Laser-assisted electron momentum spectroscopy

We consider theoretically ionization of an atomic target by fast electron impact at large energy and momentum transfer and in the presence of laser radiation. The laser electric-field amplitude is weak compared to the typical field in the target. Two frequency regimes are investigated according to whether the laser frequency is (i) much smaller than or (ii) resonant to the frequency of the transition from the ground to the first excited target state. Fast incident, scattered, and ejected electrons are described using Volkov solutions. The dressing of the bound-electron state by the laser field is accounted for within time-dependent perturbation theory in the case of the low-frequency regime and within the rotating wave approximation in the case of a resonant one. The interaction of the incident electron with the target is treated in the first Born approximation. For atomic hydrogen embedded in a linearly or circularly polarized laser field, we discuss how the polarization-vector orientation influences the momentum-dependent (e, 2e) differential cross sections assisted by exchange of few photons between the colliding system and the field. In addition, we inspect the dependence of the cross sections on the dressing of the hydrogen state.