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 $He^+$.