APPLICATIONS OF DEFORMED FERMION REALIZATIONS OF $sp(4)$

K. D. Sviratcheva, J. P. Draayer,
  Louisiana State University, Department of Physics and Astronomy, 
 Baton Rouge, Louisiana, USA

A. I. Georgieva
Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia

A fermion representation of the compact symplectic $sp(4)$ algebra provides a natural description of the pairing interaction in nuclei. In the nondeformed and deformed cases the reduction chains to different realization of $u(2)$ and $u_q(2)$ are explored for multiple orbits. One of the realizations is associated with the SU(2) group of the valene isospin. The other reductions describe pairing between identical fermions or proton-neutron configuratrions. Microscopic nondeformed and deformed Hamiltonians are expressed in terms of the generators of $sp(4)$ and $sp_q(4)$. In both cases eigenvalues of the Hamiltonian are fit to experimental ground state energies which allows the role of the deformation to be investigated. The $q$-deformation parameter varies the pairing strength, thereby providing for a nonlinear expansion of the nuclear collective motion.