Hyperfine structure and g factor in heavy Li-like ions: rigorous evaluation of the screened QED corrections

Investigations of the hyperfine splitting and the g factor in highly charged ions give an access to a test of boundstate QED in strongest electromagnetic fields available at present for experimental study. To date, accurate measurements of the ground-state hyperfine structure and of the g factor were performed in H-like ions. An extention of such kind of experiments to highly charged Li-like ions anticipated in the near future at the HITRAP facility at GSI [1]. This will provide the possibility to investigate a specific difference between the corresponding values of Hand Lilike ions, where the uncertainty due to the nuclear effects can be substantially reduced [2]. Achievement of the required theoretical accuracy for the hyperfine structure and for the g factor in the case of Li-like ions is a very interesting and demanding challenge for theory. At present, the theoretical accuracy of the specific difference of the hyperfine splitting values of Hand Li-like ions and of the g factor of Li-like heavy ions is mainly limited by uncertainties of the screened QED and higher-order interelectronic-interaction corrections. The rigorous evaluation of the these corrections requires a systematic consideration in the QED framework of third-order perturbation theory terms. In a recent PRL [3] we have evaluated the complete gauge-invariant set of the screened one-loop QED corrections in the presence of a magnetic field perturbation. As the most interesting application of these results towards tests of the magnetic sector of bound-state QED, we present here our improved theoretical predictions for the specific difference between the ground-state hyperfine splitting values of Hand Li-like Bi ions and for the g factor of Li-like Pb ion. Probing the influence of QED effects on the hyperfine splitting of highly charged ions is impeded by the uncertainty of the nuclear magnetization distribution correction [the Bohr-Weisskopf (BW) effect]. In this context, it was proposed to consider a specific difference of the ground state hyperfine splitting in H-like and Li-like ions [2]: ∆′E = ∆E(2s)−ξ∆E(1s), where ∆E and ∆E are the hyperfine splittings of Hand Li-like ions, respectively. Extracting numerically the contribution of the BW effect in different terms we found that the cancellation appears with ξ chosen to be ξ = 0.16886 for the case of Bi. In Table 1 we present most recent result for the the energy shift ∆′E employing the most accurate value obtained for the screened QED correction. The interelectronic-interaction corrections have been evaluated to first-order in 1/Z within the QED perturbation theory and to higher-orders within the large-scale configuration-interaction Dirac-Fock-Sturm