Comparison of the optical potential method and the distorted wave born approximation method in electron – atom elastic scattering.
Kariuki, Peter Kinuthia
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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.