q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su _q (2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u _q (2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0⁺ states in the deformed and nondeformed cases.