Symplectic symmetry in the nuclear shell model

Abstract

The nature of the general two-particle interaction which is compatible with symplectic symmetry in the jj coupling shell model is investigated. The essential result is that, to within an additive constant and an additive multiple of T2, the interaction should have the form of a sum of scalar products of single-particle tensors which have odd rank in the single-particle j space. An example of an interaction satisfying these conditions is a central interaction with σ1·σ2 exchange nature. The condition for good symplectic symmetry is expressed also as a set of linear constraints on the two-particle energies, again as constraints on the particle-hole energies and finally in terms of the relationship between the particle-particle and particle-hole spectra. When we deal with identical particles only, the conditions for good symplectic symmetry (or seniority) are greatly relaxed and in particular are satisfied for a short-range (δ-function) interaction, as shown earlier by Racah and Talmi.