  The effect of the electron's anomalous magnetic moment on the relativistic
electronic dressing for the process of electron-hydrogen atom elastic
collisions is investigated. We consider a laser field with circular
polarization and various electric field strengths. The Dirac-Volkov states
taking into account this anomaly are used to describe the process in the first
order of perturbation theory. The correlation between the terms coming from
this anomaly and the electric field strength gives rise to new results, namely
the strong dependence of the spinor part of the differential cross section
(DCS) with respect to these terms. A detailed study has been devoted to the non
relativistic regime as well as the moderate relativistic regime. Some aspects
of this dependence as well as the dynamical behavior of the DCS in the
relativistic regime have been addressed.
