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This book provides a comprehensive and up-to-date account of the field of low energy positrons and positronium within atomic and molecular physics. It begins with an introduction to the field, discussing the back- ground to low energy positron beams, and then covers topics such as total scattering cross sections, elastic scattering, positronium formation, exci- tation and ionization, annihilation and positronium interactions. Each chapter contains a blend of theory and experiment, giving a balanced treatment of all the topics. The book will be useful for graduate students and researchers in physics and chemistry. It is ideal for those wishing to gain rapid, in-depth knowledge of this unique branch of atomic physics. Michael Charlton obtained his degree and Ph.D. from University College London. In 1983 he was awarded a Royal Society University Research Fellowship, held at UCL. From 1991 to 1999 he was a Reader in Physics at UCL and was appointed to the Chair in Experimental Physics at the University of Wales, Swansea in 1999. Professor Charlton has published over one hundred research articles and written several reviews, notably for Reports on Progress in Physics and Physics Reports. John Watkin Humberston was an undergraduate at Manchester University and obtained his Ph.D. from University College London. From 1965 to 1966 he taught at Trinity College Dublin and became a Lecturer at UCL in 1966, where he subsequently became Senior Lecturer, Reader and Professor. During this time he had sabbatical leave at the Goddard Space Flight Center, USA, and at York University, Toronto, Canada. Professor Humberston has written numerous research articles, published mainly in Journal of Physics B, as well as several review articles in Advances in Atomic and Molecular Physics and in Physics Reports.
CAMBRIDGE MONOGRAPHS ON ATOMIC, MOLECULAR AND CHEMICAL PHYSICS: 11
General editors: A. Dalgarno, P. L. Knight, F. H. Read, R. N. Zare
1. R. Schinke: Photodissociation Dynamics 2. L. Frommhold: Collision-induced Absorption in Gases 3. T. F. Gallagher: Rydberg Atoms 4. M. Auzinsh and R. Ferber: Optical Polarization of Molecules 5. I. E. McCarthy and E. Weigold: Electron–Atom Collisions 6. V. Schmidt: Electron Spectrometry of Atoms using Synchrotron Radiation 7. Z. Rudzikas: Theoretical Atomic Spectroscopy 8. J. H. McGuire: Electron Correlation Dynamics in Atomic Collisions 9. J.-P. Connerade: Highly Excited Atoms 10. R. Bl¨umel and W. P. Reinhardt: Chaos in Atomic Physics 11. M. Charlton and J. W. Humberston: Positron Physics For Lucy and Bettina Positron Physics
M. Charlton University of Wales Swansea J. W. Humberston University College London Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press The Edinburgh Building, Cambridge , United Kingdom Published in the United States by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521415507
© Cambridge University Press 2001
This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
First published in print format 2000
ISBN-13 978-0-511-06753-2 eBook (EBL) ISBN-10 0-511-06753-4 eBook (EBL)
ISBN-13 978-0-521-41550-7 hardback ISBN-10 0-521-41550-0 hardback
Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents
Preface ix
1 Introduction 1 1.1 Historical remarks 1 1.2 Basic properties of the positron and other positronic systems 3 1.3 Basic experimental techniques 11 1.4 Slow positron beams 16 1.5 The production of positronium 27 1.6 The physical basis of the interactions of positrons and positronium with atoms and molecules 35
2 Total scattering cross sections 40 2.1 Introduction 40 2.2 Theory 42 2.3 Experimental techniques 48 2.4 General discussion of systematic errors 57 2.5 Results and discussion – atoms 63 2.6 Results and discussion – molecules 81 2.7 Partitioning of the total cross section 89
3 Elastic scattering 94 3.1 Introduction 94 3.2 Theory 95 3.3 Threshold effects 132 3.4 Angle-resolved elastic scattering 139
4 Positronium formation 150 4.1 Introduction 150 4.2 Theory 151
vii viii Contents
4.3 Experimental techniques 175 4.4 Results 185 4.5 Other processes involving positronium formation 195 4.6 Comparisons with protons 200 4.7 Differential cross sections 201 4.8 Dense gases 207
