Elastic electron scattering by excited hydrogen atoms in a laser field

We consider electron scattering by hydrogen atoms in a linearly polarized laser field. The electrons may have sufficiently high energy in order that the scattering process can be treated in the first-order Born approximation. The scattered electrons, embedded in the laser field. are described by Gordon-Volkov waves. We assume that during the scattering, the hydrogen atoms are in an excited state (in particular, in the 2s, 2p, or 3s state) and that for moderate laser field intensities. it is sufficient to describe the interaction of the target atoms with the radiation field by first-order time-dependent perturbation theory. We discuss the angular dependence of the nonlinear differential scattering cross sections for low values N of emitted or absorbed laser photons, inspecting the contributions of the various electronic and atomic terms of the matrix elements. Detailed numerical results are presented for one-photon absorption at low-field intensities. We also compare our results with those obtained from the assumption of a static atomic polarizability. describing the laser dressing of the excited atomic states.