Electron self-energy in the presence of magnetic field: hyperfine splitting and g factor

Abstract

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known $Z\alpha$-expansion coefficients is determined. For the ${}^3{\mathrm{He}}^{+}$ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.

4 pages, 1 figure

References in corpus (4)

• Complete two-loop correction to the bound-electron g factor
• Evaluation of the self-energy correction to the g-factor of S states in H-like ions
• Nonrelativistic QED approach to the bound-electron g factor
• Quantum electrodynamic corrections to the hyperfine structure of excited S states

Cited by in corpus (12)

• QED tests with highly-charged ions
• $g$-factor of Boronlike Argon ${}^{40}{\text{Ar}}^{13+}$
• Spin-dependent exotic interactions
• Calculations of QED effects with the Dirac Green function
• Higher-order corrections to spin-spin scalar interactions in HD${}^{+}$ and H${}_2^{+}$
• Nuclear polarizability effects in ${}^3$He${}^{+}$ hyperfine splitting
• Testing inter-electronic interaction in lithium-like tin
• Experimental signatures of Kalb-Ramond-like particles
• Quantum Electrodynamic Corrections to the g Factor of Helium P States
• Magnetic moment of a bound electron
• Improved constraints on exotic interactions between electron and proton in hydrogen
• Relativistic Correction to the Magnetic Moment of the Charged Lepton