Application of a simplified second Born approximation to the scattering of electrons and protons by hydrogen atoms

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Abstract
A simplification of the second Born approximation, in which the terms arising from coupling to the lowest N levels are evaluated exactly and those arising from coupling to all the higher levels with principal quantum numbers n >or= N + 1 and to the continuum states are determined approximately by using the closure relation, is employed to investigate the elastic scattering of electrons by hydrogen atoms and the 1s -> 2s and 1s -> 2p excitations of atomic hydrogen by electron and proton impact. For the case of elastic scattering the inclusion of coupling to higher states increases the total cross section above the first Born approximation at all electron impact energies. However, for the 1s -> 2s and 1s -> 2p excitations the effect of coupling to states with principal quantum numbers n >or= 3 is opposite to that of coupling to the n = 2 level, and brings the total cross sections closer to the first Born approximation at the highest impact energies (greater,similar 100 ev for incident electrons).

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