be 〈 r $^{2}$〉1 / 2 = 5 . 5211 fm [60], the nuclear spin and parity I π = 9 / 2 − , and the magnetic moment µ = 4 . 1106(2) µ$_{N}$ [61]. C. Conclusion The rigorous evaluation of the screened QED corrections to the g factor and to the hyperfine splitting of heavy Li-like ions within ab initio QED approach has been performed. Previously developed procedures for the evaluation of the one-electron QED corrections in presence of the external magnetic field and of the two-electron QED correcti ons to the energy levels have been associated and generalized. The complete gauge-invariant set of the two-electron self-energy di- agrams with external magnetic field has been calculated. Thedominant part of the two-electron vacuum-polarization correction has been calculated as well. The electric-loop diagrams have been evaluated for both Uehling and Wichmann-Kroll parts. The magnetic-loop diagrams have been evaluated in the Uehling approximation. These results improve the accuracy of the theoretical predictions for the g factor and the hyperfine splitting of heavy ions where string ent tests of the bound-state QED effects are feasible. Valuable conversations with A. N. Artemyev are gratefully acknowledged. This work was sup- ported by RFBR (Grant No. 07-02-00126-a), GSI, DFG (Grant No. 436RUS113/950/0-1), and by the Ministry of Education and Science of Russian Federation (Program for Development of Scientific Potential of High School, Grant No. 2.1.1/1136; P rogram Scientific and pedagogical specialists for innovative Russia) and by the grant of the President of Russian Federation. D.A.G. acknowledges the support by the FAIR – Russia Research Cente r, and by Saint-Petersburg Gov- ernment. V.M.S. acknowledges the support by the Alexander von Humboldt Foundation. Acknowledgments [1] N. Hermanspahn, H. H¨affner, H.-J. Kluge, W. Quint, S. Stahl, J. Verd´u, and G. Werth, Phys. Rev. Lett. 84 , 427 (2000). [2] H. H¨affner, T. Beier, N. Hermanspahn, H.-J. Kluge, W. Quint, S. Stahl, J. Verd´u, and G. Werth, Phys. Rev. Lett. 85 , 5308 (2000). 19