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.

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

References in corpus (2)

• ${\alpha }^4$ Ry corrections to singlet states of helium
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius

Cited by in corpus (8)

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• Nuclear Charge Radii of ${}^{10,11}$B
• Atomic structure calculations of helium with correlated exponential functions
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• QED and relativistic nuclear recoil corrections to the 413 nm tune-out wavelength for the $2{}^3{S}_1$ state of helium
• Calculation of Araki-Sucher correction for many-electron systems
• BBR-induced Stark shifts and level broadening in helium atom