Configuration Interaction in Complex Spectra

Abstract

The electrostatic interaction is calculated between the terms in Russell-Saunders coupling of the electron configurations $n{d}^{2}{n}^{\ensuremath{'}}s$, $n{d}^{3}$, $\mathrm{nd}{n}^{\ensuremath{'}}{s}^{2}$ and $n{d}^{2}{n}^{\ensuremath{'}\ensuremath{'}}s$. The first order eigenfunctions, for the terms of these configurations in the $\mathrm{LS}{M}_{L}{M}_{S}$ scheme with ${M}_{L}=0$, ${M}_{S}=\frac{1}{2}$ are given in terms of the zero order functions of Slater. The matrix elements between the quartets of ${d}^{2}s$ and ${d}^{3}$ are found to vanish. The sums over closed shells in non-diagonal matrix elements of electrostatic interaction are found to vanish except when the two electrons not in closed shells have the same value of $l$. This sum is evaluated in general and for the configurations $n{d}^{2}{n}^{\ensuremath{'}}s\ensuremath{-}n{d}^{2}{n}^{\ensuremath{'}\ensuremath{'}}s$. The matrix elements of magnetic spin orbit interaction are given between the initial states without configuration interaction. The electrostatic energies and magnetic splittings are then calculated for the terms of $n{d}^{2}{n}^{\ensuremath{'}}s$, $n{d}^{3}$ and $\mathrm{nd}{n}^{\ensuremath{'}}{s}^{2}$; and compared with the values observed in Ti II and Zr II. Zr II agrees particularly well, especially if the observed $^{2}D$ terms are rearranged.