# Description of mixed-mode dynamics within the symplectic extension of the interacting vector boson model

#### Abstract

In the algebraic Interacting Vector Boson Model (IVBM) it is assumed that the nuclear dynamics can be described by means of two types of vector "quasiparticles," which are also characterized by another quantum number-a "T-spin" (an analogue to the F-spin). The non-compact symplectic group Sp(12, R) appears as the group of dynamical symmetry for the problem of two interacting vector bosons. The symplectic structure allows the change in the number of phonons, needed to build the collective states, that results in larger model spaces, which can accommodate the more complex structural effects as observed in the contemporary experiment. The applications of the IVBM are extended by exploiting three new subgroup chains in the reduction of Sp(12, R) to the physical angular momentum subgroup SO(3). The corresponding exactly solvable limiting cases are applied to achieve a description of complex nuclear collective spectra of even-even nuclei in the rare earth and actinide regions up to states of very high angular momentum. The first reduction that we exploit is one that extends the rotational limit of the number preserving version of the model; namely, Sp(12, R) ⊃ U(6) ⊃ U(2) ⊗ SU(3). Another limit of the symplectic IVBM, Sp(12, R) ⊃ Sp(2, R) ⊗ SO(6), contains in a natural way the 6-dimensional Davidson potential. In both of these cases, because collective modes can be mixed, we obtain successful descriptions of both positive and negative parity band configurations. The structure of band-head configurations, whose importance is established in the first two limits, is also examined in a third reduction, Sp(12, R) ⊃ Sp(4, R) ⊗ SO(3). The distributions of energies that are obtained in this limit with respect to the number of bosons that build each of the states with fixed angular momentum, enables one to distinguish typical collective vibrational and rotational spectra. This algebraic chain also provides important links between the subgroups of the other limits. The symplectic extension of the IVBM permits a richer classification of the states than its unitary version and is shown to be appropriate for a description of rather diverse nuclear spectra. © 2009 Pleiades Publishing, Ltd.

*This paper has been withdrawn.*