Relativistic scattering in an external quasistatic electric field.

Abstract

The problem of the relativistic scattering of a charged particle in an external electric field is considered and an approximation is derived which represents the transition amplitude in terms of the on-shell field-free scattering amplitude. The field is assumed to be a slowly varying function of time, falling to zero in the remote past and distant future. It is also assumed that the field is weak enough, and the collision time short enough, that the energy of the particle is not appreciably affected by the field during the collision; in practice this represents a mild restriction on the applicability of the method. The derivation, in many respects similar to earlier treatments of scattering in a low-frequency external plane-wave field, makes use of Schwinger's proper-time representation of the external-field Green's function. In addition to the field-free amplitude the approximation requires as input the modified plane waves describing the motion of the charged particle in the field before and after the collision; these asymptotic states are shown to be adequately represented in the WKB approximation.