Parameter-dependent quasispin group

Abstract

A nonconventional generalization of the quasispin formalism for N identical particles is presented. The generators S₊ = Σ_ip_iS₊ⁱ, S₋ = Σ_ip_i⁻¹S₋ⁱ, S_z = Σ_iS_zⁱ of this quasispin group depend on the dynamical parameters p_i. This parameter-dependent quasispin group appears as a deformation of the conventional quasispin group (p_i = 1). With such a definition of the quasispin group, the 2n-projection S₊ⁿ|0> of the BCS state is seen to be an exact generalized seniority zero state. More precisely, this dynamical quasispin group provides the mathematical framework to discuss the earlier generalization of Talmi et al. Theoretical and numerical calculations of the generalized seniority zero multiplet have been carried out for the nickel and tin isotopes.