Table Of ContentTexts and
Monographs
in Physics
W. Beiglbock
series editor
Polarized Electrons
Joachim Kessler
Springer-Verlag Berlin
Heidelberg GmbH
1976
Professor Dr. JOACHIM KESSLER
Physikalisches Institut der Universitiit
Schlossplatz 7, D-4400 Munster
Professor Dr. WOLF BEIGLBOCK
Institut fUr Angewandte Mathematik der Universitiit
1m Neuenheimer Feld 294, D-6900 Heidelberg
With 104 figures
ISBN 978-3-662-12723-0 ISBN 978-3-662-12721-6 (eBook)
DOI 10.1007/978-3-662-12721-6
Library of Congress Cataloging in Publication Data. Kessler, Joachim, 1930-. Polarized electrons. (Texts
and monographs in physics). Bibliography: p. Includes index. 1. Electrons-Polarization. I. Title.
QC793.5.E628K47 539.7'2112 76-9863
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@) by Springer-Verlag Berlin Heidelberg 1976
Originally published by Springer-Verlag Berlin Heidelberg New York in 1976.
Softcover reprint of the hardcover 1st edition 1976
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a
specific statement, that such names are exempt from the relevant protective laws and regulations and
therefore free for general use.
Preface
This book deals with the physics of spin-polarized free electrons. Many
aspects of this rapidly expanding field have been treated in review articles,
but to date a self-contained monograph has not been available.
In writing this book, I have tried to oppose the current trend in science
that sees specialists writing primarily for like-minded specialists, and even
physicists in closely related fields understanding each other less than they
are inclined to admit. I have attempted to treat a modern field of physics
in a style similar to that of a textbook.
The presentation should be intelligible to readers at the graduate level,
and while it may demand concentration, I hope it will not require decipher
ing. If the reader feels that it occasionally dwells upon rather elementary
topics, he should remember that this pedestrian excursion is meant to be
reasonably self-contained. It was, for example, necessary to give a simple
introduction to the Dirac theory in order to have a basis for the discussion
of Mott scattering-one of the most important techniques in polarized
electron studies.
This monograph is intended to be an introduction to the field of
polarized electrons and not a replacement for review articles on the
individual topics discussed. It does not include electron polarization in
P decay, a field which has been covered in other books. Areas such as
electron spin resonance, in which it is not the spins of free electrons that
are oriented, are beyond the scope of this book. Well-established areas,
like Mott scattering, have naturally been treated in more detail than areas
that are just starting to develop, such as high-energy electron scattering.
Ideas or general results that have not been quantitatively established,
theoretically or experimentally~ have not been considered, since physical
results must be put on a quantitative basis.
Following two introductory chapters, the polarization effects in elec
tron scattering from unpolarized targets are discussed in Chapter 3.
Processes governed by electron exchange are treated in Chapter 4. The
numerous spin-polarization effects in ionization processes are discussed
in Chapter 5, and the following chapter deals with electron polarization
in solid-state physics. At a time when scientists are frequently asked about
VI Preface
the practical benefits of their work, it seems particularly appropriate to
consider the applications of polarized-electron physics. This is done in
Chapter 7 which also includes a section on the future prospects in this field.
In keeping with the introductory character of the book, the main
purpose of the reference lists is to aid the reader in completing or sup
plementing the information in certain sections. The newcomer to the field
should refer to the review articles wherever they exist. Primary sources
have been cited if they are directly referred to in the text or if they have not
yet been listed in review papers or other references.
It is a pleasure to express my gratitude to the many people who have
contributed to the completion of this project. Several sections have been
considerably influenced by the ideas and achievements of my coworkers
particularly Drs. G. F. HANNE, U. HEINZMANN, and K. JOST-with whom,
over the years, I have studied many of the topics discussed. The generous
hospitality of the Joint Institute for Laboratory Astrophysics gave me the
chance to write this book. The stimulating atmosphere of JILA which I
enjoyed during my stay as a Visiting Fellow provided the ideal setting for
this project. I gratefully acknowledge the excellent work of the JILA
editorial office; thanks to the numerous helpful suggest" :ms from L.
VOLSKY and the typing skill of G. ROMEY, the transformation (in record
time) of my stacks of messy, marked-up sheets into a beautiful manuscript
was a joy to behold. I am particularly grateful to Dr. M. LAMBROPOULOS
who was kind enough to read the entire manuscript; her constructive
criticisms have improved it considerably. Discussions with Prof. H. MERZ
in Miinster and with many colleagues in Boulder have helped to clarify
several passages. I appreciate the application and conscientiousness of H.
GERBERON and B. GOHLSDORF who prepared most of the illustrations. I am
also grateful for the assistance of E. RUSSEL and Dr. C. B. LUCAS in trans
lating a number of my lectures which I used in preparing parts of the
manuscript. Finally, I wish to thank those listeners, at home and abroad,
who, by their reactions to my lectures, have helped to clarify this pres
entation.
