Variational formulation and low-frequency approximation for Coulomb scattering in a laser field

Abstract

The theory of scattering of a charged particle in the presence of a laser field is formulated variationally. If the field is slowly varying, its dominant effect over a wide range of field intensities will be to modify the asymptotic motion of the projectile. A trial function is chosen which correctly accounts for the projectile-field interaction in asymptotic states. It leads to a variational approximation for the transition amplitude which generalizes earlier versions of the low-frequency approximation in two respects. Firstly, the field is not restricted to be of the form of a monochromatic plane wave but, more realistically, is taken to be a pulse of finite length. Secondly, the target may carry a net charge. The dependence of the transition amplitude on the variable ..delta..E, which represents the energy transferred to the field, is modified by the presence of the long-range Coulomb interaction; additional terms which depend logarithmically on ..delta..E are found. The variational expression for the transition amplitude consists of two factors, one depending only on the external field and the other representing the amplitude for single-photon spontaneous bremsstrahlung. The present analysis of this bremsstrahlung amplitude is based on the assumption that ..delta..E is sufficiently small so thatmore » the dominant contribution to the spatial integration comes from the asymptotic domain. The low-energy approximation obtained in this way provides a generalization of Low's theorem on spontaneous bremsstrahlung to include the effect of the Coulomb tail.« less