The U(5)?O(6) Transitional Description In The Interacting Boson Fermion Model

The Interacting Boson Fermion Model (IBFM) is the further extension of the Inter-action Boson Model. Based on the Interaction Boson Model, which describes the collective motions of the nucleus with both proton and neutron numbers even, the IBFM is developed to describe collective motions of odd mass nucleus. For odd mass nucleus, its collective motions can be described by the collective motions of an even-even core and a coupling of a valence nucleon to the core. The Hamiltonian of the model is constructed with three parts, the boson core part, a fermion part originated from the shell model, and a coupling of the core with the fermion, respectively. According to the Interaction Boson Model, when the even core is in the U(5), SU(3), and O(6) limiting cases, there are three corresponding dy-namical symmetries. In this thesis, the fermion is assumed in a single j orbit. By coupling the fermion to the even-even core in the U(5)(?)O(6) transitional region with definite total angular momentum, the basis vectors of the system is thus established. A Mathemat-ica package for diagonalizing the Hamiltonian is compiled, with which quantum transitional patterns of level energies and E2 transitional rates as functions of model parameters in the u(5)(?)O(6) transitional region can be obtained. The shape phase transitional behavior in this region is analyzed. Energy spectra and some E2 transitional rates of odd-mass Ba and Xe nuclei are calculated and compared with the corresponding experimental results.