On the algebraic treatment of the spin–orbit interaction

Abstract

The spin–orbit interaction term in the Hamiltonian H of the heavier atoms or nuclei is a quadratic operator. It does not commute with the central field Hamiltonian H0 and in many cases represents a strong interaction term. In this paper we show how to accommodate this operator within an extended Lie algebra structure that contains the symmetry algebra of H0. The representations of this extended algebra can be used then to classify the states of the Hamiltonian H.