Perturbation Calculation of the Inelastic Scattering of Electrons by Hydrogen Atoms

A perturbation calculation has been made of the inelastic scattering of fast electrons by hydrogen atoms to the $2S$ and $2P$ states, using for the perturbation only the interaction between the incident electron and the bound electron. The results are then compared, to leading order terms in the energy, with calculations by the more customary perturbation scheme. For direct scattering, the results for forward scattering amplitudes are identical using either procedure. The angular distribution and energy dependence are different. For exchange scattering, the symmetric and asymmetric perturbations give different results both in the forward direction and at angles other than zero. However, in the former scheme exchange scattering is negligible compared to the direct scattering. The calculations for direct scattering are shown to be simplified by using a somewhat different perturbation scheme (method of altered states).