Mott scattering in strong laser fields revisited

In this work, we review and correct the first Born differential cross section for the process of Mott scattering of a Dirac–Volkov electron, namely, expression (26) derived by Szymanowski et al. (Phys. Rev. A, 56, 3846 (1997)). In particular, we disagree with the expression of (dσ/dΩ) that they obtained and we give the exact coefficients multiplying the various Bessel functions appearing in the scattering differential cross section. Comparison of our numerical calculations with those of Szymanowski et al. shows qualitative and quantitative differences when the incoming total electron energy and the electric-field strength are increased particularly in the direction of the laser propagation. Such corrections are very important since the relativistic electronic dressing of any Dirac–Volkov charged particle gives rise to these coefficients that multiply the various Bessel functions, and the relativistic study of other processes (such as excitation, ionization, etc….) depends strongly upon the correctness and reliability of the calculations for this process of Mott scattering in the presence of a laser field. Our work has been accepted, Attaourti and Manaut (Phys. Rev. A, 68, 067401 (2003)) but only as a comment. In this paper, we give full details of the calculations as well as a clear explanation of the large discrepancies that their results could cause when working in the ultra relativistic regime and using a very strong laser field corresponding to an electric field strength ε = 5.89 au.