Configuration Interaction in Complex Spectra

The electrostatic interaction is calculated between the terms in Russell-Saunders coupling of the electron configurations nd²n^'s, nd³, ndn^'s² and nd²n^''s. The first order eigenfunctions, for the terms of these configurations in the LSMLMS scheme with ML=0, MS=1/2 are given in terms of the zero order functions of Slater. The matrix elements between the quartets of d²s and d³ 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 nd²n^'s-nd²n^''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 nd²n^'s, nd³ and ndn^'s²; and compared with the values observed in Ti II and Zr II. Zr II agrees particularly well, especially if the observed ²D terms are rearranged.