An exactly solvable spherical mean-field plus extended monopole pairing model

An extended pairing Hamiltonian that describes pairing interactions among monopole nucleon pairs up to an infinite order in a spherical mean field, such as the spherical shell model, is proposed based on the local E˜2 algebraic structure, which includes the extended pairing interaction within a deformed mean-field theory (Pan et al., 2004) [19] as a special case. The advantage of the model lies in the fact that numerical solutions of the model can be obtained more easily and with less computational time than the solutions to the standard pairing model. Thus, open-shell large-scale calculations within the model become feasible. As an example of the application, pairing contribution to the binding energy of 12–28O is estimated in the present model with neutron pairs allowed to occupy a no-core shell model space of 11 j  -orbits up to the fifth major harmonic oscillator shell including excitations up to 14ħω14ħω for 12O and up to 40ħω40ħω for 28O. The results for 12O are also compared and found to be in agreement with those of ab initio calculations. It is shown that the pairing energy per particle in 12–28O ranges from 0.4 to 1.8 MeV/A with the strongest one observed for a small number of pairs.