Coupled equations for medium-energy scattering. II. Electron and positron scattering from atomic hydrogen

The effective-channel approach to medium-energy scattering has been formulated previously by constructing a set of coupled equations for the elastic-scattering and average inelastic-scattering channels, with the evaluation of the average fluctuation potential and the average excitation energy to be carried out by a variational procedure. The formalism is applied here to the electron and positron scattering from atomic hydrogen in the energy range 50-500 eV. The various quantities which parametrize the effective channel are explicitly calculated. An approximate solution of the coupled equations is then obtained using a set of Green's functions in the semiclassical approximation. Contributions to the elasticscattering amplitude which arise from the static interaction and the coupling to the average inelastic-scattering channel are isolated for the purpose of ready comparison with previous calculations. The present calculation contains in effect no free adjustable parameters when the information from the total-cross-section data is incorporated into the theory through the use of the optical theorem.