Potential scattering of charged particles in the field of a low-frequency laser

Abstract

The problem of scattering of a charged particle (an electron) by a potential in the presence of single-mode classical electromagnetic field (a laser) in the dipole approximation is considered. No expansion in the strength of the field is made, but an expansion in the frequency of the field is carried out. This problem has been considered previously by Kroll and Watson, who showed that, if only the first two orders in $\omega$ are retained, then the scattering is describable by an on-shell $T$ matrix obtained in the absence of the field. They show this to be an essentially classical result. A different method is used to obtain their result and the next order in $\omega$ which yields the first off-shell correction is obtained. Far off-shell contributions are found in this order.