Mass corrections in a strong nuclear field

In the framework of quantum electrodynamics, we consider the bound states of a system of two fermions with masses $m$ (electron) and $M$ (nucleus). In the case $m\ll M$ and with radiative corrections ignored, closed expressions are obtained for the mass corrections of order $m/M$ without an expansion in $\alpha Z$ ($\alpha$ is the fine structure constant, and $Z$ is the charge of the nucleus).