Electron scattering by atomic hydrogen: the distorted-wave second Born approximation

The distorted-wave second Born approximation (DWSBA) has been applied to the elastic scattering of electrons by ground-state atomic hydrogen and to the electron impact excitation of the 1s to 2s and 1s to 2p transitions in the energy range 30 to 680 eV. Differential and total cross sections are given as well as the polarisation fraction of the Lyman alpha radiation resulting from the radiative transition 2p to 1s. A new method of choosing the average energy in the closure approximation to the second Born amplitude is introduced for elastic scattering. The approximate methods of Dewangan and Walters (1977) and Winters (1979) for including distortion effects in the second Born term are investigated. It is found that both approximations are viable for elastic scattering at high enough energies but unreliable for inelastic scattering.