Relativistic signatures in laser-assisted scattering at high field intensities

The complete Dirac-Volkov relativistic treatment of the first Born limit of laser-assisted potential scattering of electrons within a circularly polarized laser field has been compared to the nonrelativistic Bunkin-Fedorov approach. The dependence of the quiver energy on the electron four-momentum in an ultrastrong laser field leads to different energy transfer cross sections depending on the scattering geometry with respect to the laser propagation direction. Visible differences between the relativistic and non-relativistic differential cross sections for small-angle scattering occur already for 10(16) W/cm(2)} intensity of near infrared wavelength and moderate electron initial energies.