Laporte-Platt degeneracies and delta-function interactions

Abstract

The Laporte-Platt degeneracies for the spectroscopic terms of the configurations lN are equivalent, when l=2, to the repeated eigenvalues found by diagonalising a delta-function interaction delta (ri-rj) for electrons i and j. For l>2 a limited generalisation is possible, since terms of maximum multiplicity remain degenerate while much of the degeneracy of the other terms is lost. This is put in the context of group theory, the techniques of which are used to account for the invariably null matrix elements of delta (rh-ri) delta (ri-rj). Configurations involving inequivalent electrons lead to generalisations of the Laporte-Platt degeneracies, and the use of the interaction Sigma delta (ri-rj) provides checks on the matrix elements of the Coulomb interaction.