Nuclear Moments

514 Pages·1958·7.447 MB·English

by  H. KOPFERMANN (Eds.)

PURE AND APPLIED PHYSICS
A SERIES OF MONOGRAPHS AND TEXTBOOKS
CONSULTING EDITOR
H. S. W. MASSEY
University College, London, England
Volume 1. F. H. FIELD and J. L FRANKLIN, Electron Impact Phenomena
and the Properties of Gaseous Ions. 1957
Volume 2. H. KOPFERMANN, Nuclear Moments. English Version Pre-
pared from the Second German Edition by Ε. E.
SCHNEIDER. 1958
IN PREPARATION
U. FANO and G. RACAH, Irreducible Tensorial Sets
WALTER E. THIRRING, Principles of Quantum Electrodynamics. Trans-
lated from the German by J. BERNSTEIN
J. IRVING and N. MULLINEUX, Mathematics in Science and Technology
E. P. WIGNER, Group Theory and its Application to the Quantum
Mechanics of Atomic Spectra. With Additions and Corrections
by E. P. WIGNER. Translated from the German by J. J. GRIFFIN
FAY AJZENBERG-SELOVE (ed.). Nuclear Spectroscopy
ACADEMIC PRESS INC · PUBLISHERS · NEW YORK
NUCLEAR MOMENTS
H. KOPFERMANN
Erstes Physikalisches Institut der Universität
Heidelberg, Germany
ENGLISH VERSION PREPARED FROM THE SECOND GERMAN EDITION BY
Ε. E. SCHNEIDER
Physics Department, King's College, University of Durham
Newcastle upon Tyne, England
1 9 58
ACADEMIC PRESS INC · PUBLISHERS · NEW YORK
COPYRIGHT© 1958
BY
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Ill FIFTH AVENUE
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PRINTED IN THE UNITED STATES OF AMERICA
AUTHOR'S PREFACE TO THE GERMAN EDITION
Fifteen years ago when the first edition of this book was published, the
study of the moments of the ground states of stable and long-lived radio-
active nuclei was hardly more than a specialized branch of optical spec-
troscopy. Since then, very striking advances have been made largely
through the advent of radio-frequency methods. By now, the subject of
nuclear moments has grown into an important branch of nuclear physics
which is followed actively in many laboratories all over the world. Moreover,
the investigation of nuclear moments by radio-frequency techniques has
opened up new fields in chemistry and solid state physics.
For some years now, the study of spins and magnetic moments has been
extended to the excited states of nuclei. However, in view of their extremely
short lifetimes entirely different experimental methods have to be used and
their description would lead too far into experimental nuclear physics.
Consequently, the present new edition is confined to the moments of
"sufficiently long-lived" nuclear states which are almost exclusively the
ground states of nuclei.
At the time of the first edition, the very tentative efforts to use the rather
incomplete experimental material on nuclear moments as a basis for a
theoretical description of the structure of nuclei did not produce any convinc-
ing results. The great progress which has been made since then in establishing
the spins, magnetic and electric moments of nuclei, has paved the way for
the development of successful nuclear models. Such models not only allow
the measured nuclear moments to be related to the structure of nuclei but
also do useful service in the interpretation of other nuclear phenomena.
In order to incorporate in the new edition the very large volume of
mainly novel material on nuclear moments which is now available it was
necessary in practice to write a new book in which here and there sections
of the first edition were taken over. Its size has of necessity increased by
more than fifty per cent.
The first chapter deals with the investigations on the hyperfine structure
of free atoms by atomic beam methods and optical interference spectroscopy.
