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.

arXiv comment4 pages, 1 figure

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• HFS interval of the $2s$ state of hydrogen-like atoms and a constraint on a pseudovector boson with mass below $1$keV$/c^2$
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• Testing inter-electronic interaction in lithium-like tin
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• Experimental signatures of Kalb-Ramond-like particles
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• Improved constraints on exotic interactions between electron and proton in hydrogen
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