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A formal method is presented to evaluate the second-order Born approximation of the laser-assisted potential scattering. It is an implicit closure technique that includes intermediate virtual-state transitions and enables one to find the exact explicit expression of the transition amplitude. This is of interest from two standpoints: first, one can deal with ranges of parameters in which the first-order Born approximation is a poor one; second, one can set limits of on-shell approximations that are also widely used to analyze recent laser-assisted experiments. The off-shell character yields new terms in the exact amplitude, and in particular, it is shown to play a crucial role in forward scattering from a long-range potential.

Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.