The central theme which forms the foundation for the succeeding chapters,
is the development of the magnetic and electric interactions of the atomic
nucleus with its surroundings. At first sight it may appear strange that the
ν
vi PREFACE TO THE GERMAN EDITION
investigations on hyperfine structure by means of optical interference
spectroscopy, with their very inferior precision as compared with radio-
frequency methods, are described in such detail. However, one does well to
remember that the majority of spins of nuclear ground states, their magnetic
moments, and a large number of quadrupole moments were found first by
interference spectroscopy. In very many cases the radio-frequency methods
have merely confirmed these data and their merit lies in the far higher
precision which has allowed the moments to be established with very high
accuracy. Only in cases where the optical interference method fails because
of its low resolution, has radio-frequency spectroscopy led to new data.
Even now, optical interference spectroscopy is still the most versatile method
for the study of nuclear moments and its pioneering work cannot be dis-
pensed with.
A relatively large space has been devoted to the discussion of the isotope
shift of atomic spectra which is the exclusive domain of optical interference
spectroscopy. This appears to be justified because in the case of elements
with several isotopes a reliable analysis of the hyperfine structure of the
atomic spectral lines is impossible without a detailed examination of the
isotope shift. Apart from that, the isotope shift furnishes information on
the change of the nuclear charge distribution from isotope to isotope as
well as on the quadrupole moments of strongly deformed nuclei. Indeed,
results on the isotope shift have given the first indication that nuclei with
zero spin may be deformed.
The second chapter deals with investigations on nuclear moments in
free molecules. This comprises the description and interpretation of al-
ternating intensities and magnetic and electrical molecular beam radio-
frequency spectroscopy (including the determination of the magnetic moment
of the neutron). Also, the essential features of microwave spectroscopy of
free molecules, as far as this gives data on nuclear moments, are presented.
Since some readers will not be familiar with the theories of molecular structure
and molecular spectra which are required in the interpretation of observed
hyperfine structures, short summaries of these topics precede the relevant
sections.
In the third chapter all radio-frequency methods are discussed which
have so far been used for studies of nuclear moments in gases, liquids, and
crystals, namely nuclear magnetic resonance, nuclear quadrupole resonance,
and paramagnetic resonance. The latter is introduced by a brief description
of the lowest electronic states in crystals. The chapter includes short digres-
sions on spin echos, the Overhauser effect, and experiments on nuclear
PREFACE TO THE GERMAN EDITION VÜ
alignment, but applications of the resonance methods to chemistry and solid
state physics are excluded from the book.
The last chapter deals with the interpretation of the experimental results
on nuclear moments in terms of nuclear models, principally the "shell
model" which provides the currently most successful description of nuclear
structure.
In order to present the theoretical sections in a familiar manner, the
procedure adopted in the first edition has been followed again: as far as
possible the Bohr theory is used as the starting point and the formulas
developed from simple vector models by means of the correspondence
principle are then converted into their rigorous quantum-mechanical form.
Only in those cases where this method is not applicable, the direct quantum-
mechanical derivation is indicated briefly. The book does not claim to be
comprehensive in any respect but the most important published work (up
to about May, 1955) is discussed or at least mentioned.
In view of the emphasis on radio-frequency methods, large parts of the
book deal with practical electronics. Formulas of electronics should not be
loaded with the systems of units used in theoretical physics. On the other
hand, one would like to retain the familiar form of formulas for the splitting
factors of hyperfine structures derived from magnetic and electric interac-
tions. A reasonable way out of this dilemma has been attempted in the
following way: two fundamental constants are used, the electric constant
= 4π? , and the magnetic constant K = μ/4:π where ε and μ are the
Kg 0 M 0 0 0
fully dimensional fundamental constants used in most modern treatises
on practical electricity which in the MKSQ system are directly related to
the legal units of volt, ampere, etc. In the traditional, electrostatic, and
electromagnetic systems, K and K are dimensionless and have the value
C M
unity so that those readers who object to them in formulas of atomic physics
can overlook them there. All "c's" which occur in formulas through the
traditional mixture of the units, have been omitted, for example in the
Bohr magneton μ = [\e%)\m where it is reasonable to measure both e
Β
and μ in the same units (say e.m.u.). For further details the reader is referred
to Table 71 on page 458 at the end of the book.
