Off-shell low-frequency approximation for potential scattering in a strong laser field: eikonal versus [1, 1] Pade approximation

Analytical and numerical results for the T-matrix and the total cross section for scattering by a Yukawa potential in a strong low-frequency laser field are presented. They are based on our recently derived off;shell low-frequency approximation. The conditions under which the results by Daniele and co-workers can be applied are analysed. Expressions for the T-matrix and for the total cross section for scattering in a laser field in the eikonal approximation are derived. The total cross section is presented in the form of an eikonal multiple scattering series as a product of two factors. One of these factors only depends on the type of the scattering potential, while the other depends on the parameters of the scattered particle and the laser field. The results obtained are in good agreement with our earlier findings derived by using the [1, 1] Fade approximation.