Calculation of the energy levels of Ge, Sn, Pb, and their ions in the VN-4 approximation

Energy levels of germanium, tin, and lead, together with their single, double, and triple ionized positive ions have been calculated using the VN-M approximation suggested in previous work [Dzuba, Phys. Rev. A 71, 032512 (2005)] [M is the number of valence electrons (M=4)]. Initial Hartree-Fock calculations are done for the quadruply ionized ions with all valence electrons removed. The core-valence correlations are included beyond the second-order of the many-body perturbation theory. Interaction between valence electrons is treated by means of the configuration interaction technique. It is demonstrated that accurate treatment of the core-valence correlations leads to systematic improvement of the accuracy of calculations for all ions and neutral atoms