The Atomic Nucleus

985 Pages·1955·50.227 MB·English

by  Robley D. Evans

BOOK
THE ATOMIC NUCLEUS
Robley D. Evans, Ph.D.
PROFESSOR OF PHYSICS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
TATA McGRAW-HILL PUBLISHINC COMPANY LTD.
Bombay New D*lhi
THE ATOMIC NUCLEUS
1955 by McGraw-Hill, Inc.
All Rights Reserved
This book, or parts thereof, may not be reproduced in anyform
without permission of the publishers.
T M H Edition
Reprintedin India by arrangement with the McGraw-Hill, Inc.
New York.
This edition can be exportedfrom India only by the Publishers,
Tata McGraw-Hill Publishing Company Ltd.
Published by Tata McGraw-Hill Publishing Company Limited and
Printed by Mohan Makhijani at Rekha Printers Pvt. Ltd., New Delhi-15.
Preface
This book represents the present content of a two-semester course
in nuclear physics which the author has taught at the Massachusetts
Institute of Technology for the past twenty years. During this time
nuclear physics has expanded greatly in depth and breadth. Nuclear
physics was originally a subject which represented the researchinterests
ofasmallnumberofacademicscientists, andwhosemodestsizepermitted
easy coverage in a one-year graduate course. Now pure and applied
nuclearphysicsis agigantic area ofresearchand engineering. Numerous
subtopics have grown rapidlyintolarge and separate fields ofprofessional
competence, but each of these derives its strength and nourishment
from fundamental experimental and theoretical principles. It is this
fundamental core material which is discussed-here. Even this central
body ofempirical knowledge and of theoretical interpretation has grown
to be very large. This book embraces more material than mystudents
and I are now able to cover, with adequate regard for depth ofunder-
standing, in a one-year course of ninety class hours. Those topics
which seem most lively and timely are selected from it by each year's
group of students. Material which has to be excluded from the course
is thus fully available for reference purposes.
This text is an experimentalist's approach to the understanding of
nuclear phenomena. It deals primarily with the area in which theory
and experiment meet and ib intermediate between the limiting cases of a
theoretical treatise and of a detailed handbook of experimental tech-
niques. It undertakes to strike that compromise in viewpoint which
has been adopted by the majority of working physicists.
Detailed attention is given in the early chapters to several funda-
mental concepts, so that the student may learn to think in center-of-
mass coordinates and may visualize clearly the phenomena of barrier
transmission, particle interactions during collisions, and collision cross
sections. The physical aspects receive emphasis in the main text, while
the corresponding mathematical details are treated more fully in appen-
dixes. This reiteration, with varied emphasis and viewpoint, has been
preserved because of the experiences of students and colleagues.
As to prerequisites, it is expected that the reader has had at least
an introductory course in atomic physics and that his mathematical
vi Preface
equipment is in working order through the calculus and differential
equations. Prior experience in wave mechanics is not assumed, and
the necessary mathematical and conceptual portions of this subject are
developed from first principles as the need and application arise.
I have been repeatedly impressed by the varied preparation and by
the nonuniform backgrounds of seniors and first-year graduate students
as they enter this course. Each student is well prepared in some areas
but is blank in others. In an average class of fifty students there is a
nearly random distribution of areas of competence and areas of no
previous experience. These observations have dictated the level of
approach. It. must be assumed that each subfield is a new area to the
majority. With this experience in mind, the discussion of each topic
usually begins at an introductory level. Within each subfield, the dis-
cussion extends through the intermediate level and into the area of the
most recent advances in current research. The aim is to bring the
student to a level of competence from which he can understand the
current research literature, ran profitably read advanced treatises and
the many excellent monographs which are now appearing, and can under-
take creative personal research. To help encourage early familiarity
with the original papers, numerous references to the pertinent periodical
literature appear throughout.
Nuclear physics today embraces many topics which are strongly
interdependent, such as nucloar moments and ft decay, and some topics
which are nearly independent fields, such as some aspects of mass spec-
troscopy. An optimum sequential arrangement of these topics is a
difficult, if not insolvable, problem. The collection of indisputably
nuclear topics definitely does not form a linear array, in which one may
start at A and proceed to B, C, D, . . . , without having to know about
Q in the meantime. The order of topics which is used hereis that which
has developed in the classroom as an empirical solution involving "mini-
mum
regret."