5 Excitation and ionization 214 5.1 Excitation 215 5.2 Ionization – theoretical considerations 227 5.3 Ionization – experimental techniques for integrated cross sections 234 5.4 Single ionization – results 239 5.5 Multiple ionization 248 5.6 Differential cross sections 252 5.7 Inner shell ionization 259
6 Positron annihilation 264 6.1 Introduction and theoretical considerations 264 6.2 Experimental details 274 6.3 Results – positron annihilation 281 6.4 Positron drift 301
7 Positronium and its interactions 307 7.1 Fundamental studies with the positronium atom 307 7.2 Theoretical aspects of annihilation and scattering in gases 326 7.3 Experimental studies of positronium annihilation in gases 336 7.4 Slowing down 342 7.5 Bound states involving positronium 348 7.6 Studies with positronium beams 353
8Exotic species involving positrons 362 8.1 The positronium negative ion 362 8.2 Systems containing more than one positron 368 8.3 Antihydrogen 372
Appendix: Positron conference proceedings 389 References 393 Index 449 Preface
This book is concerned mainly with the interactions of positrons and positronium with individual atoms and molecules in gases. Brief mention is also made of positrons interacting with bulk matter but this is in the context of describing the slowing down of positrons in solids and the subsequent ejection of low energy positrons and positronium from the surface of the solid. A technique using the angular correlation of annihi- lation radiation, which is widely used in studies of electron momentum distributions and defects in condensed matter, is also described but again the emphasis is mainly on positron annihilation in gases. Theoretical studies of positron collisions with atomic and molecular systems have been made for many years, as also have both theoretical and experimental studies of the lifetimes of positrons diffusing in gases. Only since the development of energy-tunable monoenergetic positron beams in the early 1970s, however, has it been possible to make detailed comparisons between theoretical predictions and the increasingly accurate experimental measurements of total, partial and differential scattering cross sections. These experimental developments have in turn stimulated renewed interest in theoretical studies of systems containing positrons. In this book we have attempted to integrate both theoretical and exper- imental aspects of the field into a reasonably coherent whole, although some sections are predominantly either experimental or theoretical. Positron physics has undergone very rapid development during the past several years. Accordingly, there has developed a need for a comprehen- sive up-to-date review of the field, which we hope this book will satisfy. No other extensive review of both experimental and theoretical aspects of the field has been published previously and therefore we believe it is timely to publish this book now. We are indebted to the following people for providing information and permitting us to reproduce figures from their published work: E.A.G.
ix x Preface
Armour, K.F. Canter, R.J. Drachman, D.W. Gidley, T.W. H¨ansch, Y.K. Ho, W.E. Kauppila, R.P. McEachran, A.P. Mills Jr, W. Raith, H. Schnei- der, D.M. Schrader, A.D. Stauffer, T.S. Stein, C.M. Surko and H.R.J. Walters. Thanks are also due to the publishers of the journals from which these figures have been taken, namely the American Physical Society, the American Institute of Physics, Baltzer Science Publishers, Elsevier, and the Institute of Physics. Particular thanks are due to several of our immediate colleagues: to Dr G. Laricchia and Dr P. Van Reeth for their assistance and numerous helpful discussions, to Dr A. Garner for producing many of the figures, and to Mr P.A. Donnelly for his assistance in preparing the bibliography. Above all, however, we wish to thank Mrs Carol Broad for so ably, and with such patience, preparing the final version of the typescript and dealing with numerous modifications to the text. Also, we are indebted to the staff of Cambridge University Press for the care with which the final stages of the book’s publication have been completed. The experimental positron physics group at University College London was initiated by Professor T.C. Griffith and Dr G.R. Heyland at the instigation of the late Sir Harrie Massey. We wish to record our gratitude to these three pioneers for their seminal contributions to positron collision physics and for introducing us to this fascinating subject.
