Stimulation of two-photon annihilation of relativistic electrons and positrons

Relativistic electrons and positrons moving together opposite to a flux of soft photons can stimulate twophoton annihilation because of the Lorentzian frequency transformation of the soft photons. The product of such annihilation is hard gamma radiation concentrated in a narrow range of energies and solid angles. Formulas are given for the calculation of the principal parameters of this process and numerical estimates are obtained.