Table Of ContentAUTOIONIZATION
Recent Developments
and Applications
PHYSICS OF ATOMS AND MOLECULES
Series Editors
P. G. Burke, The Queen's University of Belfast, Northern Ireland
H. K1einpoppen, Atomic Physics Laboratory, University of Stirling, Scotland
Editorial Advisory Board
R. B. Bernstein (New York, U.S.A.) C. J. Joachain (Brussels, Belgium)
J. C. Cohen-Tannoudji (Paris, France) W. E. Lamb, Jr. (Tucson, U.S.A.)
B. W. Crompton (Canberra, Australia) P.-O. LOwdin (Gainesville, U.S.A.)
J. N. Dodd (Dunedin, New Zealand) H. O. Lutz (Bielefeld, Germany)
G. F. Drukarev (Leningrad, U.S.S.R.) M. R. C. McDowell (London, U.K.)
W. Hanle (Giessen, Germany) K. Takayanag! (Tokyo, Japan)
ATOM-MOLECULE COLLISION THEORY: A Guide for the Experimentalist
Edited by Richard B. Bernstein
ATOMIC INNER-SHELL PHYSICS
Edited by Bernd Crasemann
ATOMS IN ASTROPHYSICS
Edited by P. G. Burke, W. B. Eissner, D. G. Hummer, and I. C. Percival
AUTOIONIZATION: Recent Developments and Applications
Edited by Aaron Temkin
COHERENCE AND CORRELATION IN ATOMIC COLLISIONS
Edited b~ H. K1einpoppen and J. F. Williams
DENSITY MATRIX THEORY AND APPLICATIONS
Karl Blum
ELECTRON AND PHOTON INTERACTIONS WITH ATOMS
Edited by H. K1einpoppen and M. R. C. McDowell
ELECTRON-ATOM AND ELECTRON-MOLECULE COLLISIONS
Edited by Juergen Hinze
ELECTRON-MOLECULE COLLISIONS
Edited by Isao Shimamura and Kazuo Takayanagi
INNER-SHELL AND X-RAY PHYSICS OF ATOMS AND SOLIDS
Edited by Derek J. Fabian, Hans K1einpoppen, and Lewis M. Watson
INTRODUCTION TO THE THEORY OF LASER-ATOM INTERACTIONS
Marvin H. Mittleman
ISOTOPE SHIFTS IN ATOMIC SPECTRA
W. H. King
PROGRESS IN ATOMIC SPECTROSCOPY, Parts A, B, and C
Edited by W. Hanle, H. K1einpoppen, and H. J. Beyer
VARIATIONAL METHODS IN ELECTRON-ATOM SCATTERING THEORY
R. K. Nesbet
A Continuation Order Plan is available for this series. A continuation order will bring
delivery of each new volume immediately upon publication. Volumes are billed only
upon actual shipment. For .further information please contact the publisher.
AUTOIONIZATION
Recent Developments
and Applications
Edited by
Aaron Temkin
Laboratory for Astronomy and Solar Physics
National Aeronautics and Space Administration
Goddard Space Flight Center
Greenbelt, Maryland
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Main entry under title:
Autoionization: recent developments and applications.
(Physics of atoms and molecules)
Includes bibliographies and index.
1. Auger effect. I. Temkin, Aaron. II. Series.
QC793.5.E627A96 1985 539.7'2112 85-6334
ISBN- 13: 978-1-4684-4879-5 e-ISBN- 13: 978-1-4684-4877-1
DOl: 10.1007/978-1-4684-4877-1
© 1985 Plenum Press, New York
Softcover reprint of the hardcover 1s t edition 1985
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
CONTRIBUTORS
A. K. BHATIA
Atomic Physics Office
Laboratory for Astrophysical and Solar Physics
Goddard Space Flight Center
National Aeronautics and Space Administration
Greenbelt. M D
KWONG T. CHUNG
Department of Physics
North Carolina State University
Raleigh. NC
BRIAN F. DAVIS
Department of Physics
North Carolina State University
Raleigh. NC
GEORGE A. DoSCHEK
Eo 00 Hurlburt Center for Space Research
Naval Research Laboratory
Washington. DoC.
