Pure recoil corrections to hydrogen energy levels

Abstract

The pure recoil correction to hydrogenlike energy levels is revisited. An alternative method for its evaluation is presented. We confirm that the previous result [Doncheski et al., Phys. Rev. A 43, 2125 (1991)] of the ${\mathit{m}}^{2}$/M(Z\ensuremath{\alpha}${)}^{6}$ contribution was missing some important terms. Our result is \ensuremath{\Delta}E=(${\mathit{m}}^{2}$/M)(Z\ensuremath{\alpha}${)}^{6}$/${\mathit{n}}^{3}$[4 log(2)-7/2]. A new value of the deuteron radius is obtained by comparing theory to the measurement of the hydrogen-deuterium isotope shift.