Valence-core electron exchange interaction and the collapse of4fand5dorbitals in the cesium isoelectronic sequence

As one progresses along the isoelectronic sequence of Cs, the ground state changes from $6s_{\frac{1}{2}}$ (Cs, ${\mathrm{Ba}}^{+}$) to $5d_{\frac{3}{2}}$ (${\mathrm{La}}^{2+}$) to $4f_{\frac{5}{2}}$ (${\mathrm{Ce}}^{3+}$, ${\mathrm{Pr}}^{4+}$). The relativistic Hartree-Fock and model-potential calculations reported here are aimed at obtaining a better understanding of variations in the ordering of the states as the ion charge increases. The $5d$ and $4f$ orbitals are found to "collapse" as the increasing Coulomb and exchange attractions overcome centrifugal repulsion. Valence-core electron exchange is found to be crucial for the proper ordering of the states as well as for reliable fine-structure splittings. Furthermore, the collapse of the $5d$ and $4f$ orbitals greatly enhances the sensitivity of the properties of these states to small perturbations, so that even details of the exchange interaction, including nonlocal effects, as well as core-relaxation and -polarization effects, are required in order to compute accurate ionization potentials and fine-structure splittings.