Maximal Acceleration Corrections to the Lamb Shift of Hydrogen, Deuterium and He${}^{+}$

The maximal acceleration corrections to the Lamb shift of one–electron atoms are calculated in a non–relativistic approximation. They are compatible with experimental results, are in particularly good agreement with the $2S-2P$ Lamb shift in hydrogen and reduce by $\sim 50$ the experiment–theory discrepancy for the $2S-2P$ shift in $H{e}^{+}$.