Multiple-scattering expansion for (e,2e) collisions in the presence of a laser field

A multiple-scattering expansion is developed in this paper for the description of (e,2e) collisions in the presence of a laser field. The dressed states of the incident electron, the scattered electron, the ejected electron, and the target atom due to the laser field are considered and then the scattering matrix is expanded as a series of multiple-scattering terms based on the time-dependent multiple-scattering theory, such as ${\mathit{S}}_{\mathit{fi}}$=${\mathit{S}}_{\mathit{M}}^{\mathrm{}\left(1\right)\mathrm{}}$+${\mathit{S}}_{\mathit{M}}^{\mathrm{}\left(2\right)\mathrm{}}$+.... In the present approach, the effects of $S_M^{\mathrm{}\left(1\right)\mathrm{}}$ are almost equivalent to those of the first three orders of the Born expansion. Some aspects concerning the practical calculations of $S_M^{\mathrm{}\left(1\right)\mathrm{}}$ are also discussed at the end.