A GENERALIZED QUASI-SPIN FORMALISM

The quasi-spin formalism applied to identical fermions in jj coupling is known to lead to a classification of states in terms of Racah's seniority quantum number. This formalism is here generalized to include isotopic spin, and it is found that the quasi-spin operators then generate a rotation group in five dimensions. The classification which results is equivalent to that introduced by Flowers in 1952 for the configuration jn in terms of the seniority and the reduced isotopic spin. In LS coupling with isotopic spin the quasi-spin operators appear to span a rotation group in eight dimensions. The new formalism is thought to be useful in problems involving mixed configurations in which a charge-independent pairing force is the dominant interaction.