Second Born Calculations of(e-2e) Cross Sections at Low Energy Using a Pseudostate Set
Here we present a novel method for the calculation of cross sections for electron impact ionization of atomic targets. Calculations are carried out in coplanar geometries for incident energies lower than 54.4eV and a hydrogen target. Many theories have been proposed over the years to solve the atomic ionization problem, most of them employing variations of the Born series. Among the first Distorted-Wave Born Approximation (DWBA) calculations for ionization of atomic hydrogen are those of Madison et al.1 and Bransden et al.2 where post-collision interaction (PCI) between the scattered and ejected electrons was included only via shielding of the nucleus by the slower one. This approximation is valid when the energies of the outgoing electrons are very different. In fact, the major problem for the final state is how to take account of the Coulomb repulsion between a pair of final state free electrons. An attempt to solve this problem was made by Brauner, Briggs and Klar3 who proposed an approximation for the collision wavefunction appropriate to the final state of the system. This wavefunction satisfies the Schrödinger equation exactly in the asymptotic region but its use involves rather complicated and lengthy calculations. Some simplified treatments have been proposed. Dal Cappello and Joulakian4 retained only the angular dependent normalisation factor of the BBK ansatz. This approach is equivalent to the treatment of Whelan et al.5 where the dominant angular behaviour of the TDCS at low energies due to electron-electron interaction in final state is taken into account by the the Gamow factor N ee .
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