Relativistic electron scattering from a freely movable proton in a strong laser field

We study the electron scattering from the freely movable spin-$\frac{1}{2}$ proton in the presence of a linearly polarized laser field in the first Born approximation. The dressed state of the electron is described by a time-dependent wave function derived from a perturbation treatment (in a laser field). With the aid of numerical results we explore the dependencies of the differential cross section (DCS) on the electron-impact energy. Due to the mobility of the target, the DCS of this process is modified compared to the Mott scattering, especially in large scattering angles.