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

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

2008-04-24

arxiv.org/abs/0804.3856v1

Phys. Rev. Lett. 100 (2008) 163001

Physics

Atomic Physics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.100.163001

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 $^3{\rm He}^+$ 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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