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arXiv · 1612.06142

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

V. Patkos·V. A. Yerokhin·K. Pachucki
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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 $α^6 m^2/M$ 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 $4 σ$ 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.

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V. Patkos, V. A. Yerokhin, K. Pachucki. 2017-01-20. Higher-order recoil corrections for singlet states of the helium atom. https://doi.org/10.1103/physreva.95.012508

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