Comparative study of fast-electron-impact ionization of a hydrogen atom in circularly and linearly polarized laser fields

We consider ionization of the hydrogen atom by fast electron impact in the presence of a laser field with circular or linear polarization, in the first-order Born approximation in the scattering potential. We use a semiperturbative approach in which the interaction of the laser field with the incident and outgoing electrons is treated nonperturbatively by Gordon-Volkov wave functions, while the laser-atom interaction is treated in first-order perturbation theory. Analytical expressions, in a closed form, for the direct and exchange atomic transition amplitudes are employed. A simplified formula of the total laser-assisted triple-differential cross section (TDCS) is obtained at low values of the photon energy and small momentum of the residual ion. We study the role of laser field polarization and provide a comparative analysis of TDCSs for circularly and linearly polarized laser fields as a function of polar angles of the outgoing electrons at different photon energies. An asymmetric noncoplanar scattering geometry is examined, in which the polar and azimuthal angles of the scattered electron are fixed, while the ejected electron is detected at different angles. The numerical results for TDCSs by a circularly polarized laser field are compared to those derived by a linearly polarized laser field and notable differences are found in both magnitude and angular distributions of the TDCSs.