The Mott scattering in the presence of a linearly polarized laser field is investigated in the first Born approximation. The theoretical results indicate that at medium and large scattering angles, a large amount of multiphoton processes take place in the course of scattering. The photoabsorption ͑inverse bremsstrahlung͒ predominates the photoemission ͑bremsstrahlung͒. The sum rule for the multiphoton cross sections is notably violated. When the laser polarization deviates from the incident direction, the laser-modified ͑summed͒ cross section shows a considerable dependence on the azimuthal angle of the scattered electron. The dependencies of the cross section on the field strength, the frequency, the polarization direction, and the electron-impact energy are studied.

We study the ionization of a hydrogenic target by the impact of moderate energy electrons and in the presence of a laser field. This process, generally referred to as the laser-assisted (e, 2e), is treated non-relativistically as follows: we evaluate the S-matrix elements using Volkov and Coulomb-Volkov wavefunctions for describing respectively the continuum states of the scattered and the ejected electrons. The dressed state of the target is described by a time-dependent wavefunction derived from a perturbation treatment (of the laser field). With the aid of numerical results we explore the dependences of the fully differential cross sections on the laser field properties such as the strength, the frequency and the polarization direction, as well as on the continuum electron energies and their emission angles. Furthermore, we assess the interplay between the laser influence and the role of scattering from the residual ion by comparing the cross sections from (one-electron) ionic targets and varying the charge state of the residual ion.

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