I begin as Bethe and Bacher have done, with the fundamental prop-
erties of nuclei. These are the characteristics which are measurable for
any particular nuclide and which comprise the entries in any complete
table of the ground-level nuclear properties: charge, size, mass, angular
momentum, magnetic dipole moment, electric quadrupole moment,
isobaric spin, parity, and statistics. In order to evaluate even these
"static" properties of nuclei, it is necessary to invoke many types of
experimental and theoretical studies of the "dynamic" behavior of
nuclei, including a decay, ft decay, and nuclear reactions. The result
is that those aspects of nuclear dynamics which enlighten the static
properties are referred to early. This might have been done by saying,
"It can be shown ..." or "We shall see later that . . . ," but it
has proved more satisfactory to give, a reasonable, account of the per-
tinent dynamic aspect at the place where it is first needed. This has
been found to lead to better understanding, although it does give rise to
occasional duplication, or "varied reiteration," and, in some instances,
todivision ofdynamic topics, such as a decay and ftdecay, into twoparts.
Preface vii
Cross references appear throughout these topics, in order to reinforce
the integration of the dynamic subjects.
The middle of the book deals with the systematics of nuclei, with
binding energy and separation energy, with intrrnucleon forces and
illustrative nuclear models, and with the dynamics of nuclear reactions,
a-ray spectra, ftdecay, andradioactive-seriestransformations. Chapters
18 through 25 treat the behavior of charged particles and of photons
while passing through matter, concluding with a chapter containing
baric material on a group of "practical" scientific, military, and indus-
trial problems on the physical evaluation of penetrating radiation fields.
The final three chapters drill with the statistical theory of fluctuations
and uncertainties due to the randomicity of nuclear events, which is so
often n governing factor in the design of imclr.ar experiment. Practical
topics given detailed treatment, include the effects of resolving time,
random coincidences, sealer and counting-rate-meter fluHualiaiiH, and
the statistics of rapidly decaying sources.
Keferencr tables of many of the reasonably well-established nuclear
properties accompany the corresponding text. For more comprehensive
tables, explicit references arc made to the voluminous and valuable
standard compilations. For the latest data, thcsn compilations must
be augmented by the1 Miminarics of new nuclear data published quarterly
in NurJcar iS'ci'rwr Abstracts.
Kvory worker in nuclear physics faces ihe opportunity of making a
signilicant ,n-\v discovery. It is useful in know how discoveries have
lii-eu marie by thuM* who have preceded us. Most of ihe history of
nuclear physics ic. very recoiil and has occurred within the memory of
people still working in the field. In order to illuminate the "anatomy
of discovery" and at the stunt; time to focus on fundamental physical
principles, some chapters, such as Chap. 13, Nuclear Reactions, Illus-
trated by HIU(arj;) and Jts Associates, have been arranged with due
regard to the history ofnuclear physics and to the pitfalls and accidental
triumphs ofresearch. Thiswasdonetoencouragethestudentto develop
afeelingforthestapesthroughwhich nuclearsciencehas progressedanda
sense of the conditions under which new discoveries are made.
Problems are offered for solution at the end of many sections. These
have been selected from homework and quizzes and are the type which
one likes to work through in order to seethat the principles'ofthesubject
are understood. Many problems supplement the text by containing
their own answers, in the well-known "show that." style of Miles H.
Sherrill and the late Arthur A. Noyes.
Much help, both explicit, and general, has been received from pro-
fessional colleagues, especially Profs. V. F. Weisakopf, H. Feshbach,
and W. A. Fowler, and from the hundreds of students who have taken
the course over the many years during which this book has been in
preparation. The students' experiences have determined the content,
the order of presentation, the amount of detail needed on particular
topics, the nature and number of problems, and the topics which should
be transferred to other new courses in specialized aspects of pure or
viii Preface
applied nuclear physics. Some former students may find that their
favorite topic has been deleted altogether, in order to make space for
the remainder in an already vast field.
Each year one or more graduate students have collaborated closely
in developing and presenting certain sections of the course, and to these
men I welcome this opportunity of recalling our joint experiences of
the past two decades and of recording my thanks, especially to Alfredo
Banos, Keith Boyer, Sanborn Brown, Gordon Brownell, Randall Caswell,
Eric Clarke, Franklin Cooper, Martin Deutsch, Robert Dudley, Lloyd
Elliott, Wilfred Good, Clark Goodman, ArthurKip, AlexanderLangsdorf,
Melvin Lax, John Marshall, Otto Morriiiigstar, Robert Osborne, Wendell
Peacock, Norman Rasmusseii, Norman Rudnick, Leonard Schiff, and
Marvin Van Dilla. Special thanks go to Norman Rasmussen for exten-
sive work on semifinal revisions of the chapters dealing with the inter-
action of radiation and matter.
Miss Mary Margaret Shanahan has been tireless, accurate, and patient
in editing and typing a series of hcotographed partial editions for student
use and in preparing the entire final manuscript. The assistance of
Miss Betsy Short, Mrs. Elizabeth Backofen, Mrs. Grace Rowe, Joel
Bulkley, and Harry Watters has been invaluable. Transcending all
this, the unbounded patience, insight, and encouragement of my wife,
Gwendolyn Aldrich Evans, have made it possible to put this volume
together.
