Boson mappings of the fermion dynamical symmetry model

We introduce boson mappings of the fermion dynamical symmetry model (FDSM) 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 results and then as the starting point to obtain some hermitized mappings. By hermitizing the Dyson boson image of the FDSM Hamiltonian through a seniority dictated similarity transformation or by using a Belyaev-Zelevinsky mapping and retaining in both instances one- and two-body terms only, one obtains an IBM type Hamiltonian. FDSM and boson mapped results are then compared for a few typical cases. We reexamine, from the boson point of view, recent statements about an effective SO(6) symmetry when ¹⁹⁶Pt is analyzed in the FDSM and about the appearance of normal (maximal F-spin) and exotic states in an application of the FDSM to ¹³⁴Ba. 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 implications these considerations may have for allowed representations in the IBM and FDSM.