Relativistic Recoil Corrections to the Atomic Energy Levels

The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in ∞Z and to first order in m/M is considered. The complete ∞Z-dependence formulas for the relativistic recoil corrections to the atomic energy levels are derived in a simple way. The results of numerical calculations of the recoil effect to all orders in ∞Z are presented for hydrogenlike and lithiumlike atoms. These results are compared with analytical results obtained to lowest orders in ∞Z. It is shown that even for hydrogen the numerical calculations to all orders in ∞Z provide most precise theoretical predictions for the relativistic recoil correction of first order in m/M.