Relativistic effects in potential scattering of electrons in an ultrastrong laser field

The T matrix is derived for the potential scattering of electrons in an elliptically polarized ultra- strong laser pulse. Special attention has been paid to the scattering of electrons that are initially nonrelativistic, but, due to the effects of the strong laser pulse, the full relativistic treatment has been applied. Possible energy ranges of the scattered electrons are discussed versus the laser field intensity. The detailed expressions in the first Born approximation are derived for linearly and circularly polarized laser fields. Numerical results for the angular distributions and energy spectra of the scattered electrons on the Yukawa-type potential in circularly polarized laser fields are presented.