Spin-Dependent Operators in the Occupation-Branching Number Representation

In two preceding papers, a general method was given of building up open-shell wavefunctions which are eigen-functions of the spin operators S2. This method leads to a second quantizationtype formalism, where degenerate multiplets are described in what we call the occupation-branching number representation. In the paper referred to as Paper II, equivalent monoelectronic and bielectronic operators were defined and a diagrammatic technique was developed. In the present paper, the equivalent spin-dependent operators in the occupation-branching number representation are built up, in the cases of monoelectronic and bielectronic operators. The spin-orbit and the spin-spin coupling are the most important operators of this kind. The associated diagrammatic representation is given.