BOSON MAPPINGS OF THE FERMION DYNAMICAL SYMMETRY MODEL

We introduce boson mappings of the fermion dynamical symmetry model (F DSM) to investigate and clarify the relation between the FDSM and the proton-neutron interacting boson model (IBM). The Dyson boson mapping is employed in a dual role-it is first used to obtain exact FDSM resul ts and then as the starting point to obtain some hermitized mapping. B y hermitizing the Dyson boson image of the FDSM Hamiltonian through a seniority dictated similarity transformation or by using a Belyaev-Zel evinsky mapping and retaining in both instances one- and two-body term s only, one obtains an IBM type Hamiltonian. FDSM and boson mapped res ults are then compared for a few typical cases. We reexamine, from the boson point of view, recent statements about an effective SO(6) symme try when Pt-196 is analyzed in the FDSM and about the appearance of no rmal (maximal F-spin) and exotic states in an application of the FDSM to Ba-134. Throughout our analysis possible spurious states, which may appear as a result of an effective overcompleteness in the (linearly independent) boson basis, are properly identified. We discuss when and where these states appear in the spectra, and the possible implicatio ns these considerations may have for allowed representations in the IB M and FDSM.