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 3He+ ion, the nonperturbative remainder yields a contribution of -450Hz 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.
V. A. Yerokhin and U. D. Jentschura, "Electron Self-Energy in the Presence of a Magnetic Field: Hyperfine Splitting and g Factor," Physical Review Letters, vol. 100, no. 16, pp. 163001-1-163001-4, American Physical Society (APS), Apr 2008.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.100.163001
Keywords and Phrases
Coulomb Interactions; Gravitation; Magnetic Field Effects; Nuclear Energy; Perturbation Techniques; Uncertainty Analysis; Bound Electron G Factors; Electron Self Energy; Hydrogenlike Ions; Hyperfine Splitting; Electron Energy Levels
International Standard Serial Number (ISSN)
Article - Journal
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