Table Of Content(e, 2e) & related processes
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Series C: Mathematical and Physical Sciences - Vol. 414
(e, 2e) & related processes
edited by
Colm T. Whelan
Department of Applied Mathematics & Theoretical Physics,
University of Cambridge,
Cambridge, U.K.
H. R. J. Walters
Department of Applied Mathematics & Theoretical Physics,
Queen's University, Belfast, U.K.
A. Lahmam-Bennani
Laboratoire des Collisions Atomiques et Moleculaires,
Universite de Paris-Sud,
Orsay, France
and
H. Ehrhardt
Fachbereich Physik,
Universität Kaiserslautem,
Kaiserslautern, Germany
Springer Science+Business Media, B.V.
Proceedings of the NATO Advanced Research Workshop on
(e,2e) and related processes
Cambridge, England
September 28 - October 1,1992
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-4901-6 ISBN 978-94-011-2036-4 (eBook)
DOI 10.1007/978-94-011-2036-4
Printed on acid-free paper
All Rights Reserved
©1993 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1993
Softcover reprint of the hardcover 1st edition 1993
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical, including photo
copying, recording or by any information storage and retrieval system, without written
permission from the copyright owner.
TABLE OF CONTENTS
Preface
ix
Plenary Lectures
Colm T. Whelan, R.J. Allan, H.R.J. Walters and X. Zhang
(e,2e), effective charges, distorted waves and all that!
H.R.J. Walters, X. Zhang and Colm T. Whelan
Directions in (e,2e) and related processes 33
H. Ehrhardt and T. Rosel
Near theshold (e,2e) ionisation of helium and atomic hydrogen 75
Progress Reports
G. Stefani, M.V. Marabello, L. Avaldi and R. Camilloni
Does asymmetric (e,2e) approach the dipolar limit at intermediate energies? 83
John H. Moore, John A. Tossell, Michael A. Coplan, John W. Cooper and John P. Doering
Knockout reactions to study atomic and molecular electronic structure: the future 91
A. Pochat, R.J. Tweed, Colm T. Whelan, X. Zhang, H.R.J. Walters, R.J. Allan, F. GeJt\bart
and M. Cherid
Absolute experimental cross sections for symmetric coplanar (e,2e) collisions of 101
45 to 500eV electrons with helium
L. Spielberger, O. Jagutzki,R. Dorner, K. Froschauer, A. Gensmantel, H. Schmidt-Backing, J. Ullrich
and U. Buck
Recoil ion momentum spectroscopy: a complementary technique to (e,2e) and (e,3e) 119
J. Berakdar
Arbitrary charged particle-impact ionisation of H and He: 131
scaling properties of the cross sections
R.J. Tweed, S. Mazevet, o. Robaux and J. Langlois
Electron impact ionisation-excitation of helium: 145
calculations using coupled channel parametric potential wavefunctions
A.R.P. Rau
Democratic parameters for (e,2e) and (e,3e) kinematics 165
D.H. Madison, S. Jones, A. Franz and P.L. Altick
Asymptotically exact distorted wave calculations 171
vi
L. Frost
New experiments needed in (e,2e) 185
H. Klar
New trends: electron impact ionisation of laser excited atoms and 201
double ionisation by electron and photon impact
C. J. Joachain
Laser-assisted (e,2e) collisions 211
A. Franz and P.L. Altick
(e,2e) calculations using a correlated final state 223
Claudio Verdozzi
Solid state perspective in the theory of the Auger decay 237
R.J. Allan
High-performance computers in (e,2e) and (e,3e) interactions with atoms 259
R.E. Palmer
Energy loss and (e,2e) studies of molecules on surfaces 265
M. Gailitis
Influence of Coulomb forces on the angular momenta of products in three or 273
more fragmentary reactions
A.S. Kheifets
Multiconfiguration Hartree-Fock calculation of the autoionisation 281
resonance parameters in the (e,2e) reaction on helium atom
A. Huetz, P. Selles, D. Waymel, L. Andric and J. Mazeau
Near threshold (-y, 2e) experiments in the perpendicular plane 297
L. Avaldi, R.Camilloni, E. Fainelli, R. Multari and G. Stefani
Multicoincidence investigation of ionisation dynamics 307
A.J. Murray
Coupling the coplanar (e,2e) geometry to the perpendicular plane geometry 327
C. Dal Cappello and B. Joulakian
Double ionisation of noble gases by electron impact 341
J. Botero and J .H. Macek
Coulomb-Born approximation for the calculation of (e,2e) cross-sections 357
vii
The Hink Symposium
H. Ehrhardt
In Memorium Wolfgang Hink 381
A. Crowe and D.G. Mc Donald
Processes other than simple outer shell ionisation 383
B. Lohmann
Investigation of the angular dependence of 393
post collision interaction effects using coincidence techniques
C.D Schroter, H.-Th. Prinz, N.Keuler and W. Nakel
Relativitic (e,2e) processes under Bethe ridge conditions 403
x. Zhang, Colm T. Whelan and H.R.J. Walters
Distorted-wave calculations of triple differential cross section 409
for inner shell ionisation
Participants
423
Contributors
428
Index
435
Preface
An (e,2e) experiment is the measurement of an electron impact ionisation process
where both the exiting electrons are detected in coincidence. It is a measurement almost
at the limit of what is quantum mechanically knowable and its description presents a
substantial challenge to theory. There are at least two very good reasons for studying
(e,2e) and related processes: firstly we are only now beginning to understand the dynamics
of the collision process, the range and sophistication of the present experiments allow us to
identify kinematical regimes where delicate and subtle effects can be observed and where
present theories can be stretched to their limit; secondly the multiple coincident technique
offers the possibility of an analytic tool that could be used to probe the structure of the
target, be it atom, molecule, thin film or surface. These goals are not independent, of
course, since we cannot achieve our second objective unless we know enough about the
dynamics of the ionisation process to be able to correct for kinematical effects.