B. R. JUNKER
Office of Naval Research
Arlington. VA
C. WILLIAM MCCURDY
Department of Chemistry
Ohio State University
Columbus. OH
A. TEMKIN
Atomic Physics Office
Laboratory for Astronomy and Solar Physics
Goddard Space Flight Center
National Aeronautics and Space Administration
Greenbelt. MD
v
PREFACE
About five years ago, Professor P. G. Burke asked me to edit a sequel to an
earlier book-Autoionization: Theoretical, Astrophysical, and Laboratory
Experimental Aspects, edited by A. Temkin, Mono Book Corp., Baltimore,
1966. Because so much time had gone by and so much work had been done, the
prospect of updating the 1966 volume seemed out of the question.
In 1965 the phenomenon of autoionization, although long known, was
just starting to emerge from a comparatively intuitive stage of understanding.
Three major developments characterized that development: In solar
(astro-)physics, Alan Burgess (1960) had provided the resolution of the
discrepancy of the temperature of the solar corona as observed versus that
deduced from ionization balance calculations, by including the process of
dielectronic recombination in the calculation; Madden and Codling (1963)
had just performed their classic experiment revealing spectroscopically sharp
lines in the midst of the photoionization continuum of the noble gases; and
Feshbach (1962) had developed a theory with the explicit introduction of
projection operators, which for the first time put the calculation of auto-
ionization states on a firm theoretical footing. There were important
additional contributions made at that time as well; nevertheless, without
going into further detail, we were able to include in our 1966 volume, in
spite of its modest size, a not too incomplete survey of the important
developments at that time.
To do the equivalent now would be virtually impossible. In considering
the alternatives, I felt that laboratory experimental developments in particular
have far outstripped what can reasonably be included in the confines of
a single book. Therefore, I have omitted them completely. The situation with
regard to solar and astrophysical applications at first seemed also too vast for
inclusion. However, the unlikely has become fact by virtue of a magnificent
effort by Dr. George Doschek. His chapter, "Diagnostics of Solar and
Astrophysical Plasmas Dependent on Autoionization Phenomena," is, in my
opinion, a masterful exposition and summary of diagnostic analysis and
applications of autoionization in almost the entire realm of space physics. It is
necessarily a large part of this book. I hope the reader will find it enlightening
and useful. It will surely have a vital place in the space physics literature.
The remaining chapters I have chosen to include are devoted to theory
and calculation. Even here a severe limitation was required, but in the belief
that good theory allows good calculations, and the value of calculations cannot
exceed the quality of their theoretical underpinnings, we could be selective.
vii
Vlll PREFACE
In the category oftheory-calculation we could certainly have included an
overview of methods and programs, developing mainly from the close-
coupling formalism, that dealt directly with electron scattering including
resonances. Fortunately, there have been a number of recent reviews, so we
have not felt it mandatory to include such a review here. Too recent to be
included here and in a somewhat different category are successful develop-
ments, primarily calculational in nature, including resonances in many-body
diagrammatic and random phase approximation (RPA) techniques. In
contrast, there has been very little written of a review nature on the calculation
of electron-atom (atomic ion) resonances within the context of the Feshbach
theory. Since that theory has long provided the theoretical basis for much of
the work of the Goddard group, I believe the present volume is a very
appropriate place to present such a review. In our first article, Dr. Bhatia and I
have attempted to review, from a more pedagogical point of view rather than
from one of completeness, our work on two-electron systems (one-electron
targets) for which theory allows explicit and rigorous projection operators to
be given. We have included, however, a more detailed exposition of a recent
calculation ofthe line-shape parameter, because that requires a rather different
approach to a part of the Feshbach theory known as the nonresonant
continuum. I believe the idea of a more generally defined nonresonant
continuum may be of value in other contexts as well.
