Electron (positron) beam polarization by Compton scattering on circularly polarized laser photons

In a number of papers an attractive method of laser polarization of electrons (positrons) at storage rings or linear colliders has been proposed. We show that these suggestions are incorrect and based on errors in the simulation of multiple Compton scattering and in the calculation of the Compton spin-flip cross sections. We argue that the equilibrium polarization in this method is zero.