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BOOK

THE ATOMIC NUCLEUSRobley D. Evans, Ph.D.PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY

TATA McGRAW-HILL PUBLISHINC COMPANYBombay

LTD.

New

D*lhi

THE ATOMIC NUCLEUS

1955 by McGraw-Hill,

Inc.

All Rights Reserved This book, or parts thereof, may not be reproduced in any form without permission of the publishers.

T M H

Edition

Reprinted in India by arrangement with the McGraw-Hill, Inc.

New

York.

This edition can be exported from India only by the Publishers, Tata McGraw-Hill Publishing Company Ltd.

Published by Tata McGraw-Hill PublishingPrinted by

CompanyPvt. Ltd.,

Limited and

Mohan

Makhijani

at

Rekha Printers

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. Nuclearphysics was originally a subject which represented the research interests of a small number of academic scientists, and whose modest size permitted

easy coverage in a one-year graduate course. Now pure and applied nuclear physics is a gigantic area of research and engineering. Numerous subtopics have grown rapidly into large and separate fields of professional 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 of empirical knowledge and of theoretical interpretation has grown to be very large. This book embraces more material than my students and I are now able to cover, with adequate regard for depth of underThose topics standing, in a one-year course of ninety class hours. 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 coursethus 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 techIt undertakes to strike that compromise in viewpoint which niques. has been adopted by the majority of working physicists. Detailed attention is given in the early chapters to several fundamental concepts, so that the student may learn to think in center-ofmass coordinates and may visualize clearly the phenomena of barrieris

sections.

transmission, particle interactions during collisions, and collision cross The physical aspects receive emphasis in the main text, while the corresponding mathematical details are treated more fully in appen-

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 mathematicaldixes.

vi

Prefaceis

equipment

in working order through the calculus

and

differential

Prior experience in wave mechanics is not assumed, and equations. 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 studentsas they enter this course. but is blank in others. In

Each studentan average

is

well prepared in

some areas

nearly random distribution of areas 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

class of fifty students there is a of competence and areas of no

Within each subfield, the disusually begins at an introductory level. 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 undertake creative personal research. To help encourage early familiarity with the original papers, numerous references to the pertinent periodicalliterature

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 spectroscopy.

sequential arrangement of these topics is a 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 here is that which has developed in the classroom as an empirical solution involving "minidifficult,if

An optimumnot

insolvable,

.

.

.

,

mumI

regret."

begin as Bethe and Bacher have done, with the fundamental properties 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, In order to evaluate even these isobaric spin, parity, and statistics. " " static properties of nuclei, it is necessary to invoke many types of experimental and theoretical studies of the "dynamic" behavior ofis

a decay, ft decay, and nuclear reactions. The result that those aspects of nuclear dynamics which enlighten the static This might have been done by saying, properties are referred to early. "It can be shown ..." or "We shall see later that ," but it has proved more satisfactory to give, a reasonable, account of the perThis has tinent dynamic aspect at the place where it is first needed. been found to lead to better understanding, although it does give rise tonuclei, including.

.

.

occasional duplication, or "varied reiteration," and, in some instances, to division of dynamic topics, such as a decay and ft decay, into two parts.

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, ft decay, and radioactive-series transformations. 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 industrial 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 Practical often n governing factor in the design of imclr.ar experiment.topics given detailed treatment, include the effects of resolving time, random coincidences, sealer and count ing-rate-meter fluHualiaiiH, and the statistics of rapidly decaying sources.

many of the reasonably well-established nuclear For more comprehensive the corresponding text. properties accompany tables, explicit references arc made to the voluminous and valuable For the latest data, thcsn compilations must standard compilations. be augmented by the Miminarics of new nuclear data published quarterlyKeferencr tablesof1

in NurJcar iS'ci'rwr Abstracts.in nuclear physics faces ihe opportunity of making a It is useful in know how discoveries have discovery. 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,n-\v

Kvory worker

signilicant

at the stunt; time to focus on fundamental physical chapters, such as Chap. 13, Nuclear Reactions, Illustrated by H IU (arj;) and Jts Associates, have been arranged with due regard to the history of nuclear physics and to the pitfalls and accidental

of

discovery" and

principles,

some

of research. This was done to encourage the student to develop a feeling for the stapes t hrough which nuclear science has progressed and a 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 see that the principles 'of the subject 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 professional 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

triumphs

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 thanks, especially to Alfredo

my

Banos, Keith Boyer, Sanborn Brown, Gordon Brownell, Randall Caswell, Eric Clarke, Franklin Cooper, Martin Deutsch, Robert Dudley, Lloyd Elliott, Wilfred Good, Clark Goodman, Arthur Kip, Alexander Langsdorf, Melvin Lax, John Marshall, Otto Morriiiigstar, Robert Osborne, WendellPeacock,

Norman

Rasmusseii,

Norman Rudnick, Leonard

Schiff,

and

Marvin Van Dilla. Special thanks go to Norman Rasmussen for extensive work on semifinal revisions of the chapters dealing with the interaction of radiation and matter.

