The application of variational methods to atomic scattering problems - I. The elastic scattering of electrons by hydrogen atoms

Abstract

The variational methods proposed by Hulthen and by Kohn have been applied to the investigations of the elastic scattering of slow electrons by hydrogen atoms. Allowance has been made for both exchange and polarization effects in determining the zero-order phase shift. By comparison with results obtained by direct numerical integrations of the differential equations determining the scattering when the total wave function is assumed to have a separable form, it seems likely that both variational methods, which yield very nearly the same results, give satisfactory results except in certain sensitive cases, even when simple trial functions are employed. It is found that the inclusion of polarization (in the form of a non-separable wave function) is less important when exchange is included than when it is not. Reasons why this would be expected are given. Detailed results are obtained for electrons with energies up to 50 eV.