The inelastic scattering of fast electrons by metastable hydrogen atoms in the presence of a linearly polarized laser field is theoretically studied in the domain of field intensities below 10^10 W/cm2. The interaction of the hydrogen atom with the laser field is described by first-order time-dependent perturbation theory, while the projectile electrons interacting with the laser field are described by the Gordon-Volkov wave functions. An analytic

In the case of circular polarized field and eliptic polarized field I have studied the dependence of differential cross sections by helicity of photons. For a superposition of a linearly and a circularly polarized laser beam we shall show that circular dichroism in the angular distribution can be predicted for the nonlinear two-photon transitions, if the dressing of the atomic target by the laser field is treated in second order of perturbation theory