Low-frequency expansions for laser-assisted collisions

A variational approach to the problem of scattering in a low-frequency laser field is adopted, with trial functions chosen to be of the type originally introduced by Kroll and Watson [Phys. Rev. A 8, 804 (1973)], who used them nonvariationally. The variational calculation leads to a low-frequency approximation that includes higher-order correction terms of a relatively simple form. This provides the basis for an analysis of the accuracy of the approximation as the strength of the external field varies over a wide range of values. The cross-section sum rule is shown, for the case of a linearly polarized monochromatic field of moderate intensity, to be more accurate than had previously been realized by virtue of the cancellation of higher-order correction terms in the transition amplitude. The approach is shown to be applicable to elastic and inelastic electron-atom scattering in a multimode laser field with arbitrary polarization properties; it represents a natural generalization of the standard Kohn-type variational procedure frequently employed for field-free scattering problems, reducing to it in the absence of the field. The dressing of the target by the field, an effect which is known to have a significant influence on the scattering cross section in certain circumstances, is not accounted for in the construction of the trial function, but is properly included as part of the variational correction.