Radiative $\bm{\alpha^7m}$ QED contribution to the helium Lamb shift

TL;DR

This paper derives the last unknown radiative QED contribution to the helium Lamb shift at order $m{ ext{alpha}^7 m}$, enabling precise numerical calculations crucial for determining nuclear charge radii from helium spectroscopy.

Contribution

It provides the first divergence-free formulas for the $m{ ext{alpha}^7 m}$ QED effects in helium, facilitating complete numerical evaluation.

Findings

Formulas are free from divergences and suitable for numerical computation.

Enables accurate theoretical predictions of helium transition frequencies.

Supports precise extraction of nuclear charge radius from experimental data.

Abstract

We present a derivation of the last unknown part of the $\alpha^7m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S = 1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the $\alpha^7m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from measurements of helium transition frequencies.