Quantum-deformation algebra studied as an analytical equivalent of thes,dinteracting boson model: Energy spectra

For a complex q-deformation parameter, the analytical energy expression of ${\mathrm{SO}}_{\mathit{q}}$(6) symmetry is shown to give all the three limiting symmetries of the U(6) group as well as all the intermediate results of mixed symmetries; i.e., it works equivalently as the numerically solvable general Hamiltonian of the s, d interacting boson model (IBM). Also, a symmetry triangle, equivalent to Casten’s symbolic symmetry triangle for the IBM, is obtained. The q-deformation parameter is found to behave as the symmetry mixing parameter, similar to one in the IBM. Applications are made to a range of nuclei, covering all the possible cases.