Five-dimensional quasispin toward a complete classification of the isospin characteristics of shell-model states in the seniority scheme
A solution is proposed for the inner multiplicity problem associated with the five-dimensional quasispin description of shell-model states. A classification scheme, in terms of an orthonormal basis, leads to tractable results with definite symmetry properties under particle-hole conjugation. Explicit constructions are given for the R(5) irreducible representations (ω 1 1), (ω 13/2), (t + 1, t) for which the inner multiplicities are never greater than two. For states of seniority v = 2, reduced isospin t = 1, of a configuration j n general expressions are given for the matrix elements of an arbitrary two-body interaction, to determine their n, T dependence, and to isolate those features of the actual interaction among nucleons which are most effective in splitting the isospin degeneracy of such states.