Abstract
We report calculations of QED corrections to the $g$ factor of Li-like ions induced by the exchange of two virtual photons between the electrons. The calculations are performed within QED theory to all orders in the nuclear binding strength parameter $Z\alpha$, where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant. In the region of low nuclear charges we compare results from three different methods: QED, relativistic many-body perturbation theory, and nonrelativistic QED. All three methods are shown to yield consistent results. With our calculations we improve the accuracy of the theoretical predictions of the $g$ factor of the ground state of Li-like carbon and oxygen by about an order of magnitude. Our theoretical results agree with those from previous calculations but differ by 3-4 standard deviations from the experimental results available for silicon and calcium.
Highlights
Modern Penning-trap experiments based on the continuous Stern-Gerlach effect provide very precise measurements of the Zeeman splitting of energy levels in one- and fewelectron ions [1,2,3]
The linear Zeeman splitting is usually parametrized in terms of the g factor of the atomic system
Combined with dedicated theoretical calculations, these measurements provided the determination of the electron mass [6] and one of the best tests of bound-state quantum electrodynamics (QED) [7]
Summary
Modern Penning-trap experiments based on the continuous Stern-Gerlach effect provide very precise measurements of the Zeeman splitting of energy levels in one- and fewelectron ions [1,2,3]. In view of the very high accuracy of the measurements, theoretical investigations of atomic g factors often need to be carried out without any expansion in the nuclear binding strength parameter Zα (where Z is the nuclear charge number). In such calculations, the electron-electron interaction has to be treated by perturbation theory. Our goals will be to cross-check the previous calculations, to improve the numerical accuracy, and to study the Z dependence of the two-photon correction in the low-Z region, checking the consistency of the applied method with the Zα-expansion calculations performed recently in Ref.
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