Chapter 5 - Nuclear Spin Statistical Weights

Abstract

Total rovibronic functions, inclusive of nuclear spin, are required to be invariant or to change sign under permutation operations (or proper operations), depending on whether the number of pairs of fermions interchanged is even or odd. The behavior under permutation-inversion operations (or improper operations) depends also on parity. The symmetries of the rovibronic and nuclear spin factors of an allowed function must be such that the required total symmetry species is matched. Once the symmetry species of the nuclear spin functions have been determined by the methods of group theory, the number of nuclear spin functions (nuclear spin multiplicity) compatible with a rovibronic state of given symmetry can be determined. In the absence of improper operations, each state occurs with a positive and a negative component, which are degenerate. This corresponds to the coexistence of two optical isomers.