Atomic structure calculations in a factorized shell

Abstract

A method is described for calculating matrix elements of operators in a basis in which the spin-up and spin-down spaces of an atomic l shell are both split into separate parts. Instead of elaborate tables of fractional parentage coefficients, only a few reduced matrix elements are required. These are tabulated for d, f, g and h electrons. The transformation coefficients relating the states in the new basis to the familiar LS states are given for f electrons. An operator e h that separates and classifies repeating terms of the configuration h N (in analogy to the separation achieved by Racah for f N ) is shown to take a simpler form if parts off diagonal with respect to N are added to it, thereby accounting for some puzzling coincidences in the eigenvalues of e n .