Radiative polarization of electrons in a strong laser wave

We reanalyze the problem of radiative polarization of electrons brought into collision with a circularly polarized strong plane wave. We present an independent analytical verification of formulas for the cross section given by Ivanov et al. [Eur. Phys. J. C 36, 127 (2004)]. By choosing the exact electron's helicity as the spin quantum number we show that the self-polarization effect exists only for the moderately relativistic electrons with energy gamma = E/mc(2) less than or similar to 10 and only for a non-head-on collision geometry. In these conditions polarization degree may achieve values up to 65%, but the effective polarization time is found to be larger than 1 s even for a high-power optical or infrared laser with intensity parameter xi = |E|mc(2)/E-c(h) over bar omega similar to 0.1 (E-c = m(2)c(3)/e (h) over bar). This makes such a polarization practically unrealizable. We also compare these results with the ones of some papers where the high degree of polarization was predicted for ultrarelativistic case. We argue that this apparent contradiction arises due to the different choice of the spin quantum numbers. In particular, the quantum numbers that provide the high degree of polarization represent neither helicity nor transverse polarization, which makes the use of them inconvenient in practice.