Complete $\alpha^7\,m$ Lamb shift of helium triplet states

TL;DR

This paper derives the complete $ ext{alpha}^7 m$ correction for helium triplet states, improving theoretical energy predictions and confirming some experimental results while highlighting discrepancies in others.

Contribution

It provides the full formula for $ ext{alpha}^7 m$ corrections to helium triplet states and performs numerical calculations to enhance theoretical accuracy.

Findings

Theoretical predictions agree with the measured $2^3S - 2^3P$ transition energy.

Significant discrepancies are observed for $2^3S- 3^3D$ and $2^3P - 3^3D$ transitions.

Improved accuracy of ionization energies by over an order of magnitude.

Abstract

We have derived the complete formula for the $\alpha^7\,m$ contribution to energy levels of an arbitrary triplet state of the helium atom, performed numerical calculations for the $2^3S$ and $2^3P$ states, and thus improved the theoretical accuracy of ionization energies of these states by more than an order of magnitude. Using the nuclear charge radius extracted from the muonic helium Lamb shift, we obtain the theoretical prediction in excellent agreement with the measured $2^3S - 2^3P$ transition energy [X.~Zheng et al., Phys. Rev. Lett. {\bf 199}, 263002 (2017)]. At the same time we observe significant discrepancies with experiments for the $2^3S- 3^3D$ and $2^3P - 3^3D$ transitions.