Hyperfine splitting and g factors of heavy few-electron ions

High-precision measurements of the ground-state hyperfine structure of heavy highly charged ions [1-4] and the g factor of H-like carbon [5] and oxygen [6] have triggered a great interest to related theoretical calculations. In particular, the 2002 CODATA value for the electron mass is derived mainly from the experimental and theoretical g factor values for H-like carbon and oxygen and it is 4 times better than that of the 1998 CODATA value. An extension of these experiments to highly charged Liand B-like ions presently being prepared [7, 8] will provide tests of the magnetic sector of quantum electrodynamics (QED) in strong fields in the specific differences between H-, Li-, and B-like ions [9, 10]. For the hyperfine structure in Hand Li-like ions the limitation of the total accuracy is set by the Bohr-Weisskopf correction. This uncertainty is considerably reduced in the specific difference between the groundstate hyperfine structure values of Hand Li-like ions with the same nucleus [9]. Similarly, the accurate knowledge of the experimental and theoretical values of a specific difference between the g factors of Hand B-like highly charged ions could also lead to an independent determination of the fine structure constant α [10]. The achievement of the required theoretical accuracy is a very interesting and demanding challenge for theory. As a further step toward this goal we have performed ab initio QED calculations of the ground-state hyperfine structure of the H-, Li-, and B-like sequences in the middle-Z region [11]. Similar calculations have been carried out for the g factor of heavy few-electron ions. Below we report briefly on our recent improvments in the predictions for the hyperfine splittings. For an ion with one electron (e.g., ns or np1/2 state) over closed shells the hyperfine splitting can be written in the form