  Two-photon free-free transitions in elastic laser-assisted electron-hydrogen
collisions are studied in the domain of high scattering energies and low or
moderate field intensities, in the third order of perturbation theory, taking
into account all the involved Feynman diagrams. Based on the analytical
expressions of the transition amplitudes, the differential cross sections for
two-photon absorption/emission are computed at impact energy $E_i=100$ eV. The
effect of field polarizations on the angular distribution and on the frequency
dependence of the differential cross section is analyzed.
