Relativistic all-order calculations of Th, Th$^{+}$ and Th$^{2+}$ atomic properties

TL;DR

This paper employs a relativistic hybrid CI + all-order approach to accurately calculate excitation energies, g-factors, transition rates, and lifetimes of thorium ions, providing benchmark data and insights into their atomic properties.

Contribution

It introduces a combined relativistic CI and all-order method for heavy atoms and ions, offering new benchmark calculations for thorium and its ions with improved accuracy.

Findings

Identification of vanishing g-factors in thorium spectra

Benchmark transition rates and lifetimes for Th$^{2+}$

Comparison with experimental data validates the method

Abstract

Excitation energies, term designations, and $g$-factors of Th, Th$^{+}$ and Th$^{2+}$ 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 Th$^{2+}$. To estimate the uncertainties of our results, we compared our values with the available experimental lifetimes for higher $5f7p\ ^3G_{4}$, $7s7p\ ^3P_{0}$, $7s7p\ ^3P_{1}$, and $6d7p\ ^3F_{4}$ levels of Th$^{2+}$. 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 Th$^{2+}$.