Author:
Jones S.,Stelbovics A. T.
Abstract
The finite-difference method for electron{hydrogen scattering is
presented in a simple, easily understood form for a model collision problem in
which all angular momentum is neglected. The model Schrödinger equation
is integrated outwards from the atomic centre on a grid of fixed spacing
h. The number of difference equations is reduced each
step outwards using an algorithm due to Poet, resulting in a propagating
solution of the partial-differential equation. By imposing correct asymptotic
boundary conditions on this general, propagating solution, the particular
solution that physically corresponds to scattering is obtained along with the
scattering amplitudes. Previous works using finite differences (and finite
elements) have extracted scattering amplitudes only for low-level transitions
(elastic scattering and n = 2 excitation). If we
are to eventually extract ionisation amplitudes, however, the numerical method
must remain stable for higher-level transitions. Here we report converged
cross sections for transitions up to n = 8, as a
first step towards obtaining ionisation (e;
2e) results.
Subject
General Physics and Astronomy
Cited by
5 articles.
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