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 mod al restricted to L = 0 bosons. Both models accommodate isovector and i soscalar pairing on an equal footing. We develop in detail the group s tructure 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 sho w 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 equiv alent. In the two SO(5) limits of the SO(8) model, involving pure isos calar and pure isovector pairing respectively, equivalence of the mode ls can likewise be shown. Away-from these symmetry limits, however, th e assumption that the Hamiltonian of IBM-4 with L = 0 bosons is Hermit ian and has at most two-boson interactions implies some differences wi th respect to the SO(8) model.