Comparison of the optical potential method and the distorted wave born approximation method in electron – atom elastic scattering.
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Date
2015-11
Authors
Kariuki, Peter Kinuthia
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
The optical potential (OP) method has been widely used in electron-atom elastic
scattering since for a given distorting potential, a solution valid to all orders of
perturbation series can be obtained. The first-order distorted-wave Born approximation
(DWBA) is only valid to first order. However by use of a distorting potential that
accurately models the electron-atom interaction, the DWBA method can yield quite
reliable results for elastic scattering and possibly for inelastic scattering as well. In this
study, elastic differential cross sections (DCS) and integral cross sections (ICS) have
been calculated using the OP method and the DWBA method for the alkali atoms sodium
and potassium at intermediate electron-impact energies E 7 200eV . In both methods,
and for both atoms, distorting potentials in the form of the sum of the static potential, the
local Furness-McCarthy exchange potential, a non-local polarization potential involving
discrete excited states of the atoms, and a local absorption potential, have been used. For
the sodium atom the 3p, 3d, 4s, and 4p, excited states were used in the polarization
potential, while for the potassium atom 4p, 5p, 3d, and 5s, excited states were used.
Exchange effects have also been incorporated in the distorted-wave Born approximation
method through the exchange T-Matrix element. In doing so, the frozen-core
approximation has been applied which allows for exchange between the incident electron
and the valence atomic electron, as well as the core electrons. For both sodium and
potassium the present differential cross sections in the OP and DWBA calculations are in
very good agreement with various experimental DCS at small scattering angles at all
electron-impact energies considered. This indicates that the optical potential used
describes adequately polarization effects which influence small-angle scattering. It is
found that the difference between the DWBA and OP methods increases with decrease in
electron-impact energy. This difference is as a result of the exchange T-matrix element in
the DWBA calculations. The difference between the two methods decreases as the
distorting potential becomes more accurate (complete) as the DWBA calculations
converge to the OP results. Comparison with available experimental and theoretical
results shows the need to use a complex distorting potential to account for loss of flux
into inelastic channels.
Description
A Thesis is Submitted in Partial Fulfillment of the Requirements for the
Award of the Degree of Doctor of Philosophy in the School of Pure and
Applied Sciences of Kenyatta University