Even-even near-spherical vibrational nuclei, with energy ratio = + + + + / / R E E 4 2 4 2 1 1 1 1 in the range 2-2.5, are investigated within the framework of interacting boson model and q-deformed version of this model, using the ( )U 5 dynamical symmetry. The parametrization of the ( ) U 5 Hamiltonian and q-deformed version are found leading to a description of energy spectra of 33 nuclei with a root mean square deviation from the experimental level energies less than 100 keV. The findings support the fact that we are very near to the critical point symmetries in the real q-deformed vibrational Hamiltonian.

A simple systematic procedure to construct the three-level unitary and orthogonal algebras which appear in the bosonic three -level pairing models and for arbitrary choice of level degeneracies is presented. We draw attention to the existence of the three types of dynamical symmetry. The new analytical expressions of the energies are derived. The results presented show very clearly the duality between orthogonal algebras and the quasi-spin algebras for the three-level system with pairing interactions. The seniority selection rules of the transition operators in three level boson system are given. Illustrative calculations are carried out for U 21 algebra.