Triaxial Shapes in the Interacting Vector Boson Model

A new dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U^{\ast}(3) \otimes SU(1,1) \supset SU^{\ast}(3) \supset SO(3)$, is introduced. The $SU^{\ast}(3)$ algebra considered in the present paper closely resembles many properties of the $SU^{\ast}(3)$ limit of IBM-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the $SU^{\ast}(3)$ energy surface, in particular the addition of a Majorana interaction and an O(6) term to the model Hamiltonian, is studied. The effect of these perturbations results in the formation of a stable triaxial minimum in the energy surface of the IVBM Hamiltonian under consideration. Using a schematic Hamiltonian which possesses a perturbed $SU^{\ast}(3)$ dynamical symmetry, the theory is applied for the calculation of the low-lying energy spectrum of the nucleus $^{192}$Os. The theoretical results obtained agree reasonably with the experimental data and show a very shallow triaxial minimum in the energy surface for the ground state in $^{192}$Os, suggesting that the newly proposed dynamical symmetry might be appropriate for the description of the collective properties of different nuclei, exhibiting triaxial features.