In the framework of the first Born approximation and using the Dirac–Volkov formalism, we investigate the relativistic model describing the laser assisted elastic differential cross sections (DCSs) for positron scattering by the hydrogen atom. Both the DCSs for electron and positron are notably modified by the circularly polarized laser field, particularly in the regime of high energies and medium intensities. Comparing the two numerical DCSs, we recover the well-known result that the elastic scattering differential cross sections with and without laser field for a hydrogen atom by electron and positron impact are the same (Greiner and Reinhardt. Quantum Electrodynamics, 2nd ed., Springer Verlag, New York, Berlin, Heidelberg. 1994). The numerical results reveal that the differential cross section for positron – hydrogen atom scattering is significantly reduced with the increase of the electric field strength.
Elliptically polarized laser assisted elastic electron-hydrogen atom collision and differential scattering cross-section