Abstract
The paper considers some kinematic conditions for the inverse Compton scattering of photons by relativistic electrons and the polarizations of 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 was 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 was also discovered, when the initial photon momentum is perpendicular to that of the initial electron.
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