Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogen-like ions

TL;DR

This paper presents precise calculations of nuclear recoil effects on the Lamb shift in hydrogen-like atoms, resolving previous discrepancies between numerical and analytical methods, especially for hydrogen.

Contribution

It provides all-order numerical results for nuclear recoil corrections to the Lamb shift, improving accuracy and resolving prior disagreements in hydrogen.

Findings

Recoil corrections are larger than previously estimated for hydrogen.

Numerical results agree with analytical approaches for higher Z.

The study enhances understanding of nuclear recoil effects in atomic physics.

Abstract

Accurate calculations of the nuclear recoil effect to the Lamb shift of hydrogen-like atoms are presented. Numerical results are reported for the $ns$ states with $n \leq 5$ and for the $2p_{1/2}$ and $2p_{3/2}$ states. The calculations are performed to the first order in the electron-nucleus mass ratio and to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine structure constant). The obtained results provide accurate predictions for the higher-order remainder beyond the known $Z\alpha$-expansion terms. In the case of hydrogen, the remainder was found to be much larger than anticipated. This result resolves the previously reported disagreement between the numerical all-order and the analytical $Z\alpha$-expansion approaches for the nuclear recoil effect in the hydrogen Lamb shift.