Generalized seniority for favored J [not equal to] 0 pairs in mixed configurations

Abstract

By assigning a pseudo-spin and pseudo-orbital angular momentum (b-spin and c-spin) to the single-particle states in a mixed configuration of identical nucleons, it is possible to classify as B = 0 objects both the favored pair operators of the surface delta interaction (SDI) and the multipole moment operators, (the latter under suitable assumptions). The favored pair is defined for each J as the specific superposition of two-particle states acted upon by this separable interaction. The SDI is diagonal in the total B- and C-spins; the eigenvalues of a (B, C) multiplet are independent of the total angular momentum J, (J = B + C); and all states with are degenerate (v = total seniority). For the case of a degenerate doublet of levels (lj, l+2)j + 1), e.g. () or (), the specification, B = 0, defines the fa the number of nucleons not members of favored pairs. Exact calculations for the () system show that states with cluster closely about their centers of gravity; therefore, to a good approximation the SDI can be replaced by a generalized pairing interaction depending only on B and v. Possible generalizations are discussed for the case of many degenerate single-particle levels, where this generalized pairing interaction is no longer a good approximation.