The last four years have seen great advances in the field, catalysed in part by support
from the European Community under the SCIENCE programme. At the present time the
range of new experiments and projects is exhilarating; measurements are now being per
formed at threshold on Hydrogen, on the inner shell levels of Gold and Silver by projectiles
with relativistic energies, with spin polarised electrons on Lithium, on a myriad of molecules
in symmetric non-coplanar kinematics and on Helium in a multitude of different geometries.
Recently the technique has been extended and the first excitation-ionisation, (e,3e), (,,2e)
experiments reported. Theory too has been active and much has been learned about the
complexities of the interactions between the particles before and after the ionising event
but much remains to be done.
In Cambridge in September 1992 the (e,2e) community had a Workshop and this vol
ume contains the invited papers that were presented. It was our good fortune that most of
the leaders in the field came, with a near equal mix of theoreticians and experimentalists.
As well as the large European contingent we were delighted to welcome speakers from Aus
tralia, Latvia and the United States. The meeting was organised into Plenary Lectures,
designed as review talks, and invited research contributions. A special symposium on inner
shell ionisation was held in tribute to the late Professor Wolfgang Hink of the University
of Wiirzburg who had made such important contributions to the field. With future devel
opments in mind we were pleased to have as speakers not only practitioners in the (e,2e)
field but also experts in surface physics and high performance computational techniques.
The workshop took place thanks to the munificence of NATO, and I would like to take
this opportunity to thank Dr Luigi Sertorio and his staff in Brussels for their courtesy and
the practical assistance which made this meeting possible. I am grateful to the organis
ing committee and to the members of the Applied Mathematics and Theoretical Physics
Department at Cambridge for giving so generously of their time and energy. It was a Work
shop characterised by both excellent contributions and an open friendly exchange of ideas.
I would like to thank all who came, for the quality of their Science and the pleasantness of
their company.
Colm T. Whelan
Magdalene College &
Department of Applied Mathematics & Theoretical Physics
University of Cambridge
IX
(e ,2e), effective charges, distorted waves and all that!
Colm T. Whelan ., R. J. Allan H. R. J. Walters X. Zhang
#, +, +
*
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver St,
CB3 YEW
# SERC Daresbury Laboratory, Warrington WA4 4AD ,UK
+Department of Applied Mathematics and Theoretical Physics, The Queen's University of Belfast,
BT7 lNN ,Northern Ireland
Abstract
An overview of the theory of (e,2e) processes is presented. Effective charges are introduced and
the Peterkop relation discussed. The distored wave Born approximation is considered and applied
to the calculation of triple differential cross-sections. A derivation of the distorted wave impulse
approximation is given and the difficulties encountered in the choice of off-shell Coulomb T-matrix
highlighted. It is shown that 3 body effects are significant in both the initial and final channels for
the ionisation of Heat energies of 50e V and below.
It is our belief that a short review of 'Memorable Results' in (e,2e) Physics would be a 'Good
Thing'.l In this paper we attempt to do just that.