Miss Mary Margaret Shanahan has been tireless, accurate, and patient 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 volumein editing

together.

ROBLEY D. EVANS

Contents

Preface

VINTRODUCTION

Historical Sketch of the

Development

of the

Concept

of the

Atomic Nucleus

I

CHAPTER 1 CHARGE or ATOMIC NUCLEIIntroduction1.

667.

2. 3.

Chemical Origin of Atomic Number Number of Electrons per Atom. X-ray Scattering Charge on the Atomic Nucleus. a-Ray Scattering

11

4.5.

Frequency of K- and L-series The Displacement Law

X

Rays

21

25

CHAPTER 2RADIUS or NUCLEIIntroduction1.

2. 3.4.

5.

Concepts Concerning the Size of Nuclei Coulomb-energy Difference between Isobars Coulomb Potential inside a Nucleus The Nuclear Potential Barrier Wave Mechanics and the Penetration of Potential Barriersof.

The Growth

28 2831

6.7.

Lifetime of

a-Ray Emitters Anomalous Scattering of a Particles

.... .......

38 45 49 7481

8. 9.

Cross Sections for Nuclear Reactions Produced by Charged Particles Nuclear Cross Sections for the Attenuation of Fast Neutrons

....

.

.

89

94

CHAPTER 3 MASS OF NUCLEI AND OF NEUTRAL ATOMSIntroduction1.

The DiscoveryNomenclature

2.3.

of Isotopes of Nuclei

and Isobars

.

96 96

98101

4.5.

Mass Spectroscopy Atomic Mass from Nuclear Disintegration Energies Tables of Atomic Mass

117135

CHAPTER 4 NUCLEAR MOMENTS, PARITY, AND STATISTICSIntroduction1.

140

Nuclear Angular

Momentum

141

x2.3. 4.

ContentsNuclear Magnetic Dipole Moment Anomalous Magnetic Moments of Free Nucleons Relationships between / and MElectric

148151

5.

Quadrupole.

Moment.

155 163174 177

6.7.

Parity

The

Statistics of

Nuclear Particles

CHAPTER

5

ATOMIC AND MOLECULAR EFFECTS OF NUCLEAR MOMENTS, PARITY, AND STATISTICSIntroduction.1.

....

1S1

2.

3.

Extraimclear Effects of Nuclear Angular Momentum iiml StiitisLicb. Extranuclcar Effects of Nuclear Magnetic Dipole Moment Extranuclear Effects of Nuclear Electric Quadrupole Moment

181

1D111)7

.

CHAPTER

6

EFFECTS or NUCLEAR MOMENTS AVD PARITY ON N U C LEA H T R A N S I TI O N SIntroduction Conservation of Parity and Angular Moiufutuiii Penetration of Nuc.lrur Harrier Lifetime in tf Decay.

.....

1.

.

.

202 2(M.

2.

.

.

20120f>

3.4. 5. 6. 7.

.

-

Radiative TransitionsInternal Conversion

in

Nuclei

.

211 21822*. *

Nutlfur Ipomers Determination oi Angulnr

Momentum and

Purity

of

Exeited Level,?

frorrj p,

and8.

7- Transit inn Probabilities Angular Corn-hit ion of Successive liadintiruis

,

9.

Angular Distribution

I'L

Nuclear Reactions.

.

2H2 234 214

ISOTOPICIntroduction.1.

CHAPTER 7 ABUNDANCE RATIOS

....

..... .

...

Ratios fromIsotope

Mass Spectrosoopy

2. 3.

Isotope Shift in Line Spectra Stiift in the Hand Spectra of Diatomic Molecules

.... .....

250 2502f)(>

4. 5.6. 7.

Isotope Ratios from Radioactive Decay Constants Chemical and Physical Scales of Atomic Weight

.....

r 2. >8

8.9.

by Enrichment Methods Szilard-Chalmera Reaction for the Enrichment of Radioactive Isotopesof Isotopes.

The Separation Thr Separation

Mass-spectrograph ic Identification of Nuclides in Nuclear Reactions of Isotopes by Direct Selection Methods.

2(2 202 2642