On the accuracy of soft-photon approximations for resonance free-free transitions

The connection between resonances occuring in the scattering of electrons on atoms (molecules) with or without the presence of a classical laser field is demonstrated for aN-state model-atom in 1st order perturbation theory with respect to the laser field. It is possible to predict the position, the shape and the background of resonances in the laser field from the sole knowledge of the corresponding scattering amplitudes without the laser field. At first, a soft-photon approximation for individual partial wave amplitudes is derived. This approximations is then tested numerically for a 2-state square well potential model. Details about the accuracy of the soft-photon approximation are obtained by comparing with the numerically exact results. Finally our findings are applied to give an interpretation of recent experimental data.