An algebraic pairing model with Sp(4) symmetry and its deformation

Abstract

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector-pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0+ ground states, they also have a large effect on the energies of excited states, including especially excited 0+ states. In this paper, we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp(q)(4) to different realizations of u(q)(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0+ states of even–even and odd–odd nuclei in the 1d3/2, 1f7/2 and 1f5/2 2p1/2 2p3/2 1g9/2 shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Spq(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton–neutron interaction along with nonlinear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0+ energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.