Relativistic all-order calculations of Th, Th⁺ and Th²⁺ atomic properties

Excitation energies, term designations, and g-factors of Th, Th⁺ and Th²⁺ are determined using a relativistic hybrid configuration interaction (CI) + all-order approach that combines configuration interaction and linearized coupled-cluster methods. The results are compared with other theory and experiment where available. We find some "vanishing" g-factors, similar to those known in lanthanide spectra. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for Th²⁺. To estimate the uncertainties of our results, we compared our values with the available experimental lifetimes for higher 5f7p\ ^3G₄, 7s7p\ ^3P₀, 7s7p\ ^3P₁, and 6d7p\ ^3F₄ levels of Th²⁺. These calculations provide a benchmark test of the CI+all-order method for heavy systems with several valence electrons and yield recommended values for transition rates and lifetimes of Th²⁺.