Ionisation is a subtle and delicate process, and different dynamical effects will manifest themselves
depending on the geometry and the kinematics. An approximation which is good for one experimen
tal set up may be largely inappropriate for another. In this review we will consider the ionisation
of Hydrogen in coplanar asymmetric geometry where post collisional interactions (pci) between the
exiting electrons are significant. We will also consider the ionisation of the Noble gases in various
energy sharing geometries where multiple scattering processes are important and show that, for a
range of energies above threshold, that polarisation and pci interactions playa role in determining
the shape of the Triple Differential Cross Section(TDCS). We are concerned to present an account
of some of the basic theoretical approximations which have been employed in these geometries, in
such a way that their physical content, their strengths and weaknesses will be immediately obvious.
A major difficulty in all ionisation problems is the long range nature of the Coulomb forces. In the
first section we will consider the elegant technique of Rudge, Seaton and Peterkop where through the
use of momentum dependent effective charges, satisfying the Peterkop relation, an asymptotically
exact theory can be formulated. We will investigate to what extent it is possible to have a successful
effective charge description for the electron impact ionisation of Hydrogen in asymmetric geometry,
within the context of first order perturbation theory. For the same geometry we will consider
sophisticated approximations which do not obey the condition of asymptotic exactness but which
stress the importance of accurately describing the interaction of the ion and the two exiting electrons
within some finite region where they are assumed close together. We will show that there is no formal
difficulty in violating the Peterkop relation provided that we are willing to accept the validity
of a finite range theory. We will compare results in all these approximations with the absolute
experimental data of Ehrhardt and his colleagues and with the asymptotically exact approximation
of Brauner, Briggs and Klar.
The second section is devoted to a review of applications of the Distorted Wave Born approximation
(DWBA) to the description of (e,2e) processes in geometries where multiple scattering effects are
thought to be important. We remark that it gives good agreement with the shape of the measured
TDCS over a wide range of impact energies for energy sharing kinematics and works well for in-
c. T. Whelan et aL (eds.), (e, 2e) & related processes, 1-32.
e 1993 Kluwer Academic Publishers.
2
ner shell ionisation, however for impact energies below 100eY on Helium ,in coplanar symmetric
geometry, only poor accord with experiment is found.
In the third section we attempt to explain some outstanding puzzles in the theory of (e,2e) reactions.
We consider the strange fact that contrary to physical intuition ,for highly asymmetric geometries,
models where the fast outgoing electron is in no way screened by the slow, often give good agreement
with experiment. We show that this agreement is almost certainly fortuitous.
At 200 eY on Helium there is a sharp disagreement between the absolute experimental determina
tion of the TDCS made by the Brest group and earlier measurements by Yan Wingerden and his
collaborators. The former being supported by the DWBA while the later is in good accord with the
Distorted Wave Impulse approximation (DWIA) calculations. We reconsider the DWIA and remark
that there is an ambiguity inherent in the formulation as to which form of the off-shell Coulomb
T-matrix one should use and that for at least one choice the discrepancy with DWBA (and Brest)
disappears.
Finally we reconsider the failure of the DWBA approximation at low energies and demonstrate that
this is most likely due to the neglect of the influence of polarisation and pci effects. Atomic units
= = =
in which h/27r me e 1 are used throughout.
1.1 General Theory of Ionisation, effective charges
Suppose we have an electron with momentum ko, energy Eo which collides with a Hydrogen atom
in the ground state and that after the collision two electrons one fast with momentum kj ,energy
Ej, and one slow,k.,E. are detected.
The total energy and momentum are conserved:
k~ = k~ + k~ - 2€o + 2Erecoil, (1)
ko = kj + k. + krecoil, (2)
where €o is the energy of the ground state (-0.5 a.u. for Is) and krecoil , Erecoil are the momentum
and energy of the recoiling ion. We define the momentum transfer
=
K ko -kj. (3)
Because of the large mass difference between the proton and the electron we may neglect Erecoil in
(1). From (2) we have
=
krecoil K - k •. (4)
Therefore we see that for fixed K, Ilk. II we have maximal recoil of the nucleus when k. lies in the
-K direction and minimal when k. is parallel to K. The proton has on average a momentum of one
atomic unit prior to the collision 2, and therefore if the magnitude of krecoil is significantly greater
than unity then it must follow that the nucleus has experienced a force during the collision.
Because we include exchange in our formalism we have found it convenient to adopt the operationally
sound definitions of 'slow' and 'fast' detected electrons. We use this notation throughout this paper
i.e anything with the subscript's' applies to the slow electron ,anything subscripted 'f' applies to
the fast . It should be noted, however, that all our theoretical results are quite general and can be
equally well applied to symmetric as asymmetric geometries. We assume that before the collision
the system is in a state i and after is in a state j.
Let w+(rj, r.) be the desired solution of the Schrodinger equation, with outgoing wave boundary
conditions, appropriate to the initial state
(5)
where "'o(r.) is the Hydrogen atom ground state wave function.
