Abstract
An overview of theoretical approaches to ionization of atomic systems by electron impact in the presence of laser radiation is given. Basic approximations for calculating multiphoton (e, 2e) transition amplitudes are discussed, with special emphasis on the first Born approximation in the projectile-target interaction. Various methods for the treatment of the dressing of initial and final (ionized) atomic-target states by a laser field are brought into focus, ranging respectively from the Floquet theory to the time-dependent perturbation theory and two-level approximation and from the Coulomb-Volkov models to the Sturmian-Floquet approach.
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