Quasispin groups and their generalisations

Abstract

The generators of the full quasispin group SO(8) and of its subgroup SO(7) are constructed from coupled products of annihilation and creation operators for nucleons. The mutually commuting generators for each of these groups are used to identify the irreducible representations occurring in the nuclear l shell for which l<or=3. The embedding of SO(8)*SO(2l+1) in SO(16l+8) is examined, and the apparent confluence of spinor and non-spinor representations when l=0 is shown to correspond to the well known automorphism for D4. A quasispin group complementary to G2 is sought in the nuclear f shell without success. The extension of isospin and spin to an additional spin space leads to the introduction of a unitary symplectic group USp(8) within the new quasispin scheme.