The fermion SO(8) model and its connection with an IBM-4 with L = 0 bosons

We discuss two related models of generalized pairing in nuclei. One is a fermion model based on the algebra SO(8). The other is an IBM-4 model restricted to L = 0 bosons. Both models accommodate isovector and isoscalar pairing on an equal footing. We develop in detail the group structure of the IBM-4 with L = 0 bosons and then discuss its relation to the SO(8) model through the use of boson mapping techniques. We show that a Dyson boson mapping of the SO(8) model leads to a version of IBM-4 very similar to the boson model we developed. Indeed, in the SU(4) limit that is common to the two models, we find that they are equivalent. In the two SO(5) limits of the SO(8) model, involving pure isoscalar and pure isovector pairing respectively, equivalence of the models can likewise be shown. Away from these symmetry limits, however, the assumption that the Hamiltonian of IBM-4 with L = 0 bosons is Hermitian and has at most two-boson interactions implies some differences with respect to the SO(8) model