Qualitative and quantitative results of a relativistic calculation of
the S-matrix transition amplitudes and cross sections for Mott scatter
ing of initially polarized electrons in the presence of an ultraintens
e single-mode laser field are presented. Exact Dirac-Volkov wave funct
ions within a circularly polarized light field are used to describe th
e ''dressed'' electron and the collisional stage with the Coulomb pote
ntial is treated in the first-Born approximation. We discuss the influ
ence of the laser field on the degree of polarization of the scattered
electrons, depending on its intensity, and consider effects arising i
n different geometries in ultrastrong fields.