The magnetic field is characterized in the present edition exclusively by
the magnetic flux density (magnetic induction) which in agreement with
G. Mie and A. Sommerfeld deserves the name "magnetic field strength/'
The fact that "gauss" is used throughout as the unit of the magnetic field
and never volt · sec/m2 is a concession to workers in the field of nuclear
moments who always use gauss. Unfortunately, in this book it is not possible
to use the letter Β as symbol for the magnetic flux density since Β without
viii PREFACE TO THE GERMAN EDITION
suffix is reserved for the "quadrupole coupling constant" and with suffix ν
for the "rotational constant" of free molecules. Thus the symbol Η is used
which, after what has just been said, can hardly lead to confusion.
I wish to thank many colleagues and collaborators. P. Brix, H. Friedburg,
Η. Krüger, U. Meyer-Berkhout, and A. Steudel have assisted me in many
ways in the arrangement of the book and in the formulation of individual
sections. I had very illuminating discussions with Maria Goppert-Mayer,
H. Jensen, and F. Sauter; I am indebted to the two first named for allowing
me to look over the manuscript of their book on the shell model. My very
special thanks go to E. Schneider (Newcastle), the translator and editor of
the English edition of this book, who has made valuable suggestions partic-
ularly on the presentation of the third chapter but also on many other topics.
The solution of the problem of units is his suggestion also. H. Bucka has
very kindly undertaken the recalculation of the relativity corrections. I am
indebted to G. Herzberg for Fig. 116.
The publishers have been most generous in allowing me to insert small
paragraphs in the text, even in page proof, regarding important new work
published in 1954 and 1955. My best thanks for this too.
Heidelberg
August 1955
H. KOPFERMANN
PREFACE TO THE ENGLISH EDITION
In preparing the present English edition of Kopfermann's Kernmomente
—largely in parallel with the German version—I have endeavored to be
faithful to the spirit, if not to the letter, of the original: I have closely
followed the physical arguments and mathematical derivations, but have
adapted the notation and have allowed myself minor deviations from the
text wherever I regarded this to be more acceptable to English and American
readers than a literal interpretation. There are a number of more substantial
amendments and additions which, apart from the different treatment of
spin echos, in section 56, do not cover more than a few lines each.
The text includes references and, in some cases, short paragraphs on
recent work, up to August 1956, published after the completion of the German
edition. Some of the tables in the book, particularly Tables 4, 5, and 53,
have been extended. The tables of nuclear moments at the end of the book
(Tables 62, 63, 66) have been extended considerably and include recent
data up to about May 1957.
An amended version of the section on the dynamical nuclear model has
been adopted which has been specially prepared by the author and includes
the recent work by Nilsson (section 72b, pp 430ff).
The present edition contains, in addition to the author index, and a
greatly extended subject index, an element index and a detailed explanation
of symbols (pp 459ff).
As regards the electromagnetic units, my attitude tends to be far from
apologetic. If anything I should apologize to the other side: in view of
an increasing number of research publications in most respectable journals
on topics of pure physics in which fellow-fighters for rational electricity
gallantly use "B" for the magnetic field where traditionally it used to be
"H," I feel now much less happy about the compromise solution of writing
"H" and thinking "B" which I proposed with some enthusiasm in 1953
to the then rather reluctant author. Nevertheless, 1 have not allowed this
compromise on the question of mere notation to affect my strong convictions
on the deeper issues of the nature of the magnetic field and of magnetic
point sources, particularly on the non-existence of magnetic poles and hence
true magnetic dipoles. They are implied in remarks in the text and footnotes
on pp. 5, 43, 122, and 289, and in the consistent use, throughout the book,
ix
χ PREFACE TO THE ENGLISH EDITION
of the terms "magnetic moment'' and "point magnet" in place of "magnetic
dipole moment" and "magnetic point dipole." For want of a better generally
acceptable term I had to retain "magnetic dipole radiation."