ROBLEY D. EVANS
Contents
Preface V
INTRODUCTION
HistoricalSketchoftheDevelopmentofthe ConceptoftheAtomic Nucleus I
CHAPTER
1
CHARGE or ATOMIC NUCLEI
Introduction 6
1. Chemical Origin of Atomic Number 6
2. Number of Electrons per Atom. X-ray Scattering 7
43.. FCrheaqrugeenocnytohfeKA-toamnidcL-NsuecrlieeussX. Raa-yRsay Scattering . 2111
5. The DisplacementLaw 25
CHAPTER 2
RADIUS or NUCLEI
Introduction 28
1. The Growth of Concepts Concerningthe Size of Nuclei 28
2. Coulomb-energy Differencebetween Isobars . 31
3. Coulomb Potentialinsidea Nucleu.s... 38
4. The Nuclear Potential Barrier 45
5. Wave Mechanics and the Pene.tr.ati.on.of Potential Barriers 49
6. Lifetime of a-Ray Emitters ... 74
7. AnomalousScatteringofa Particles 81
8. CrossSectionsfor Nuclear Reactions Produced by Charged Part.icl.es.... 89
9. Nuclear Cross Sectionsfor the Attenuation of Fast Neutrons 94
CHAPTER 3
MASS OF NUCLEI AND OF NEUTRAL ATOMS
Introduction 96
1. The Discovery of Isotopes and Isobars . 96
2. Nomenclature of Nuclei 98
3. Mass Spectroscopy 101
4. Atomic Mass from Nuclear Disintegration Energies 117
5. Tables of Atomic Mass 135
CHAPTER 4
NUCLEAR MOMENTS, PARITY, AND STATISTICS
Introduction 140
1. NuclearAngular Momentum 141
x Contents
2. Nuclear Magnetic Dipole Moment 148
3. Anomalous Magnetic Moments of Free Nucleons 151
4. Relationships between / and M 155
5. Electric Quadrupole Moment 163
6. Parity . . 174
7. The Statistics of Nuclear Particles 177
CHAPTER 5
ATOMIC AND MOLECULAR EFFECTS OF NUCLEAR MOMENTS,
PARITY, AND STATISTICS
...
Introduction. 1S1
1. Extraimclear Effects of Nuclear Angular Momentum iiml StiitisLicb. 181
2. Extranuclcar Effects of Nuclear Magnetic Dipole Moment . 1D1
3. Extranuclear Effects of Nuclear Electric Quadrupole Moment . 11)7
CHAPTER 6
EFFECTS or NUCLEAR MOMENTS AVD PARITY ON
NUCLEAH TRANSITIONS....
Introduction 202
.
1. Conservation of Parity and Angular Moiufutuiii . . . 2(M
2. Penetration of Nuc.lrur Harrier . . . 201
3. Lifetime in tf Decay . - 20f>
4. Radiative Transitions in Nuclei . 211
5. Internal Conversion 218
6. Nutlfur Ipomers 22*.*
7. Determination oi Angulnr Momentum and Purity of ExeitedLevel,?frorrj p-
and 7-Transitinn Probabilities , 2H2
8. Angular Corn-hition of Successive liadintiruis 234
,
9. Angular Distribution I'L Nuclear Reactions. . 214
CHAPTER 7
ISOTOPIC ABUNDANCE RATIOS
... ... ...
Introduction. 250
1. Ratios from Mass Spectrosoopy . . .... 250
2. Isotope Shift in Line Spectra . .... 2f)(>
3. Isotope Stiift in the Hand Spectra of Diatomic Molecules ... 2.r>8
4. Isotope Ratiosfrom Radioactive Decay Constants . 2(2
5. Chemical and Physical Scales of Atomic Weight . 202
6. Mass-spectrographic Identification of Nuclides in Nuclear Reactions . 264
7. The Separation of Isotopes by Direct Selection Methods . . 2<<i
8. Thr Separation of Isotopes by Enrichment Methods . 2h'9
9. Szilard-ChalmeraReaction fortheEnrichmentof RadioactiveIsotopes . 273
10. Separation of Radioactive Isomers 275
CHAPTER 8
SYSTEMATIC^ OF STABLE NUCLEI
Introduction 276
1. Constituents of Atomic Nuclei 276
2. Relative Abundance of the Chemical Elements .... 279
3. Empirical Rulesof Nuclear Stability 284
Contents xi
CHAPTER 9
BINDING ENERGY OF NUCLEI
...
Introduction. 294
1. Packing Fraction . . .... 294
2. Total Binding Energy 295
3. Average Binding Energy . 297
4. Separation Energy for One Nucleon 302
CHAPTER 10
FORCES BETWEEN NUCLEONS
...
