Generalized low-frequency approximation for scattering in a laser field

The time-independent approach to scattering in a laser field is used as the basis for a derivation of a low-frequency approximation, in which field-free scattering amplitudes enter into the determination of transition amplitudes in the presence of an intense radiation field. The scatterer is here represented by a local, short-range potential. For the case of a linearly polarized single-mode field, the result reproduces that obtained earlier by Kroll and Watson, who based their analysis on a semiclassical description. In the present derivation a plane-wave field of arbitrary polarization is treated; the field may consist of a superposition of low-frequency modes, the propagation direction being the same for each mode. In preparation for the derivation of the low-frequency approximation, a general analysis is given of the properties of the asymptotic states which describe the propagation of a charged particle in the field. This analysis should also be useful in other applications of the scattering formalism.