Quantum Algebraic Description of the Pairing Correlations in a Single-j Nuclear Shell

Abstract

Pairing in a single-j shell is described in terms of two Q-oscillators, one describing the J=0 fermion pairs and the other corresponding to the J≠0 pairs, the deformation parameter Τ = lnQ being related to the inverse of the size of the shell. Using these two oscillators an SUQ(2) algebra is constructed, while a pairing Hamiltonian giving the correct energy eigenvalues up to terms of first order in the small parameter can be written in terms of the Casimir operators of the algebras appearing in the UQ(2) > UQ(1) chain, thus exhibiting a quantum algebraic dynamical symmetry. The additional terms introduced by the Q-oscillator are found to improve the agreement with the experimental data for the neutron pair separation energies of the Sn isotopes, with no extra parameter introduced.