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 renewed interest has been devoted to the investigation of electron-scattering processes in very strong laser fields. Here, we reconsider the scattering of 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 shown in a first-order Born approximation that at nearly relativistic scattering conditions, in which the space-dependence of the laser field cannot be ignored, characteristic angular and polarization effects can be encountered for specific scattering configurations that will not show up in the nonrelativistic case where the radiation field is treated in the dipole approximation. We also demonstrate that even for laser-field intensities at which nonrelativistic calculations should apply one can observe discrepancies between relativistic and nonrelativistic results.