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Axial asymmetry in the IVBM

The dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3) \otimes \overline{U_{n}(3)} \supset SU^{\ast}(3) \supset SO(3)$, is considered and applied for the description of nuclear collective spectra exhibiting axially asymmetric features. The effect of the introduction of a Majorana interaction to the $SU^{\ast}(3)$ model Hamiltonian on the $γ$-band energies is studied. The theoretical predictions are compared with the experimental data for $^{192}Os$, $^{190}Os$, and $^{112}Ru$ isotopes. It is shown that by taking into account the full symplectic structures in the considered dynamical symmetry of the IVBM, the proper description of the energy spectra and the $γ$-band energy staggering of the nuclei under considerations can be achieved. The obtained results show that the potential energy surfaces for the following two nuclei $^{192}Os$ and $^{112}Ru$, possess almost $γ$-flat potentials with very shallow triaxial minima, suggesting a more complex and intermediate situation between $γ$-rigid and $γ$-unstable structures. Additionally, the absolute $B(E2)$ intraband transition probabilities between the states of the ground state band and $γ$ band, as well as the $B(M1)$ interband transition probabilities between the states of the ground and $γ$ bands for the two nuclei $^{192}Os$ and $^{190}Os$ are calculated and compared with experiment and for the $B(E2)$ values with the predictions of some other collective models incorporating the $γ$-rigid or $γ$-unstable structures. The obtained results agree well with the experimental data and reveal the relevance of the used dynamical symmetry of IVBM in the description of nuclei exhibiting axially asymmetric features in their spectra.