MCDHF-CI calculations for Hg and Cd with estimates for unknown clock transition frequencies

Abstract

By use of the \textsc{grasp2018} package we perform Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) for the $^{1}S_{0}$ and $^{3}P_{0,1}^o$ levels in neutral cadmium and mercury. By supplying the resultant atomic state functions to the \textsc{ris4} program, we evaluate the mass and field shift parameters for the $^{1}S_{0}-\,^{3}P_{0}^o$ (clock) and $^{1}S_{0}-\,^{3}P_{1}^o$ (intercombination) lines. We make revised estimates of the nuclear charge parameters $\lambda^{A,A'}$ and differences in mean-square charge radii $\delta\langle r^2\rangle^{A,A'}$ for both elements and point out a discrepancy with tabulated data for Cd. In constructing a King plot with the Hg lines we examine the second-order hyperfine interaction for the $^{3}P_{0,1}^o$ levels. Isotope shifts for the clock transition have been estimated from which we predict the unknown clock line frequencies in the bosonic Hg isotopes and all the naturally occurring isotopes of Cd.