Abstract
A tractable form of the fixed-scatterer approximation retaining up to double-scattering terms has been proposed. This formalism can be employed to investigate the elastic as well as inelastic processes at intermediate and high energies. The results for the differential cross section for the elastic scattering and for excitation of the $n=2$ states of H atom in ${e}^{\ensuremath{-}}$-H scattering are found to be very encouraging, computational labor involved for $s\ensuremath{-}s$ transitions being comparable to that of the first Born calculations.
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