Vibrational, rotational, and triaxiality features in extended O(6) dynamical symmetry of IBM using three-body interactions

The shape transition between the vibrational U(5) and deformed $$\gamma$$-unstable O(6) dynamical symmetries of sd interacting boson model has been investigated by considering a modified O(6) Hamiltonian, providing that the coefficients of the Casimir operator of O(5) are N-dependent, where N is the total number of bosons. The modified O(6) Hamiltonian does not contain the number operator of the d boson, which is responsible for the vibrational motions. In addition, the deformation features can be achieved without using the SU(3) limit by adding to the O(6) dynamical symmetry the three-body interaction $$\left[ QQQ\right] ^{(0)}$$, where Q is the O(6) symmetric quadrupole operator. Moreover, triaxiality can be generated through the inclusion of the cubic d-boson interaction $$\left[ d^\dag d^\dag d^\dag \right] ^{(3)}\cdot [{\tilde{d}}{\tilde{d}}{\tilde{d}}]^{(3)}$$. The classical limit of the potential energy surface (PES), which represents the expected value of the total Hamiltonian in a coherent state, is studied and examined. The modified O(6) model is applied to the even–even $$^{124-132}$$Xe isotopes. The parameters for the Hamiltonian and the PESs are calculated using a simulated search program to obtain the minimum root mean square deviation between the calculated and experimental excitation energies and B(E2) values for a number of low-lying levels. A good agreement between the calculations and experiment results is found.