Electron--hydrogen-atom collisions in the presence of a laser field: Born-Oppenheimer approximation

The collision of an electron and a hydrogen atom in the presence of a laser field is studied within a previously proposed approximation (based on the space-translation approximation) for the bound states of the hydrogen atom. The Green's-function formalism is applied to derive an expression for the scattering amplitude associated to multiphoton processes. The Born-Oppenheimer approximation is obtained and numerical calculations are performed for the 1s → 2s inelastic excitation. It is shown as expected that exchange effects are important only for scattering processes involving low-energy electrons