Boulder, Colorado JOACHIM KESSLER
August, 1975
Contents
1. Introduction
1.1 The Concept of Polarized Electrons . . . . . . . . . .. 1
1.2 Why Conventional Polarization Filters Do Not Work with
Electrons ...................... 2
2. Description of Polarized Electrons
2.1 A Few Results from Elementary Quantum Mechanics 7
2.2 Pure Spin States . . . . . . . . . . . . . . . . 9
2.3 Statistical Mixtures of Spin States. Description of Electron
Polarization by Density Matrices . . . . . . . . . . . . 14
3. Polarization Effects in Electron Scattering from Unpolarized Targets
3.1 The Dirac Equation and Its Interpretation . . . . . 21
3.2 Calculation ofthe Differential Scattering Cross Section 33
3.3 The Role of Spin Polarization in Scattering . . . . . 40
3.3.1 Polarization Dependence ofthe Cross Section . 40
3.3.2 Polarization of an Electron Beam by Scattering 44
3.3.3 Behavior of the Polarization in Scattering . . . 45
3.3.4 Double Scattering Experiments . . . . . . . 49
3.4 Simple Physical Description of the Polarization Phenomena 51
3.4.1 Illustration of the Rotation of'the Polarization Vector 52
3.4.2 Illustration of the Change in the Magnitude of the
Polarization Vector . . . . . . . . . . . . . . . 52
3.4.3 Illustration of the Asymmetry in the Scattering of a
Polarized Beam . . . . . . . . . . . . . . . . . 55
3.4.4 Transversality of the Polarization as a Consequence of
Parity Conservation. Counterexample: Longitudinal
Polarization in p Decay . . . . . . . . 56
3.4.5 Equality of Polarizing and Analyzing Power . . . . . 59
VIII Contents
3.5 Quantitative Results 61
3.5.1 Coulomb Field 61
3.5.2 Screened Coulomb Field 63
3.6 Experimental Investigations . 68
3.6.1 Double Scattering Experiments 69
3.6.2 Triple Scattering Experiments 72
3.6.3 Experimental Equipment: Mott Detectors and
Polarization Transformers . . . . . . . . . 76
3.7 Inelastic Scattering, Resonance Scattering, Electron-Molecule
Scattering. Further Processes Used for Polarization Analysis 83
4. Exchange Processes in Electron-Atom Scattering
4.1 Polarization Effects in Elastic Exchange Scattering 87
4.2 Experiments on Polarization Effects in Elastic Exchange
Scattering . . . . . . . . . . . . . . . . . . 95
4.3 Polarization Effects in Inelastic Exchange Scattering 100
4.3.1 One-Electron Atoms 100
4.3.2 Two-Electron Atoms 109
4.4 M011er Scattering . . . . . 116
5. Polarized Electrons by Ionization
5.1 Photoionization of Polarized Atoms 123
5.2 Fano Effect . . . . . . . . . . 125
5.2.1 Theory of the Fano Effect . 125
5.2.2 Illustration of the Fano Effect. Experimental Results 133
5.3 Autoionizing Transitions ....... 139
5.4 Multiphoton Ionization . . . . . . . . . . . . . 143
5.5 Collisional Ionization of Polarized Atoms . . . . . 147
5.5.1 Collisional Ionization of Polarized Metastable
Deuterium Atoms . 147
5.5.2 Penning Ionization 149
6. Polarized Electrons from Solids
6.1 Magnetic Materials 153
6.1.1 Photoemission 155
6.1.2 Field Emission 159
6.2 Nonmagnetic Materials 163
Contents IX
7. Further Applications and Prospects
7.1 Investigations of the Structure of Matter . . . . 171
7.1.1 Low-Energy Electron Diffraction (LEE D) 171
7.1.2 Electron-Molecule Scattering 179
7.1.3 Electron Microscopy ..... 181
7.1.4 Why Isn't Nature Ambidextrous? 182
7.1.5 High-Energy Physics ..... 183
7.2 g - 2 Experiments for Measuring the Anomalous Magnetic
Moment of the Electron. Electron Maser 185
7.3 Sources of Polarized Electrons 195
7.4 Prospects 205
References . 211
Subject Index . 217
1. Introduction
1.1 The Concept of Polarized Electrons
An ensemble of electrons is said to be polarized if the electron spins have a preferential
orientation so that there exists a direction for which the two possible spin states are
not equally populated. Reasons are given for the interest in polarized electrons.
In early experiments with free electrons the direction of their spins was
seldom considered. The spins in electron beams that were produced by
conventional methods (such as thermal emission or the photoelectric
effect) had arbitrary directions. Whenever the spin direction played a role,
one had to average over aU spin orientations in order to describe the experi
ments properly.
Only in recent years has it been found possible to produce electron
beams in which the spins have a preferential orientation. They are called
polarized electron beams in analogy to polarized light in which it is the
field vectors that have a preferred orientation. To put it more precisely:
An electron beam (or any other electron ensemble) is said to be polarized
if there exists a direction for which the two possible spin states are not
equally populated.
If all spins have the same direction one has the extreme case of a totally
polarized ensemble of electrons (Fig. 1.1). If not all, but only a majority of
the spins has the same direction, the ensemble is called partially polarized.
Fig. 1.1. Ensemble of totally polarized electrons
There are many reasons for the interest in polarized electrons. One
essential reason is that in physical investigations one endeavors to define
