Correlation effects on the fine-structure splitting within the 3d⁹ ground configuration in highly-charged Co-like ions

A comprehensive theoretical study of correlation effects on the fine-structure splitting within the ground configuration 3d⁹ of the Co-like Hf⁴⁵⁺, Ta⁴⁶⁺, W⁴⁷⁺, and Au⁵²⁺ ions is performed by employing the multi-configuration Dirac-Hartree-Fock method in the active space approximation. It shows that the core-valence correlation with the inner-core 2p electron is more significant than with the outer 3p and 3s electrons, and the correlation with the 2s electron is also noticeable. The core-core correlation seems to be small and can be ignored. The calculated ² D_3/2,5/2 splitting energies agree with the recent electron-beam ion-trap measurements Phys. Rev. A 83 032517 (2011), Eur. Phys. J. D 66 286 (2012) to within the experimental uncertainties.