Laser-modified electron scattering from a slowly ionising atom

When an electron scatters from an atom in the presence of a laser field which is resonant with an atomic transition, off-shell effects enter into the cross section. These only become significant at higher laser intensities where the atom may also be ionised by the laser. Cross-sections are obtained for electron-atom scattering in which these off-shell effects appear and in which the slow ionisation of the atom by the laser is included. Experiments are suggested in which simplifications can occur and which still retain these 'exotic' effects.