Coherent phase control in electron scattering by hydrogen atoms in a bichromatic laser field

We consider electron scattering by hydrogen atoms in a bichromatic linearly polarized laser field of frequencies omega and 3 omega and we discuss the coherent control of the scattering process as a function of the relative ph ase phi between the two components of the radiation held. The electrons are assumed to have sufficiently high energies in order to permit the descript ion of the scattering process in the first-order Born approximation. The sc attered electrons, embedded in the bichromatic laser held of moderate power , as well as the laser dressing of the hydrogen atoms in their ground state are described by time-dependent perturbation theory. We discuss the angula r dependence of the nonlinear differential scattering cross sections for th e low values N = +/-2 of absorbed or emitted laser photons as a function of the relative phase phi between the two radiation field components. We also compare our results with those obtained from the assumption of a static po tential describing the target atom.