Exact second-order distorted-wave calculation for hydrogen including second-order exchange

Over the years there have been many theoretical studies of the electron-hydrogen-atom scattering problem including some recent highly sophisticated works. While agreement between experiment and theory is satisfactory for low energies, experiment and theory are not in accord in the intermediate energy range. For the case of perturbation series calculations, the feasibility of distorted-wave calculations exact to second order has been demonstrated. Previous calculations have not included second-order exchange and in this paper it is shown that this effect is the primary cause for the disagreement between experiment and theory. When second-order exchange is included, reliable results for elastic scattering are obtained for incident electron energies of 30 eV and higher, and for 2s and 2p excitation reliable results for quantities depending on magnet sublevel differential cross sections are obtained for 50 eV and higher. The existing experimental data indicate that there is still a problem with the phases of the 2p amplitudes for scattering angles greater than 70' at 54 eV.