Free-Free Transitions in Intense High-Frequency Laser Fields

A nonperturbative theory is developed for free-free transitions of electrons colliding with atoms in intense high-frequency laser fields. The energy of the incoming electrons is assumed to be smaller than that of the photons. Rather simple expressions are derived for the multiphoton absorption amplitudes. Large deviations from the laser-free case are shown to appear in elastic scattering. The theory applies at already existing laser frequencies but extends beyond, to the extreme ultraviolet range.