Potential scattering in a slowly varying laser field: relativistic generalizations

Abstract

A variational approach to the problem of relativistic potential scattering in a laser field is developed. The field is assumed to be slowly varying compared with the collision time and to have a well defined direction of propagation, but is otherwise arbitrary. A trial function is chosen having the correct gauge-transformation property and accounting in an approximate manner for the simultaneous interaction of the projectile with the centre of force and with the laser field. The variational calculation provides a low-frequency approximation for the transition amplitude of improved accuracy compared with those obtained in previous treatments of this problem. The analysis is first given in terms of a spin-zero wave equation and then extended to allow for the scattering of a Dirac particle. A relativistic analogue of the Kroll-Watson approximation (1973) is obtained when the field is taken to be monochromatic and certain higher-order correction terms are dropped.