Excitation energies, polarizabilities, multipole transition rates, and lifetimes in $\mathrm{Th}\mathrm{IV}$

Excitation energies of the $n{s}_{1∕2}$ $(n=7–10)$, $n{p}_j$ $(n=7–9)$, $n{d}_j$ $(n=6–8)$, $n{f}_j$ $(n=5–7)$, and $n{g}_j$ $(n=5,6)$ states in $\mathrm{Th}\mathrm{IV}$ are evaluated. First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 96 possible $n{l}_j\text{−}{n}^{\prime }{l}_{j^{\prime }}^{\prime }$ electric-dipole transitions. Multipole matrix elements ($7s_{1∕2}\text{−}6d_j$, $7s_{1∕2}\text{−}5f_j$, and $5f_{5∕2}\text{−}5f_{7∕2}$) are evaluated to obtain the lifetimes of the $5f_{7∕2}$ and $7s_{1∕2}$ states. Matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and a relativistic all-order method restricted to single and double excitations. Scalar and tensor polarizabilities for the $5f_{5∕2}$ ground state in ${\mathrm{Th}}^{3+}$ are calculated using relativistic third-order and all-order methods. These calculations provide a theoretical benchmark for comparison with experiment and theory.