Fine-structure analyses with orthogonal operators

Abstract

The single-electron operator representing the spin-orbit interaction in the 3d shell is augmented by a collection of operators, each of which acts on two electrons at a time and possesses identical ranks k in the spin and orbital spaces with k=1 or 2. Orthogonality is guaranteed by labelling each operator by a distinct set of irreducible representations of various Lie groups. The operators are able to represent all terms deriving from the non-relativistic limit of the Breit interaction for 3d electrons as well as those terms deriving from the leading types of electrostatically correlated spin-orbit (EL-SO) effects. Fits to the experimental data of Cr IV 3d3 and Ni IV 3d7 yield mean errors of only 1.91 and 3.87 cm-1 respectively. A comparison of the values of fine-structure parameters with those deduced from Hartree-Fock calculations gives good agreement for Cr IV 3d3 apart from a single parameter that is particularly sensitive to EL-SO.