The Configuration Interaction between the Odd Terms in the Iron Group

Abstract

Using Racah's methods, the matrix components of the electrostatic interaction between the terms of the configurations ${d}^{n\ensuremath{-}2}\mathrm{sp}$ and ${d}^{n\ensuremath{-}1}p$ are expressed as linear combinations of Slater integrals. The result consists of two parts. One part represents the interaction between the terms of the parent configurations. The second part results from the coupling of the $p$ electron to the parent groups and contains the Slater integrals ${R}^{2}(sp,dp)$ and ${R}^{1}(sp,pd)$. The appropriate linear combinations of these integrals are formed by means on the coefficients of fractional parentage, the Racah coefficients, and a spin-dependent factor. A tabulation of coefficients sufficient for the construction of the matrix components for the entire iron group is given.