All-order calculations of the spectra of Ba II, Ra II, Fr I, and superheavy elements E119 I and E120 II

A technique based on summation of dominating classes of correlation diagrams to all orders in Coulomb interaction is used to calculate the energies of the lowest s, p, and d states of Ba II, Ra II, Fr I, E119 I, and E120 II. Breit and quantum electrodynamic corrections are also included. Comparison with experiment for Ba II, Ra II, and Fr I demonstrates that the accuracy of the calculations is on the level of 0.1%. The technique has been applied to predict the spectra of superheavy elements E119 and E120(+). The role of the ladder diagrams [Dzuba, Phys. Rev. A 78, 042502 (2008)], which is the most recent addition to the method, has been emphasized. Their inclusion significantly improves the accuracy of the calculations and expands the applicability of the method.