Low-frequency approach to multiphoton free-free transitions induced by realistic laser pulses

Multiphoton free-free transition amplitudes are derived from time-dependent perturbation theory for intense laser pulses of finite duration and slowly varying shape. The expressions obtained are general enough to exhibit effects caused by the off-shell behavior of the electron-atom (molecule) system without the laser field. A time-averaging procedure is derived by which the cross-section calculation for a laser pulse with a slowly varying shape is reduced to the knowledge of the single-mode constant-laser-intensity cross section. We find that recent experimental data can be explained qualitatively with the help of this averaging procedure.