In a second article, Dr. Bhatia and I have undertaken the process of
implementing the Feshbach approach to more than two-electron systems. As a
prerequisite for actually doing calculations, we have found it necessary to
precisely define the projection operators (P and Q) in complete and explicit
terms. We have chosen to include a part of that analysis here because it also
serves the pedagogical aims we have also attempted to fulfill. In the second
part ofthat chapter we have discussed approximations ofthese operators that
we have called quasi-projection operators (I' and ~). Historically our
introduction of these quasi-projection operators preceded our recent develop-
ment of the projection operators themselves. Notwithstanding, quasi-
projections allow for meaningful calculations to be done, and we have briefly
reviewed some of them.
The fact that one can calculate with projectors without them being
idempotent (the latter property usually being implicit in the definition of the
name "projection operator") is not confined to the specific quasi-projection
operators we have introduced. In the third chapter of this book Drs. K. T.
Chung and Brian K. Davis describe a hole-projection formalism wherein
electrons in inner orbitals are projected out of an otherwise general ansatz for
the wave function of the total system by a projection-type operator, which can
certainly be considered in the category of quasi projectors. Their theory relies
on a mini-max theorem which (although rigorously proved only in a one-
PREFACE IX
electron context) states that the physically meaningful state is realized when
the energy is minimized with respect to the parameters of the complete wave
function, but at the same time the energy is maximized with respect to the
parameters describing the excluded orbitals (the holes). It is clear that the
formalism should be particularly effective in calculating inner-shell vacancies
of many-electron systems; however, even for 3-electron systems, to which the
calculations have thus far been confined, as the article will show, the results are
very impressive. In their summation the authors refer to a recent paper
wherein they have combined their hole-projection method with elements of
complex rotation to calculate widths. I expect that augmentation to become
an important addition to the methodology.
Complex rotation is the subject of the last set of articles in this volume.
The basic idea can be expressed in many ways, but for the purposes of this
Preface one way is to notice that a stationary (i.e., bound)-state wave function
has the time dependence exp ( - iEt/h), where E is a real number. Therefore, if a
state is decaying, it should be describable by a complex time dependence
W = E - ir/2; then its imaginary part will automatically describe the decay
width (the inverse of the decay time) of the resonance. From the calculational
point of view this has the implication that certain states, which are not
quadratically integrable on the real axis, do become integrable off the real axis.
This (measure zero) set of discrete states are uncovered-according to a basic
theorem of Balslev and Combes-if the electronic coordinates are rotated in
the complex plane beyond a minimum amount which, not surprisingly, is
related to the width of the resonance. From the calculational point of view,
however, this is a most important fact, because it removes boundary
conditions from the problem. Thus, it implies that one can, in principle,
calculate a many-electron resonant state without knowing the wave function
of the target system. This, in turn (and again, in principle), overcomes a major
shortcoming of the projection-operator approach, wherein although the
eigenfunctions of QHQ are discrete and exist on the real axis, the projection
operator Q does depend on the eigenfunctions of the target system and
therefore must be approximated for more than one-electron target systems. In
addition, both shape and Feshbach resonances can emerge from the complex
rotation approach.
Briefly stated, Dr. B. R. Junker concentrates on applications to atoms
and ions, whereas Dr. C. M. McCurdy deals with molecular systems; both
authors have made a concerted effort to coordinate their respective treat-
ments. An important element of the approach of these two articles is the idea
that it is preferable to retain the Hamiltonian in its real form and put the
complex nature of the calculation completely in the ansatz for the wave
function. How best to do this is not yet completely settled, but I believe these
treatments go a long way in elucidating the technique. For simpler systems
x PREFACE
(e.g., He -) the results are probably the most reliably accurate of any thus far
obtained. We are pleased to have these two contributions from two expert
practitioners whose interests are calculational as well as theoretical.
I would like to thank all the authors for their contributions, and Professors
P. G. Burke and H. Kleinpoppen for their encouragement. I am as usual
indebted to Dr. A. K. Bhatia, in this case for his additional help in preparing
the index.
Silver Spring. Maryland AARON TEMKIN
