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arXiv · 0804.3856

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

V. A. Yerokhin·U. D. Jentschura
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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 $Zα$-expansion coefficients is determined. For the $^3{\rm He}^+$ 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.

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V. A. Yerokhin, U. D. Jentschura. 2008-04-24. Electron self-energy in the presence of magnetic field: hyperfine splitting and g factor. https://doi.org/10.1103/physrevlett.100.163001

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