Higher-order recoil corrections for singlet states of the helium atom

TL;DR

This paper calculates higher-order recoil corrections for helium's singlet states using nonrelativistic QED, aiming to resolve discrepancies in nuclear charge radius measurements from isotope shift data.

Contribution

It derives and numerically evaluates $ ext{alpha}^6 m^2/M$ corrections for helium, improving the theoretical understanding of finite nuclear mass effects in atomic transitions.

Findings

Confirmed a 4-sigma discrepancy in nuclear charge radius difference.

Highlighted the need for experimental verification of transition frequencies.

Provided accurate numerical results for low-lying helium states.

Abstract

We investigate the finite nuclear mass corrections in the helium atom in order to resolve a significant disagreement between the $2^3S - 2^3P$ and $2^3S - 2^1S$ transition isotope shifts. These two transitions lead to discrepant results for the nuclear charge radii difference between $^4$He and $^3$He. The accurate treatment of the finite nuclear mass effects is quite complicated and requires the use of the quantum field theoretical approach. We derive $\alpha^6 m^2/M$ correction with the help of nonrelativistic QED and dimensional regularization of the three body Coulombic system, and present accurate numerical results for low lying states. The previously reported $4 \sigma$ discrepancy in the nuclear charge radius difference between $^3$He and $^4$He from two different atomic isotope shift transitions is confirmed, which calls for verification of experimental transition frequencies.