Relativistic corrections to the Bethe logarithm for the $2^{3}S$ and $2^{3}P$ states of He

Abstract

With this work we start a project of calculating the QED contribution of order ${\alpha }^{7}m$ to the $2^{3}P$-$2^{3}S$ transition energy in helium, aiming for an accurate determination of the nuclear charge radius $r_E$ from measurements of the corresponding transition frequency. Together with the complementary determination of $r_E$ from muonic helium, this project will provide a stringent test of universality of electromagnetic interactions of leptons in the Standard Model. We report a calculation of the relativistic corrections to the Bethe logarithm for the $2^{3}S$ and $2^{3}P$ states, which is the most numerically demanding part of the project.

Includes corrections from Erratum

References in corpus (6)

• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle
• ${\alpha }^4$ Ry corrections to singlet states of helium
• Nonrelativistic QED approach to the Lamb shift
• Precision spectroscopy of helium in a magic wavelength optical dipole trap
• Improved theory of helium fine structure
• High-precision spectroscopy of the forbidden 2 3S1 - 2 1P1 transition in quantum degenerate metastable helium

Cited by in corpus (15)

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• Nuclear Charge Radii of ${}^{10,11}$B
• QED calculations of energy levels of helium-like ions with $5\le Z\le 30$
• Atomic structure calculations of helium with correlated exponential functions
• Nonradiative ${\alpha }^{7}m$ QED effects in Lamb shift of helium triplet states
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• QED calculation of ionization energies of $1snd$ states in helium
• Quantum electrodynamic corrections to the $1s3d$ states of the helium atom
• Higher-order QED corrections to the hyperfine splitting in ${}^3$He
• QED $m{\alpha }^7$ effects for triplet states of helium-like ions
• Transition Frequencies and Hyperfine Structure in ${}^{113,115}$In${}^{+}$: Application of a Liquid-Metal Ion Source for Collinear Laser Spectroscopy
• Collinear laser spectroscopy of highly charged ions produced with an electron beam ion source
• Calculations of Bethe logarithms for Hydrogen and Helium atoms using B-splines in different gauges
• Splitting Isotope Shift in the $1s2p{}^3{P}_{0,1,2}$ Fine-Structure Triplet in ${}^{12,13,14}$C${}^{4+}$: Experiment and Theory
• Nonrelativistic quantum electrodynamic approach to polarizabilities of light atoms