Analysis of the SU(3) symmetry versus rotor model

The SU(3) symmetry, the subgroup in the dynamic chain of the SU(6) group in the interacting boson model (IBM), corresponds to the Bohr-Mottelson rotor model for axially symmetric deformed nuclei. It is synonymous but not identical to it. The common characteristics of the two models and their contrasting features are illustrated. The effect of adding the pairing term in the IBM SU(3) Hamiltonian to bring it closer to the rotor model is highlighted. The modified SU(3) Hamiltonian expression breaks the degeneracy of the beta and gamma bands in the SU(3) spectrum. The different ways to produce the forbidden E2 transitions across the different (lambda, mu)-multiplets are discussed. The related features of SL(3, R) symmetry group are illustrated. We point out that the additional pairing term affects only certain states, preserving the rotational features of the other states in the SU(3) spectrum.