We consider electron-atom scattering in a circularly polarized laser field at sufficiently high electron energies, permitting to describe the scattering process by the first order Born approximation. Assuming the radiation field has sufficiently moderate intensities, the laser-dressing of the hydrogen target atom in its ground state will be treated in second order perturbation theory. Within this approximation scheme, it is shown that the nonlinear differential cross sections of free-free transitions do neither depend on the {\it dynamical phase} $\phi$ of the radiative process nor on the {\it helicity} of the circularly polarized laser light. Relations to the corresponding results for linear laser polarization are established

We consider high-energy electron scattering by hydrogen atoms in the presence of a laser field of moderate power and higher frequencies. If the field is a superposition of a linearly and a circularly polarized laser beam in a particular configuration, then we can show that circular dichroism in two-photon transitions can be observed not only for the differential but also for the integrated cross sections, provided the laser dressing of the atomic target is treated in second-order perturbation theory and the coupling between hydrogenic bound and continuum states is involved.

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We consider electron scattering by hydrogen atoms in a bichromatic linearly polarized laser field of frequencies ω and 3ω and we discuss the coherent control of the scattering process as a function of the relative phase ϕ between the two components of the radiation field. The electrons are assumed to have sufficiently high energies in order to permit the description of the scattering process in the first-order Born approximation. The scattered electrons, embedded in the bichromatic laser field 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 angular dependence of the nonlinear differential scattering cross sections for the low values N = ±2 of absorbed or emitted laser photons as a function of the relative phase ϕ between the two radiation field components. We also compare our results with those obtained from the assumption of a static potential describing the target atom.

Abstract. The effect of the relative phase between the components of a bichromatic field of frequencies ω and 3ω is discussed in the case of free-free transitions in laser-assisted electronhydrogen scattering. For fast projectile and low field intensities, the role of target dressing is pointed out.