Relativistic calculations of inelastic collisions between electrons and atoms

The Feynman S-matrix formalism is used to consider the inelastic collisions of electrons with a hydrogen atom. The two leading Feynman diagrams are calculated, and the 1s-2s transition is treated in detail. Results are given for scattering amplitudes at energies of 1.0–8.0 (atomic units) and for various scattering angles, as well as the differential cross sections for direct scattering in the energy region 1.36–118.5 keV. On the basis of comparison with nonrelativistic calculations, we conclude that relativistic effects are appreciable and increase with energy. Total cross sections are calculated in both nonrelativistic and relativistic approximations. The difference between them increases with energy and is 15–20% for energies of 20–50 keV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 7–12, August, 1977.