Elastic and inelastic scattering of electrons and positrons by atomic hydrogen at intermediate and high energies in the unitarised eikonal-Born series method

The eikonal-Born series approximation is unitarised by using an improved Wallace-type amplitude to construct the direct scattering amplitude. The new unitarised eikonal-Born series (UEBS) direct amplitude obtained in this way is first tested successfully in potential scattering. It is then generalised to electron- and positron-atom collisions, and applied to elastic (1s-1s), 1s-2s and 1s-2p transitions in atomic hydrogen. The large momentum transfer properties of the UEBS direct amplitude are analysed for these three transitions, and the structure of the third term of the Born series is investigated by using the unitarity relations. Exchange effects are also discussed. The theoretical results are compared with those obtained from other theories and with recent measurements, for impact energies ranging from 54.4 to 400 eV.