  The Kapitza-Dirac effect, which refers to electron scattering at standing
light waves, is studied in the Bragg regime with counterpropagating
elliptically polarized electromagnetic waves with the same intensity,
wavelength, and degree of polarization for two different setups. In the first
setup, where the electric-field components of the counterpropagating waves have
the same sense of rotation, we find distinct spin effects. The spins of the
scattered electrons and of the nonscattered electrons, respectively, precess
with a frequency that is of the order of the Bragg-reflection Rabi frequency.
When the electric-field components of the counterpropagating waves have an
opposite sense of rotation, which is the second considered setup, the standing
wave has linear polarization, and no spin effects can be observed. Our results
are based on numerical solutions of the time-dependent Dirac equation and the
analytical solution of a relativistic Pauli equation, which accounts for the
leading relativistic effects.