Many people have helped me in the preparation of this book. Above
all I should like to thank my friend and colleague H. C. Bolton who has read
very carefully through the whole of the manuscript and has made many
helpful suggestions on points of presentation as well as on points of physics,
particularly in the theoretical sections. I have to thank P. A. Forrester for
his painstaking work of preparing most of the first 40 illustrations, and
Mrs. O. Teasdale for modifying the remainder of the illustrations which
have been taken over from the German edition. My thanks are due to
C N. Owston, K. Thompson, and J. M. Titman for help in the preparation
of the tables and in proofreading and to Miss Mary Walker and Mrs. E. Marshall
for their meticulous typing of text and tables.
The Publishers have been most patient in face of my slow progress and
most generous over last minute corrections and additions. I should like to
express my appreciation for this and for the very efficient cooperation of
their editorial staff throughout all phases of the preparation of this book.
It is a great pleasure to mention colleagues and friends, in this country
and in the United States, to whom I am indebted for information on new
results prior to publication and for illuminating discussions and valuable
suggestions: B. Bleany (Oxford), H. G. Dehmelt (Seattle), O. R. Frisch
(Cambridge), W. Gordy (Duke University), D. J. E. Ingram (Southampton),
H. G. Kuhn (Oxford), T. A. Littlefield (Newcastle), R. Livingston (Oak
Ridge), K. W. Meissner (Purdue University), J. G. Powles (London),
M. H. L. Pryce (Bristol), N. F. Ramsay (Harvard), G. W. Series (Oxford),
K. F. Smith (Cambridge), K. W. H. Stevens (Nottingham).
Finally, I should like to say as a special and personal tribute to the
Author : I have learned much and have enjoyed it thoroughly, every (nuclear)
moment of it ! May the Reader do the same !
To my wife, for her encouragement and indulgence and for many a night
spent together over proofs and indexes, I simply say: "Thank you!"
Newcastle upon Tyne
November 1957
ERICH SCHNEIDER
CHAPTER I
NUCLEAR MOMENTS IN FREE ATOMS
I. Survey of Experimental Methods
When high resolution spectroscopy is applied to the study of atomic
spectral lines emitted as electric dipole radiation in the visible and ultra-
violet, many lines are found to consist of several closely spaced components.
This splitting, called hyperfine structure (hfs), has been known nearly as
long as interference spectroscopy itself, and has formed the subject of a
large number of experimental investigations. Yet, in the absence of a guiding
idea, the laws and regularities underlying this phenomenon remained obscure
for a long time. Progress had to await a sufficient understanding of the fine
structure (fs) of atomic spectra. The number of possible types of motion of
the electron within the outer parts of the atom had to be recognized, and
with it its possible quantum numbers, before the new degree of freedom, as
reflected in the hfs, could be ascribed to an angular momentum of the atomic
nucleus.
W. Pauli, in 1924, was the first to advocate the idea that the hfs owes its
existence essentially to a magnetic coupling between atomic nucleus and
electrons (magnetic hyperfine structure) and he predicted on this basis the
fundamental features of the Zeeman and Paschen-Back effects of the hfs
(Pa 24).
In a classic investigation, E. Back and S. Goudsmit succeeded three
years later in fitting a large part of the hfs of the spectrum of Bi I into a
consistent scheme of energy levels and, by observing the Paschen-Back
effect, in establishing unambiguously the angular momentum quantum
number of the bismuth nucleus. All the characteristic regularities of the
magnetic hfs already show up in this paper, in particular the far-reaching
validity of the Lande interval rule, which must be regarded as a necessary
consequence of magnetic coupling (BG 27).
Hyperfine structure research entered a new phase when H. Schuler
introduced the hollow cathode cooled with liquid air. With this he could
reduce the Doppler effect of the hfs components to such an extent that the
investigation of very close-lying levels became possible (Sch 30). The
ι