Application of Slater-Condon Theory with Configuration Interaction to the 5d106s6p, 5d96s26p, 5d106s7p, and 5d106s5f Configurations in Hg i, Tl ii, Pb iii, and Bi iv

Abstract

The calculations were based on fitting radial parameters to the observed energy levels, but with a requirement of regularity in the behavior of each parameter value along the isoelectronic sequence. Some parameters or ratios of parameters were fixed at values based on isoelectronic comparisons or adjusted Hartree-Fock values. The calculated levels, $g$ values, and $\mathrm{LS}$ percentage compositions are given for each atom, and comparisons with experimental data are made. The results support new $5d^{9}6s^{2}6p$ levels recently found in Hgi, Tlii, and Biiv, and one experimental $5d^{9}6s^{2}6p$ level in Pb iii is rejected as unreal. The calculated ratio of the lifetimes of the Hgi $5d^{10}6s6p{}_{}{}^3{}_{}{}^{}P_1^0{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}P_1^0{}_{}{}^{}$ levels is compared with the experimental value. Some comparisons of calculated and observed isotope shifts are made for Hgi, Tlii, and Pbiii. The leading percentages in the $\mathrm{jj}$ coupling scheme are listed for levels having assigned $\mathrm{jj}$ names ($5d^{9}6s^{2}6p$ levels in all four atoms and $5d^{10}6s7p$ levels in three atoms).