The screened QED corrections of first order in $\alpha$ and $1/Z$ to the $g$ factor and the hyperfine splitting of lithiumlike ions are evaluated within ab initio quantum-electrodynamical approach. The complete gauge-invariant set of the two-electron self-energy diagrams in the presence of the magnetic field and a dominant part of the two-electron vacuum-polarization diagrams are calculated. The most accurate values of the $g$ factor of Li-like lead and uranium are presented. The theoretical prediction for the specific difference of the hyperfine splittings of H- and Li-like bismuth is improved.

• Received 18 February 2010

DOI:https://doi.org/10.1103/PhysRevA.81.062112