Laser-assisted relativistic ionization of the metastable atomic hydrogen H(2S) by electron impact in the coplanar binary geometry

In this paper, we present a detailed analytical computation of the triple differential cross section, in the first Born approximation, for the relativistic electron-impact ionization of the metastable atomic hydrogen H(2S) in the symmetric coplanar geometry and in the presence of a circularly polarized laser field. We introduce as a first step the Dirac–Volkov plane wave Born approximation 1 where we take into account only the relativistic dressing of the incident and scattered electrons. Then, we introduce the Dirac–Volkov plane wave Born approximation 2 where we take totally into account the relativistic dressing of the incident, scattered and ejected electrons. This paper is an extension of the previous one (Jakha et al. in Chin J Phys 77:1048, 2022), where we studied the same process in the absence of any external field. The combination of these two complementary works can provide a thorough and comprehensive study that can pave the way for any future experimental investigation.