A method for calculating the laser-assisted, electron-potential scattering differential cross section that is based on the Floquet-Lippmann-Schwinger equation is presented. The method is applied to the laser-assisted, low-energy electron-helium scattering in a ${\mathrm{CO}}_2$ laser field, in the static no-exchange approximation, for the scattering geometry in which the polarization vector of the laser field is parallel to the direction of the incident electron. We compare our results with the low-frequency approximation of Kroll and Watson [Phys. Rev. A 8, 804 (1973)] and find, overall, reasonable agreement. An alternative derivation of the Kroll and Watson low-frequency approximation, starting from the Floquet-Lippmann-Schwinger equation, is given in an appendix.

• Received 5 March 1999

DOI:https://doi.org/10.1103/PhysRevA.60.2255