Abstract
The perturbative effects of the inter-electronic Coulomb interaction between atomic configurations can be reproduced by effective operators acting within a particular configuration under study. These effective operators may be resolved into orthogonal operators that act on N electrons at a time. For the atomic l shell, the symplectic labels associated with a given quasi-spin rank K can be found by referring to the branching rules for U(4l+2) to Sp(4l+2) even though the generators of U(4l+2) do not commute with the generators Q of the quasi-spin group SOQ(3). A given N-electron Hermitian orthogonal operator belonging to an irreducible representation of U(4l+2) is shown to correspond to even or odd K according to whether N is even or odd. For anti-Hermiticity, the connection is reversed. For the d shell, the groups U(10), Sp(10) and SO(5) are shown to provide an unambiguous classification of all operators of the type T(00)0, that is, for those scalar with respect to S, L and J. there are 1, 0, 4, 4, 12 and 0 operators corresponding to N=0, 1, 2, 3, 4 and 5. A complete tabulation of the matrix elements of these 21 operators is provided.