions must be taken. Isotopes with half-lives of a few hours or days do not present a problem of permanent contamination but usually represent serious health hazards by virtue of the high energy radiation associated with short half-lives. Mate- rials with long half-lives are always serious contaminants in that they may seriously interfere with subsequent experimental results and may or may not be health hazards too. In particular, there is a group of isotopes which constitute a special health hazard irrespective of the energy or type of their radiation. This includes all isotopes with long half-lives that have a tendency 450 Sec. 19.2] THE SAFE HANDLING OF RADIOACTIVE MATERIALS 451 to remain fixed in the human body when breathed in the form of dust, ingested, or introduced through lesions. Among these, certain alpha emitters are the most dangerous because of the great damage inflicted on tissues by the heavy ionization produced by alpha particles. The elaborate protective measures developed and practiced in the national laboratories where large quantities of radioactive materials are processed clearly demonstrate by their practically perfect record in health physics that every precaution taken to minimize the health hazard and danger from con- tamination is fully warranted. The general principles and much of the detail of these practices is now sufficiently well known to enable any laboratory contemplating the use of radioactive materials to institute the necessary procedures and install the proper facilities for its particular needs. The follow- ing sections are intended to outline these problems and practices, but refer- ence to the literature cited is suggested for more exhaustive discussions. 19.2. Medical Considerations.1 Perhaps the most obvious hazards to the health of laboratory personnel from radioactive materials are external irradiation by gamma rays and beta particles and internal irradiation from active material inadvertently taken into the body by inhalation, ingestion, or other means. The types of injuries or subsequent pathological changes following such exposures depend upon the radiation dose, the tissues irra- diated, and various other factors such as the physical characteristics of the radiation involved and duration of exposure. The medical treatment of radiation damage is not well developed; some of the changes induced are insidious in onset, and some are associated with grave consequences. Since every effort must be made to ensure against significant exposure, emphasis should be placed on prophylaxis. The situation may be compared in some ways to the handling of infectious diseases in the laboratory or the use of poisonous reagents. Provided that guesswork as to radiation exposure is supplanted by measurement of radiation intensity and personnel monitoring and such possibilities as air contamination are explored, with adequate pre- cautions taken, work may proceed with confidence and safety. In addition to safeguarding laboratory personnel, thought should be given to the possibility of contaminating other areas and involving persons outside the laboratory, e.g., by sending contaminated laboratory coats to the laundry or spreading activity through contaminated clothing and shoes. These considerations, the problem of radioactive waste disposal, and others are treated in the succeeding sections. In many instances it is not possible to avoid some degree of external irradiation while working with radioisotopes; hence the need for knowledge of "safe" exposures or tolerance doses has arisen. Much has been written about this question, and reference may be made to a recent review by 1 This section is by R. Lowry Dobson. 452 1S0T0PIC TRACERS AND NUCLEAR RADIATIONS [Chap. 19 Parker [9]. By the tolerance dose is meant the amount of radiation that an individual may receive and suffer no observable ill effects. It is usually expressed as a dosage rate, as the amount allowable per day or per week. For several years in this country the accepted figure for x- and gamma rays has been 0.10 r per day. Factors taking into account the relative biological effectiveness of other types of radiation have modified this figure for neutrons, protons, and alpha particles. Table 40 gives the tolerance daily doses accepted by the Atomic Energy Commission for various types of radiation: Table 40. Daily Tolerance Doses [10] x-rays 0 . 10 r Gamma rays 0 . 10 r Beta particles 0.10 rep Fast neutrons* 0.02 rep Thermal neutrons 0 . 02-0 . 05 rep Alpha particles 0.01 rep * Also applies to protons. A lower tolerance figure has been advocated by some, and recently the National Advisory Committee on Radiation Protection has recommended 0.30 r per week for x- and gamma rays with proportionately lower figures for other types of radiation. The recommendation regarding exposure of the hands is that a dose three times that for total body irradiation be allowed, or approximately 1 r per week. This committee has also suggested that 300 r be taken as the upper limit for accumulated lifetime exposure. It seems probable that these lower allowable doses will be generally accepted in the near future. The hazards associated with the presence of radioactive material inside the body depend upon the metabolism of the material, its radiation char- acteristics and half-life. Some substances, for example, when ingested, are not absorbed from the gut, others are readily absorbed; radium is a familiar example of a substance that may find its way to the blood stream by way of the gastrointestinal tract or the pulmonary tract and is deposited in bone. Its presence in the skeleton over long periods of time has been associated with the development of malignant bone tumors. Osteogenic sarcomas and anemias may be expected also with other long half-life isotopes that have affinity for the skeleton. Certain isotopes such as radio sodium are more widely distributed and result in general body radiation. Care must be taken in the laboratory that radioactive vapors and dusts are not allowed to contaminate the air and result in internal radiation follow- ing inhalation. Obviously, smoking and eating in the laboratory are hazardous. Fairly elaborate medical supervision of personnel has been carried out in Manhattan District and Atomic Energy Commission laboratories which Sec. 19.3] THE SAFE HANDLING OF RADIOACTIVE MATERIALS 453 does not perhaps seem to be warranted in smaller laboratories where lesser amounts of activity are used. In the government laboratories periodic physical examinations, complete blood counts, and urinalyses have been done on all potentially exposed persons, as well as such special studies as examinations of the fingers for skin effects and assay of the urine for radio- activity as an indicator of internal deposition. In laboratories where medicolegal considerations are taken into account, it would seem wise to provide for initial physical examination, chest x-ray, and clinical laboratory studies in an attempt to rule out the presence of malignancies or blood dyscrasias which might be linked to radiation exposure. Periodic examinations, especially of the blood, and terminal examinations would also seem indicated. In laboratories where these considerations are not important, it would nevertheless