Nonlinear effects in the laser-assisted scattering of a positron by a muon

The scattering of a positron by a muon in the presence of a linearly polarized laser field is investigated in the first Born approximation. The theoretical results reveal: (1) At large scattering angle, an amount of multiphoton processes take place in the course of scattering. The photon emission processes predominate the photon absorption ones. (2) Some nonlinear phenomena about oscillations, dark angular windows, and asymmetry can be observed in angular distributions. We analyze the cause giving rise to dark windows and geometric asymmetry initially noted in the potential scattering. (3) We also analyze the total differential cross-section, the result shows that the larger the incident energy is, the smaller the total differential cross-section is. The reasons of these new results are analyzed.