The paper deals with kinematic conditions for the inverse Compton scattering
of photons by relativistic electrons and the polarizations of the colliding
particles, which affect the value of the differential cross section of the
process. A significant influence of the electron and photon helicity on the
value of the cross section has been found. In the ultrarelativistic case, a
surprising effect of an almost twofold increase in the cross section of
scattering in the direction of the initial electron momentum has also been
discovered, when the initial photon momentum is transverse to that of the
initial electron.Comment: 11 pages, 6 figure