Abstract
A variation-iteration procedure is described for determining the amplitude for scattering in the presence of a laser field. The essential limitation of the method lies in the requirement that the interaction of the charged projectile with the external field be sufficiently weak, relative to its interaction with the target, to justify use of perturbation theory to account for the effect of the field in intermediate states of the collision process. This still allows for fields which are strong enough to significantly affect the motion of the projectile in initial and final states (leading, for example, to multiphoton transitions) and this strong interaction is treated nonperturbatively. The first two terms in the modified perturbation expansion are analyzed in detail. They are expressed in terms of those matrix elements which describe one- and two-photon free-free transitions in the absence of an external field. The method is not restricted to a consideration of fields of low frequency but the first-order amplitude obtained here does reduce, in that limit, to the known form of low-frequency approximation and the second-order amplitude provides a correction. The theory is described in the context of nonrelativistic potential scattering. A discussion is included of some of the special features of the second-order amplitude associated with potentials having a long-range Coulomb tail.