Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high $Z$ lithium like atoms in all orders in $\alpha Z$

Abstract

The relativistic nuclear recoil corrections to the energy levels of low-laying states of hydrogen-like and high $Z$ lithium-like atoms in all orders in $\alpha Z$ are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low $Z$ the results of the calculation are in good agreement with the $\alpha Z$ -expansion results. It is found that the nuclear recoil contribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) of hydrogen is $-1.32(6)kHz$. The total nuclear recoil correction to the energy of the $(1s{)}^{2}2p_{\frac{1}{2}}-(1s{)}^{2}2s$ transition in lithium-like uranium constitutes $-0.07eV$ and is largely made up of QED contributions.

19 pages, latex, accepted for publication in Phys. Rev. A

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