Electron–H-atom collisions in the presence of a laser field: One-photon free-free transitions

Abstract

We report the derivation of an analytical expression of the one-photon transition amplitude for free-free transitions occurring in the course of the collision of fast electrons with a hydrogen atom, in the presence of a laser. The calculation is performed within the framework of the conventional time-dependent perturbation theory to lowest nonvanishing order. The projectile electron wave function is approximated as a plane wave and the infinite sums running over the H-atom spectrum are accounted for exactly by using a compact representation of the Coulomb Green’s function. As an illustration of the usefulness of our formalism, we discuss the occurrence of dips of two distinct origins in the cross sections and compare the respective importances of absorption and stimulated emission.