Correlation and relativistic effects within the trivalent Lu-like sequence

Energies of the three-electron-above the closed-shell lutetium-like ions ([Xe]4f145d3, [Xe]4f145d26s, [Xe]4f145d26p and [Xe]4f145d6s6p states) with Z = 74-100 are determined using second-order relativistic many-body perturbation theory. Our calculations start from a Er-like V(N-3) Dirac-Fock potential ([Xe]4f14, where [Xe] = 1s22s22p63s23p63d104s24p64d105s25p6). Second-order Coulomb and Breit-Coulomb interactions are included. Correction for the frequency dependence of the Breit interaction is taken into account in the lowest order. The Lamb shift correction to energies is also included in the lowest order. The three-electron contributions to the energy are compared with the one- and two-electron contributions. They are found to contribute about 10-20% of the total second-order energy. The ratios of the third- and second-order corrections to the one-electron contributions are found to be about 5-10%. A detailed discussion of the various contributions to the energy levels is given for Lu-like tungsten (Z = 74). Comparisons are made with available experimental data. Trends of excitation energies including splitting of the doublet and quartet terms as functions of nuclear charge Z = 73-100 are illustrated graphically for some states. These are the first ab initio calculations of excitation energies in Lu-like ions. The results for the W3+ ion are particularly important for fusion application.