Boson mapping of the proton-neutron dynamical symmetry model

In the present work the boson mappings relevant to the fermionic dynamical symmetric model is studied. The proton-neutron dynamical symmetry model situation of no broken pairs and no scattering of pairs between normal and abnormal parity levels is considered. A several boson mapping procedures which transcribe the Hamiltonian model into a boson one were discussed and obtained results were compared. In particular we deal with the Dyson mapping, seniority mapping, and Belyaev-Zelevinsky mapping. The finite Dyson mapping yields extract results. Its nonunitary nature, however, makes a direct comparison with the standard phenomenological IBN difficult. The other two mappings lead to Hermitian structures for which comparison becomes possible once the associated infinite series expansion have been truncated. The results of the various mapping produced were compared in different regions of the Z=50-82, N=82-126 shell. 190 Os is analyzed extensively and the concept of an effective SO(6) symmetry in proton-neutron symmetry model is examined. It should be noted that the correspondence between the IBM and proton-neutron symmetry model has also been studied a group of theoretical point of view