Evaluation of the screened vacuum-polarization corrections to the   hyperfine splitting of Li-like bismuth
  The rigorous calculation of the vacuum-polarization screening corrections to the hyperfine splitting in Li-like bismuth is presented. The two-electron diagrams with electric and magnetic vacuum-polarization loops are evaluated to all orders in alpha*Z, including the Wichmann-Kroll contributions. This improves the accuracy of the theoretical prediction for the specific difference of the hyperfine splitting values of H- and Li-like bismuth. 
O.V. Andreev, D.A. Glazov, A.V. Volotka, V.M. Shabaev and G. Plunien
physics.atom-ph