Other Coupling Schemes — Intermediate Cases

Abstract

The angular momentum coupling schemes covered in the preceding chapters are limiting cases. No real atom has pure LS-coupling or jj-coupling. Often, the spin–orbit interaction and the angular part of the electron–electron repulsion are of similar order of importance, and adding one as a perturbative term before the other leads to erroneous results. The angular momentum vector coupling becomes more complex if there are some interactions between different groups of electrons that are stronger than some of those inside the groups. Two such examples, J ₁K-coupling and LK-coupling are described in this chapter. Before that, we look into some angular momentum interactions that we have hitherto ignored. Finally, we handle cases that must be described by a superposition of LS-coupling and jj-coupling, and we also discuss departures from the central-field approximation where the perturbation Hamiltonian has non-diagonal terms between different electronic configurations.