Abstract
An extension of the U(3) limit of the vibron model is proposed to incorporate fermionic degrees of freedom in the algebraic model of nuclear clusterization. This approach enables us to treat explicitly nucleons or holes occupying single-particle states of an oscillator shell in one of the clusters. The dynamical symmetries of the vibron-fermion model built on the U(3) boson dynamical symmetry are explored, and the coupled vibron-fermion bases are constructed. Closed expressions are obtained for the energy spectrum in each case. We suggest that the {alpha}-cluster states of the {sup 19}F nucleus may be good examples for the application of the SU(3){times}U(2) dynamical symmetry. This phenomenologic algebraic model shows some similarity with the local potential cluster model of Buck {ital et} {ital al}.
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