In the framework of the symplectic extension of the Interacting Vector Boson Model (IVBM) a good description of the first excited positive and negative parity bands of the nuclei in the rare earth and the actinide region is achieved. The bands investigated in the model are extended to very high angular momenta as a result of their consideration as "yrast" bands with respect to the symplectic classification of the basis states. The analysis of the eigenvalues of the model Hamiltonian reveals the presence of an interaction between these bands. Due to this iteraction the ∆L = 1 staggering effect between the energies of the states of two bands is also reproduced including the "beat" patterns.

A new dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain Sp(12, R) ⊃ U (3, 3) ⊃ U * (3) ⊗ SU (1, 1) ⊃ SU * (3) ⊃ SO(3), is introduced. The SU * (3) algebra considered in the present paper closely resembles many properties of the SU * (3) limit of IBM-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the SU * (3) energy surface, in particular the addition of a Majorana interaction and an O(6) term to the model Hamiltonian, is studied. The effect of these perturbations results in the formation of a stable triaxial minimum in the energy surface of the IVBM Hamiltonian under consideration. Using a schematic Hamiltonian which possesses a perturbed SU * (3) dynamical symmetry, the theory is applied for the calculation of the low-lying energy spectrum of the nucleus

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