Introduction. .... 309
1. General Characteristics of Specifically Nuclear Force*! ... 309
2. GroundLevel of the Deuteron . . 313
3. Neutron-Proton Scattering at to 10 Mev . ... 317
4. Electromagnetic Transitions in the n-p System . 330
5. The Proton-Proton Force at to 10 Mev . . . 338
G. Equivalence of (/in) and (pp) Forces . . . 344
7. Summary of Central Forces . ... . 345
8. Effects of Tensor Forces . . 348
9 High-energy n-p and p-p Scattering 350
CHAPTER 11
MODELS OF NUCLEI
Introduction 357
1. Summary of Experimental Evidence Which.Sh.ou.ld Be Represented by the
Model 357
. .
2. The Nuclear Shell Model 358
3. The Liquid-drop Model . . 365
4. Statistical Model of Excited Levels 397
CHAPTER 12
CONSERVATION LAWS FOR NUCLEAR REACTIONS
... ...
Introduction 408
. . . .
1. Physical Quantities Which Are Conserved in Nuclear Ktwtions.... .. 408
2. Determination of the Q Value for Nuclear Reactions . 410
CHAPTER 13
NUCLEAR REACTIONS, ILLUSTRATED BY Bl (,p)
AND TTS ASSOCIATES
....
Introduction 422
.
1. Energy Distribution of Protons from BH\rt,p)C113 423
2. Discovery of the Neutron from B -+- r* . . 420
\\. Discovery of Artificial Kiidumctivity from H + tr . 430
4. Resonances in the Formation of the Compound Nucleus 434
. .
56.. SEnuemrmgayrLyososf.itnheI.neDlea.lst'iTc.iniScn.aatttieorninogf Nuclear. Hni'rgy Levels f.rom Inact.io4n. 44038
Energetics
CHAPTER 14
ENERGY 1fiorEMnwE UK NurLE/ui-itrAr'iio\ (Yv.s SUCTIONS
Introduction. 441
. .
1. Resonance Theory r>f Nuclear Cross Sections . . . 444
2. Continuum Theory of Nuclear Cross Sections . 45'-
xii Contents
CHAPTER 15
RADIOACTIVE-SERIES DECAY
.... .........
Introduction. . .... 470
1. Decay of a. Single Radioactive Nuclide . . 470
2. Radioactive-Henes D^cay. Growth of a Daughter.Pr.od.uct. . 477
3. Accumulation of Daughter Atoms . . 478
4. Time of Maximum Activity of Daughter Product. Ideal Equilibrium . 479
5. Ratio of Activity of Parent and Daughter. Transient Equilibrium 480
6. Yield of a Radioactive Nuriide Produced by Nuclear Bombardment 484
7. Growih of a Granddaughter Product . .. .... 486
8. General Equations of Radioactive-series Growth and .Dec.ay.... 490
9. Accumulation of Stable En.d P.ro.duc.ts.. .... 494
10. Summation Rules . .496
11. Approximate Method? for Short Accumulation Times..... .. 500
12. Graphical Methods for Series Growth and Decay 502
,
CHAPTER 16
SPECTRA
.........
...
Introduction ......... 511
. .
1. Fine Structure of a-Ray Spectra . ...... 511
2. Genealogy of Nuclides Which Emit a Ra}rs ...... 517
3. The Nuclear Energy Surface, for Heavy Nuclid.es........ 523
4. Systematics of a Decay Energies . 527
CHAPTER 17
0-RAY SPECTRA
.......
...
Introduction. . . ...... 536
1. Experimental Characteristics of the /3-Ray Continuum....... 536.
2. The Neutrino . .. ........... 541
3. Fermi Theory of Decay . . 548
CHAPTER 18
lONIZATION OF MATTER BY ClIARQED PARTICLES
...... ....
Introduction. . . . .... 567
1. Classical Theory of Inelastic Collisions with Atomic Electrons 570
2. Quantum-mechanical Theoriesof Inelastic Collisionswith Atomic Electrons 574
3. Comparison of Classical and Quantum-mechanical Theories . . 584
4. Energy Loss per Ion Pair by Primary and Secondary lonization. . . 586
5. Dependence of Colli.sio.n L.oss.es.on.the.Ph.ysi.cal.and Chem.ica.l .Sta.te.of .the
Absorber ................. 587
.
6. Certiiikov Radiation 589
CHAPTER 19
ELASTIC SCATTERING OF ELECTRONS AND POSITRONS
...... .....
1. Scattering of Electrons by Nuclei ....... 592
2. Scattering of Swift Electrons by Electrons . 597
CHAPTER 20
RADIATIVE COLL.ISI.ONS.O.F E.LEC.TR.ONS.W.ITH.A.TOM.IC NUCLEI
...
Introduction. ............... 600
.
1. Theory of Bremsstrahlung 600
2. ComparisonofVariousInteractionsbetweenSwiftElectronsandAtoms. . 606