The eikonal distorted wave Born approximation for the excitation of hydrogen by impact with hydrogen and helium in the intermediate energy range

An eikonal approximation is applied to atom-atom scattering in the intermediate energy range. The theory and the form of the eikonal approximation are reviewed. Also a brief survey of previous theoretical methods for all energy ranges is included. In particular, the differential and total cross sections for the excitation of hydrogen to the 2s and 2p states by impact on hydrogen and helium atoms have been calculated using the eikonal distorted wave Born approximation (DWBA) for the incident energy range of 2.25-100 keV. The eikonal DWBA differential cross sections are compared to the differential cross sections given by the first Born approximation. The eikonal DWBA results predict a lower cross section for smaller angles and a much slower fall off with larger angles than the first Born approximation. For H-He scattering at 10 keV, the eikonal DWBA differential cross section is compared to experimental data. It was found to agree quite well in shape and slope but differed in magnitude by a factor of four. The eikonal DWBA total cross sections were compared to other theoretical calculations and were found to follow closely to the multistate impact parameter calculations. In the limit of high energies and very small angle scattering, the results for the eikonal DWBA total cross section were shown to reduce to the 2-state distortion approximation. Also for H-He scattering, a comparison of total cross sections is made between the eikonal DWBA results and experimental data. Agreement is found to be poor at the lower energies where the eikonal DWBA results are not expected to be valid and good at the higher energies --Abstract, pages ii-iii