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

Abstract

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 localẼ2 algebraic structure, which includes the extended pairing interaction within a deformed mean-field theory [F. Pan, V. G. Gueorguiev, and J. P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)] 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 12−28 O 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 14hω for 12 O and up to 40hω for 28 O. The results for 12 O 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 12−28 O ranges from 0.4-1.8 MeV/A with the strongest one observed for a small number of pairs.

On the importance of np-pairs in the isovector pairing model

“…pp /k pp in 24 Mg and 28 Si, respectively. In short, the number of isovector nppairs is larger in odd-odd N = Z nuclei as described by the charge-independent mean field plus isovector pairing model.…”

“…and those of the neutron quasi-spin group SU I (2){τ [24] and shown in the Supplementary Material Supplementarymaterial.pdf (SM), which provides details of the O(5) basis and the reduced matrix elements needed in the calculation. For any orbit, the irreducible representation (irrep) of O( 5) is denoted by (Ω − v/2, t), where the O(5) seniority number of valence nucleons v and the reduced isospin t indicate that there are v nucleons coupled to the isospin t, which are free from the angular momentum J = 0 and T = 1 pairs.…”

“…where μ and ν are eigenvalues of ς 0 and τ 0 , respectively, Λ and I are the proton and neutron quasi-spin quantum numbers, in which v π and v ν are the proton and neutron seniority numbers, respectively, with [24]…”

An exact solution of spherical mean-field plus a special separable pairing model

“…It has been shown that the set of Gaudin-Richardson equations can be solved easily by using the extended Heine-Stieltjes polynomial approach [21][22][23][24]. The deformed and spherical mean-field plus the extended pairing models have also been proposed, which can be solved more easily than the standard pairing model, especially when both the number of valence nucleon pairs and the number of single-particle orbits are large [25,26].…”

Exact solution of the mean-field plus separable pairing model reexamined

“…The Gaudin-Richardson equations in this case can be solved more easily by using the extended Heine-Stieltjes polynomial approach [6][7][8][9]. The deformed and spherical mean-field plus the extended pairing models have also been proposed, which can be solved more easily than the standard pairing model, especially when both the number of valence nucleon pairs and the number of single-particle orbits are large [10,11].…”