The Theory of Complex Spectra

Abstract

Part I. Calculation of the first order energies for configurations involving almost closed shells. A method is developed for calculating the electrostatic energy matrix for a configuration consisting of a closed shell minus $\epsilon$ electrons plus $\eta$ other electrons with the same simplicity as for the corresponding configuration consisting of $\epsilon +\eta$ electrons. One classifies the states according to the quantum numbers of the "missing" and of the added electrons and calculates Slater's integral ($J-\delta K$) for each pair of electrons in the usual way except that one attaches a negative sign to an integral connecting a "missing" with an added electron. It is then shown quite generally that the matrices of magnetic interaction are identical in $\mathrm{LS}$ coupling for the two configurations mentioned above except for a reversal of sign of the spin-orbit coupling parameter corresponding to the almost closed shell.