Ground-state $g_j$ factors of the ${\mathrm{Cd}}^{+},$ ${\mathrm{Yb}}^{+},$ and ${\mathrm{Hg}}^{+}$ ions

Accurate calculations of $g_j$ factors of the ground state of the ${\mathrm{Cd}}^{+},$ ${\mathrm{Yb}}^{+},$ and ${\mathrm{Hg}}^{+}$ ions are presented by employing the normal order unrelaxed $\mathrm{\Lambda }$-approach relativistic coupled-cluster $\left(\mathrm{\Lambda }\text{−}\mathrm{RCC}\right)$ theory. Contributions from the quantum electrodynamics (QED) are estimated from the free electron QED contributions and the roles of electron correlation effects are analyzed with different cutoff of occupied and virtual active orbitals in the $\mathrm{\Lambda }$-RCC method. Our final $g_j$ factors come out to be 2.002291(4), 2.002798(113), and 2.003128(41) for the ${\mathrm{Cd}}^{+},$ ${\mathrm{Yb}}^{+},$ and ${\mathrm{Hg}}^{+}$ ions, respectively. Our result for ${\mathrm{Hg}}^{+}$ agrees up to the fourth decimal places with its experimental value 2.0031745(74) indicating that our calculations of the other ions are of similar accuracies. The understanding of roles of electron correlation effects from this study will be useful in improving accuracies of the $g_j$ factors in the considered ions further by adding more physical effects in the future and performing calculations with similar accuracies in other heavier atomic systems. The reported $g_j$ factors can also be used to scrutinize the background noise related to the stray magnetic fields in the laser-cooled microwave ion clocks using the above ions.