Nedoreshta V. Interaction of the electrons with the muons in the light field

The general relativistic theory of resonant and nonresonant scattering of an electron by a muon in the field of elliptically polarised light wave was developed. The conditions, under which the cross-section of resonant scattering of an electron by a muon in the light wave field exceeds the corresponding one in the the external field absence with respect to five orders of magnitude are derived. In fact the external light field essentially reduced the scattering cross-section rate if the velocity of particles oscillation in the wave field is on order of magnitude grater than or equal to the translational motion velocity of the particles. The analytical expression for the nonresonant cross-section of the muon pair production in the electron-positron annihilation in the moderately strong elliptically polarised wave was derived. It is factorable on the corresponding one in the external field absence and the probability of laser wave photons emission (absorption).