Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift

Abstract

We present a derivation of the last unknown part of the ${\alpha }^{7}m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S=1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the ${\alpha }^{7}m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from measurements of helium transition frequencies.

arXiv comment28 pages, corrected numerous misprints

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Cited by in corpus (9)

• Complete ${\alpha }^{7}m$ Lamb shift of helium triplet states
• Atomic structure calculations of helium with correlated exponential functions
• Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules
• The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules
• Revised ${}^3$He nuclear charge radius due to electronic hyperfine mixing
• Fine and hyperfine splitting of the low-lying states of ${}^9$Be
• Higher-order QED corrections to the hyperfine splitting in ${}^3$He
• QED $m{\alpha }^7$ effects for triplet states of helium-like ions
• Proposal for suppressing ac Stark shift in the He($2{}^3{S}_1\to 3{}^3{S}_1$) two-photon transition using magic wavelengths