Infrared radiation in electron-atom scattering

Abstract

The theory of electron-atom scattering in a radiation field, either spontaneously produced or external, is formulated in such a way that the effectively strong interaction of the electron with soft photons (those with frequencies lying below some cutoff ..omega../sub s/) is properly accounted for at the outset. Effects of the residual interaction can then be included using standard perturbation theory. This approach follows that taken some years ago by Bloch and Nordsieck in their fundamental treatment of infrared radiation in potential scattering. The fact that the target is taken here to be a compound system which itself interacts with the field introduces additional complications. A gauge transformation is introduced which helps considerably in the analysis of these multiparticle effects. Particularly simple results are obtained by treating both the cutoff frequency ..omega../sub s/ and the residual interaction strength as quantities of first order and neglecting second-order corrections. The cross section obtained in this way, when summed over all final states containing soft photons, is expressed in terms of the cross section for scattering in the absence of any interaction with the field. The first-order correction term, not present in the earlier Bloch-Nordsieck version, can be interpreted in terms of the classicalmore » bremsstrahlung radiation emitted as the result of an instantaneous collision. The low-frequency approximation for the scattering amplitude derived here contains as a limiting case the result obtained by Low and others for single-photon bremsstrahlung. It also reduces in the appropriate limit to the recently derived approximation for electron-atom scattering in a low-frequency laser field.« less