seem wise to provide, in addition to personnel monitoring with film badges or pocket electroscopes, at least for hematological observation of those workers who are potentially exposed to significant amounts of radiation or who may work with radiation for long periods of time. There is no evidence that chronic exposure to radiation in the tolerance range will alter the normal blood picture, but blood counts may reveal abnormalities suggestive of radiation changes and lead to investigation of overexposures which might otherwise have gone unnoticed, or they may reveal incidental abnormalities such as anemia which should be corrected before work with radioactive material is undertaken. In any case where there has been an accidental ingestion or inhalation of active material, or where it has been introduced into a wound, every effort should be made to prevent absorption or deposition of the radioactivity in the body. The methods employed will, of course, depend upon the circum- stances, the type of material, etc. If the isotope has a long half-life and follows a metabolic pathway that keeps it in the body for long periods of time, the situation is very urgent. Copious washing of a contaminated wound is indicated immediately with consideration given to avoiding the spread of contamination to uninvolved areas; in rare instances, debridement may be warranted. Gastric lavage in cases of ingestion is indicated. Efforts should be made to determine from the material being handled exactly how great the problem is. Subsequent medical treatment will depend on indi- vidual circumstances. 19.3. Laboratory Design. The special features required in the design of a laboratory intended for radiochemical processes depend chiefly on the maxi- mum level of activity that can be anticipated in future operations. When the quantity of materials handled approaches the 100-millicurie level, special precautions must be taken with regard to the health hazard in providing effective shielding and ease of decontamination. Although shielding can 454 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 19 be somewhat simpler for all activities at the microcurie level, or even at the millicurie level for materials that emit only beta or alpha particles, the danger of contamination should always be regarded as serious, particularly where long-lived isotopes are involved. Radiochemistry and other processing therefore should be confined strictly to those rooms prepared for these processes so that the spread of contamination by possible exchange of instru- ments, waste, clothes, etc., can be rigidly controlled. It is also clear that entirely separate rooms placed as far as practicable from active materials must always be maintained for radioassay and for experimentation with prepared active materials. The most important feature is an adequately shielded and readily decon- taminated hood. Concrete is probably the most economical material for this kind of structure, and it enables easy fabrication. The thickness of all sides including top and bottom should be great enough to attenuate the intensity of all gamma radiation to considerably less than that which will deliver a tolerance dose of 0.1 r per day at any accessible outside surface. The floor of the hood should slope downward to localize the spread of contamination caused by spillage, and it should be sufficiently large to enable nearly all operations with active materials to be performed under the hood. If the exhaust chimney passes through other portions of the building, particular care must be taken to ensure against leakage of fumes due to corrosion and also excessive accumulation of possible active condensates. Normally when volatile or gaseous active materials are processed in the hood, some means is provided for condensing and collecting the material. In addition to a hood, each radiochemistry laboratory should contain a permanent vault or cove for storing all radioactive materials not in immediate use. Concrete or lead structures are the most suitable for this purpose. With properly designed compartments, each with its separate closure, access to one compartment and its contents is possible without danger of excessive radiation exposure from other materials stored in the vault. Wall thickness should be sufficient to attenuate gamma radiation to negligible intensity in all directions, and closures should be carefully checked with Geiger counters to detect possible leakage of radiation scattered through cracks or poorly fitting closures when high-intensity gamma emitters are stored. Improvised storage coves hastily assembled with lead bricks should be avoided except in emergency since there is often a tendency to neglect bottom and back shielding and to overlook radiation leakage. Additional permanent or semipermanent laboratory fixtures may include large general shields of lead surrounding areas or apparatus handling high- intensity gamma- and beta-active material. Surface finishing materials for table and bench tops and other working areas may be expendable absorbing materials such as masonite or they may be Sec. 19.4] THE SAFE HANDLING OF RADIOACTIVE MATERIALS 455 permanent, inert materials such as stainless steel or monel metal. Both types of surface material have certain advantages that must be considered according to the specific requirements of the laboratory when a choice is made. Absorb- ing materials, by taking up spilled or splashed liquid, do not allow radioactive dust to be readily formed. It can also be replaced at reasonable cost and effort after contamination. Stainless steel can be thoroughly cleaned, if necessary, with dilute acid, but it still has a tendency to allow dust to form unless the most diligent efforts are taken to avoid it. If contamination becomes serious, stainless steel is also expensive to replace. All surfaces, particularly floors, should be nonabsorbing, smooth, and as free from cracks as possible. Wood floors for example are undesirable since it is impossible to avoid cracks between boards in their construction, and it is virtually impossible to remove subsequent contamination without replacing the floor. Concrete is also undesirable since it is impossible to decontaminate without removal. 19.4. Special Laboratory Equipment. Special laboratory equipment as well as procedures for handling radioactive materials must be designed primarily to safeguard personnel from irradiation while manipulating any pieces of apparatus containing active material. The variety and complexity of handling equipment that should be made available will be found to differ considerably from one laboratory to another and from time to time since the amount of protection from radiation which must be afforded by such equip- ment will depend upon the level of activity, the kind of radiation and, to some extent, the specific requirements of the handling procedure. Thus for high-intensity high-energy gamma-active materials, general shields enclosing the entire operation and remote handling devices are required, whereas for some isotopes that emit only soft beta particles, rubber gloves and shielding in air alone may suffice. For this reason the kind of handling equipment, shielding, and details of a process, however simple, should be carefully pl