Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions

TL;DR

This paper presents precise calculations of the two-loop self-energy correction to the Lamb shift in hydrogen-like ions for various states and nuclear charges, extending accuracy and range of previous results.

Contribution

The study provides improved numerical accuracy and extends the range of nuclear charges for two-loop self-energy calculations in hydrogen-like ions, consistent with theoretical $Z ext{alpha}$-expansion.

Findings

Numerical accuracy improved by an order of magnitude.

Extended the nuclear charge range to Z=30-100.

Results are consistent with known $Z ext{alpha}$-expansion coefficients.

Abstract

The two-loop self-energy correction to the Lamb shift of hydrogen-like ions is calculated for the $1s$, $2s$, and $2p_{1/2}$ states and nuclear charge numbers $Z = 30$-$100$. The calculation is performed to all orders in the nuclear binding strength parameter $Z\alpha$. As compared to previous calculations of this correction, numerical accuracy is improved by an order of magnitude and the region of the nuclear charges is extended. An analysis of the $Z$-dependence of the obtained results demonstrates their consistency with the known $Z\alpha$-expansion coefficients.