Journal article
Towards a direct numerical solution of Schrödinger's equation for (e, 2e) reactions
Australian Journal of Physics, Vol.52(3), pp.621-628
1999
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.
Details
- Title
- Towards a direct numerical solution of Schrödinger's equation for (e, 2e) reactions
- Authors/Creators
- S. Jones (Author/Creator)A.T. Stelbovics (Author/Creator)
- Publication Details
- Australian Journal of Physics, Vol.52(3), pp.621-628
- Publisher
- CSIRO Publishing
- Identifiers
- 991005543320607891
- Copyright
- © CSIRO 1999.
- Murdoch Affiliation
- School of Mathematical and Physical Sciences; Centre for Atomic, Molecular and Surface Physics
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
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- Citation topics
- 2 Chemistry
- 2.15 Physical Chemistry
- 2.15.664 Dissociative Electron Attachment
- Web Of Science research areas
- Physics, Multidisciplinary
- ESI research areas
- Physics