M. Charlton J.W. Humberston 1 Introduction
1.1 Historical remarks The prediction, and subsequent discovery, of the existence of the positron, e+, constitutes one of the great successes of the theory of relativistic quantum mechanics and of twentieth century physics. When Dirac (1930) developed his theory of the electron, he realized that the negative energy solutions of the relativistically invariant wave equation, in which the total energy E of a particle with rest mass m is related to its linear momentum p by E2 = m2c4 + p2c2, (1.1) had real physical significance. He therefore postulated that the ‘sea’ of electron states with negative energies between −mc2 and −∞ was normally fully occupied in accordance with the Pauli exclusion principle, and would be unobservable. A vacancy in this ensemble, however, would manifest itself as a positively charged particle with a positive rest mass which, on the basis of uncalculated Coulomb energy corrections and the particles then known, Dirac assumed to be the proton. It was soon realized that this was not the case and that the theory actually predicted the existence of a new particle with the rest mass of the electron and an equal but opposite charge – the positron. The positron was subsequently discovered by Anderson (1933) in a cloud chamber study of cosmic radiation, and this was soon confirmed by Blackett and Occhialini (1933), who also observed the phenomenon of pair production. There followed some activity devoted to understanding the various annihilation modes available to a positron in the presence of elec- trons; radiationless, single-gamma-ray and the dominant two-gamma-ray processes were considered (see section 1.2). The theory of pair production was also developed at this time (see e.g. Heitler, 1954).
1 2 1 Introduction
In 1934 Mohoroviˇci´c proposed the existence of a bound state of a positron and an electron which, he (incorrectly) suggested, might be responsible for unexplained features in the spectra emitted by some stars. However, as summarized by Kragh (1990), Mohoroviˇci´c’s ideas on the properties of this new atom were somewhat unconventional, and the name ‘electrum’ which he gave to it did not become widespread but was later replaced by the present appellation, positronium (Ruark, 1945), with the chemical symbol Ps. Other significant developments took place in the 1940s. In 1949 DeBenedetti and coworkers discovered that the two gamma-rays emitted following positron annihilation in various solids deviated from precise collinearity, i.e. the angle between them was not exactly 180◦, as would be expected from the annihilation of an electron–positron pair at rest. Although this deviation amounted to only a few milliradians, it was correctly interpreted as being due mainly to the effect of the motion of the bound electrons in the material, the positron having essentially ther- malized. Somewhat earlier, DuMond, Lind and Watson (1949) had made an accurate measurement of the energy and width of the annihilation gamma-ray line using a crystal spectrometer. They found the width to be greater than that associated with the instrumental resolution, and they attributed this to Doppler broadening arising predominantly from electronic motion. These investigations laid the foundations for later advances in positron solid state physics, which were themselves to underpin the development of low energy positron beams. In 1946 Wheeler undertook a theoretical study of the stability of various systems of positrons and electrons, which he termed polyelectrons. He found, as expected, that positronium was bound, but that so too was its negative ion (e−e+e−). This entity, Ps−, was not observed until much later (Mills, 1981), after the development of positron beams. Positronium itself was eventually discovered in 1951 by Deutsch and its properties were investigated in an elegant series of experiments based around positron annihilation in gases. Many of the techniques developed then are still in use today. This advance stimulated further experimen- tal and theoretical studies of the basic properties of the ground state 3 of positronium (particularly the triplet 1 S1 state, ortho-positronium), including the hyperfine structure, the annihilation lifetime, elucidation of the selection rules governing annihilation and the calculation of the spectrum of photon energies emitted in the three-gamma-ray annihilation mode. Some of these topics are described in detail elsewhere in this book. The recent production of relativistic antihydrogen (Baur et al., 1996; Blanford et al., 1998), and the prospect of its formation at very low energies (see Chapter 8), when detailed spectroscopic and other studies of this system should become possible, makes it appropriate to mention the 1.2Basic properties of the positron and other positronic systems 3 antiproton. This particle, whose existence had been predicted by analogy with the positron, was discovered in 1955 by Chamberlain, Segr`e, Weigand and Ypsilantis using the 6.2 GeV Bevatron accelerator at the Lawrence Berkeley Laboratory, California, USA. For positron collision physics, a revolutionary advance came with the discovery and development of low energy positron beams. In