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.



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)


Document Type

Article - Journal

Document Version

Final Version

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© 2008 American Physical Society (APS), All rights reserved.

Publication Date

01 Apr 2008

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Physics Commons