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We report multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations on the thallium (Tl) electron affinity, as well as on the excited energy levels arising from the ground configuration of ${\mathrm{Tl}}^{\ensuremath{-}}$. The results are compared with the available experimental values and further validated by extending the study to its homologous, lighter element, indium (In), belonging to group 13 (III.A) of the Periodic Table. The calculated electron affinities of In and Tl, 383.4 and 322.8 meV, agree with the latest measurements by within 1%. Three bound states ${}^{3}{P}_{0,1,2}$ are confirmed in the $5{s}^{2}5{p}^{2}$ configuration of ${\mathrm{In}}^{\ensuremath{-}}$, while only the ground state ${}^{3}{P}_{0}$ is bound in the $6{s}^{2}6{p}^{2}$ configuration of ${\mathrm{Tl}}^{\ensuremath{-}}$. The isotope shifts on the In and Tl electron affinities are also estimated. The E2 and M1 intraconfiguration radiative transition rates within $5{s}^{2}5{p}^{2} {}^{3}{P}_{0,1,2}$ of ${\mathrm{In}}^{\ensuremath{-}}$ are used to calculate the radiative lifetimes of the metastable ${}^{3}{P}_{1,2}$ levels.

Large-scale ab initio calculations of the electronic contribution to the electric quadrupole hyperfine constant B were performed for the 5s25p6s1,3Po1 excited states of neutral tin. To probe the sensitivity of B to different electron correlation effects, three sets of variational multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. In addition, a fourth set of calculations was based on the configuration interaction Dirac-Fock-Sturm theory. For the 5s25p6s 1Po1 state, the final value of B/Q=703(50) MHz/b differs by 0.4% from the one recently used by Yordanov et al. [Commun. Phys. 3, 107 (2020)] to extract the nuclear quadrupole moments Q for tin isotopes in the range 117−131Sn from collinear laser spectroscopy measurements. Efforts were made to provide a realistic theoretical uncertainty for the final B/Q value of the 5s25p6s 1Po1 state based on statistical principles and on correlation with the electronic contribution to the magnetic dipole hyperfine constant A.

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable $^{2}D_{3/2,5/2}$ states of ${\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkalilike systems.