a study of secondary electron emission by positrons, Cherry (1958) found that ‘positrons in the energy interval 0–5 eV, very numerous in comparison to those in equal intervals at somewhat higher energies, were emitted from a chromium-on-mica surface when it was irradiated by a 64Cu positron beta spectrum’. However, the efficiency of conversion from fast to slow positrons was only approximately 10−8. This work was, in fact, predated by that of Madansky and Rasetti (1950), who unsuccessfully searched for low energy positron emission from a variety of samples. These experi- ments were largely ignored until the late 1960s and the work of Groce et al. (1968). The decisive breakthrough in the development of positron beams prob- ably came with the work of Canter et al. (1972) who discovered the smoked MgO moderator. Although only a very small fraction, 3 × 10−5, of the incident β+ activity was converted into a usable low energy beam, this advance paved the way for the ensuing rapid progress. Later in the same decade, the phenomenon of positron emission and re-emission from various surfaces, carefully prepared under ultra-high vacuum conditions, was investigated, mainly by Mills and his coworkers (see e.g. Mills, 1983a), and a physical understanding was obtained of the processes involved. As this understanding grew, so too did the efficiency of moderation (as the conversion process from fast to slow positrons is known); this culminated in the solid neon moderator (Mills and Gullikson, 1986) and variants thereof, which have moderation efficiencies close to 10−2, fully six orders of magnitude greater than that in the seminal observation by Cherry (1958). The mechanisms involved in the emission and re-emission of positrons from surfaces, and the attendant formation of beams with well-defined energies, are central to the main theme of this book and are described in greater detail in section 1.4.
1.2 Basic properties of the positron and other positronic systems 1 Positrons The positron has an intrinsic spin of one half and is thus a fermion. According to the CPT theorem, which states that the fundamental laws 4 1 Introduction of physics are invariant under the combined actions of charge conjugation (C), parity (P) and time reversal (T), its mass, lifetime and gyromagnetic ratio are equal to those of the electron, and it has the same magnitude of electric charge, though of opposite sign. There are at present no known exceptions to the CPT theorem. Experimentally it has been shown from studies involving trapped par- ticles that the gyromagnetic ratios of the electron and the positron are equal to within 2 parts in 1012 (Van Dyck, Schwinberg and Dehmelt, 1987). The magnitudes of the charges of the electron and the positron have been found by Hughes and Deutch (1992) to be equal to 4 parts in 108 in an analysis of the measured charge-to-mass ratios and the values of the Rydberg constant derived from the energy spectra of hydrogen and positronium. A more stringent, though indirect, limit of 1 part in 1018 for the difference in charge magnitude was derived by M¨uller and Thoma (1992), in a method based on limits for the neutrality of atomic matter. They concluded that, because equal numbers of electrons and positrons contribute to the vacuum polarization of atoms, there would be an overall net charge on matter unless the charges of the two particles balanced precisely. Current theories of particle physics predict that, in a vacuum, the positron is a stable particle, and laboratory evidence in support of this comes from experiments in which a single positron has been trapped for periods of the order of three months (Van Dyck, Schwinberg and Dehmelt, 1987). If the CPT theorem is invoked then the intrinsic positron lifetime must be ≥ 4 × 1023 yr, the experimental limit on the stability of the electron (Aharonov et al., 1995). When a positron encounters normal matter it eventually annihilates with an electron after a lifetime which is inversely proportional to the local electron density. In condensed matter lifetimes are typically less than 500 ps, whilst in gases this figure can be considered as a lower limit, found either at very high gas densities or when the positron forms a bound state or long-lived resonance with an atom or molecule. Annihilation of a positron with an electron may proceed by a number of mechanisms, and the Feynman diagrams for the radiationless process, which results in electron emission, and for the single-, two- and three- gamma processes are given in Figure 1.1. The positron can also annihilate with an inner shell electron in a radiationless process, the consequent energy release giving rise to nuclear excitation (see Saigusa and Shimizu, 1994, for a summary). The most probable of these annihilation processes, when the positron and electron are in a singlet spin state, is the two- gamma process, the cross section for which was derived by Dirac (1930) to be 1.2Basic properties of the positron and other positronic systems 5
Fig. 1.1. Feynman diagrams of the lowest order contributions to (a) radiation- less, (b) one-gamma, (c) two-gamma, (d) three-gamma-ray annihilation. A2+ and A+ denote the charge states of the remnant atomic ion.