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

Abstract

We investigate the finite nuclear mass corrections in the helium atom in order to resolve a significant disagreement between the $2^{3}S-2^{3}P$ and $2^{3}S-2^{1}S$ 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.

arXiv comment29 pages. arXiv admin note: substantial text overlap with arXiv:1610.04060

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• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
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• Frequency measurements of transitions from the $2^3{P}_2$ state to the $5^1{D}_2$, $5^3{S}_1$, and $5^{3}D$ states in ultracold helium