Relativistic coupled-cluster method: Intrashell excitations in the f2 shells of Pr+3 and U+4.

Abstract

The relativistic Fock-space coupled-cluster method for the direct calculation of ionization potentials and excitation energies (including fine structure) is applied to the 4${\mathit{f}}^{2}$ levels of ${\mathrm{Pr}}^{+3}$ and the 5${\mathit{f}}^{2}$ levels of ${\mathrm{U}}^{+4}$. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. Correlation is treated by the coupled-cluster singles-and-doubles approximation, which includes single and double virtual excitations in a self-consistent manner, incorporating therefore the effects of the Coulomb and Breit interactions to all orders in these excitations. Extensive basis sets of kinetically balanced four-component Gaussian spinors are used to span the atomic orbitals. All levels appear in correct order. The average error of the excitation energies with the best basis is 222 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{Pr}}^{+3}$ and 114 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{U}}^{+4}$. Fine-structure splittings are obtained with even better accuracy.