Relativistic electron scattering from freely movable proton/μ⁺ in the presence of strong laser field

We have investigated the electron scattering from the freely movable spin-1/2 particle in the presence of a linearly polarized laser field in the first Born approximation. The laser-dressed state of electrons is described by a time-dependent wave function which is derived from a perturbation treatment. With the aids of numerical simulations, we explore the dependencies of the differential cross section on the laser field intensity as well as the electron-impact energy. Due to the mobility of the target, the differential cross section of this process is smaller than that of Mott scattering.