QED in strong fields: hyperfine structure and g factor in heavy ions

Investigations of the hyperfine splitting and g factor in highly charged ions provide access to a test of bound-state QED in strongest electromagnetic field available for experimental study. To date, accurate measurements of the ground-state hyperfine structure and of the g factor were performed in several H-like heavy ions and in H-like carbon and oxygen ions, respectively. An extension of such kind of experiments to highly charged Li-like ions will provide the possibility to investigate a specific difference between the corresponding values for H- and Li-like ions, where the uncertainty due to the nuclear effects can be substantially reduced. In this talk we present ab initio QED calculations of the hyperfine splitting and g factor of heavy high-Z ions. Special attention is focused on recent results of our rigorous evaluation of the complete gauge-invariant set of the screened one-loop QED corrections to the hyperfine structure and g factor in highly charged Li-like ions. The current status of the evaluations of the two-photon exchange corrections is also reported. As a result, the specific difference between the ground-state hyperfine splitting values of H- and Li-like Bi ions and for the g factor of the Li-like Pb ion are presented.