Angular and polarization effects in relativistic potential scattering of electrons in a powerful laser field

In view of recent advances in the development of powerful laser sources ren ewed interest has been devoted to the investigation of electron-scattering processes in very strong laser fields. Here, we reconsider the scattering o f electrons by a potential in a strong electromagnetic plane wave. Since to a first order of approximation spin effects can be neglected, we describe the scattered electron by a laser-dressed Klein-Gordon particle. It is show n in a first-order Born approximation that at nearly relativistic scatterin g conditions, in which the space-dependence of the laser field cannot be ig nored, characteristic angular and polarization effects can be encountered f or specific scattering configurations that will not show up in the nonrelat ivistic case where the radiation field is treated in the dipole approximati on. We also demonstrate that even for laser-field intensities at which nonr elativistic calculations should apply one can observe discrepancies between relativistic and nonrelativistic results.