Quantum Deformation Algebra Studied as an Analytical Equivalent of s, d Interacting Boson Model: Energy Spectra

For a complex q-deformation parameter, the analytical energy expression of  SO 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.