Calculation of the energy levels of Ge, Sn, Pb, and their ions in the $V^{N-4}$ approximation

Energy levels of germanium, tin, and lead, together with their single, double, and triple ionized positive ions have been calculated using the $V^{N-M}$ 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.

Figure 1

Electron density of the $s$, $p$, $d$, and $f$ electrons of Pb I and Pb V.

Figure 2

Details of electron densities of Pb I and Pb V at large distances.

Figure 3

Electron denisties of Ba I and Ba III at large distances.