Relativistic Bethe logarithm for triplet states of helium-like ions

TL;DR

This paper calculates relativistic corrections to the Bethe logarithm for helium-like ions' triplet states, enhancing theoretical energy predictions and addressing discrepancies with experimental data.

Contribution

It provides the first calculation of relativistic $m extalpha^7$ corrections to the Bethe logarithm for specific helium-like ion states, including the large-Z limit.

Findings

Relativistic corrections are computed for $2^3S$ and $2^3P$ states.

Large-Z limit agrees with hydrogen theory.

Results improve the accuracy of helium-like ion energy calculations.

Abstract

We report a calculation of relativistic corrections of order $m\alpha^7$ to the Bethe logarithm for the $2^3S$ and $2^3P$ states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of helium-like ions and for checking the evaluation of the $m\alpha^7$ effects in helium performed in [V. Patk\'o\v{s}, V. A. Yerokhin, K. Pachucki, Phys. Rev. A 103, 042809 (2021)], where a significant discrepancy with experimental results was found. The large-$Z$ limit of the relativistic Bethe logarithm is determined numerically, in excellent agreement with the analytical results obtained from the hydrogen theory.