Off-shell effects in laser-assisted electron scattering at low frequency

Differential cross sections for the scattering of electrons by a short-range potential in the presence of an intense, linearly polarized, low-frequency field are obtained in three different ways: within the Kroll-Watson approximation, within the impulse approximation and through an exact Floquet calculation. Examples are given where the cross section for small-angle scattering with emission or absorption of photons is larger by several orders of magnitude than predicted by the Kroll-Watson approximation. The enhancement can be ascribed to off-shell contribution's and is correctly reproduced by the impulse approximation. However, no such enhancement is found in model calculations for helium. The accuracy of the impulse approximation in the vicinity of a resonance is also studied.