Isovector neutron-proton pairing with particle number projected BCS

Abstract

The particle number projected BCS (PBCS) approximation is tested against the exact solution of the SO(5) Richardson-Gaudin model for isovector pairing in a system of non-degenerate single particle orbits. Two isovector PBCS wave functions are considered. One is constructed as a single proton-neutron pair condensate, while the other corresponds to a product of a neutron pair condensate and a proton pair condensate. The PBCS equations are solved using a recurrence method and the analysis is performed for systems with an equal number of neutrons and protons distributed in a sequence of equally spaced 4-fold (spin-isospin) degenerate levels. The results show that although PBCS improves significantly over BCS, the agreement of PBCS with the exact solution is less satisfactory than in the case of the SU(2) Richardson model for pairing between like particles.

14 pages,8 figures

References in corpus (8)

• Competition Between T=0 and T=1 Pairing in Proton-Rich Nuclei
• Pairing and Isospin Symmetry in Proton-Rich Nuclei
• Neutron-Proton Correlations in an Exactly Solvable Model
• Boson mappings and four-particle correlations in algebraic neutron-proton pairing models
• Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian
• Accuracy of BCS-based approximations for pairing in small Fermi systems
• Integrability and exact spectrum of a pairing model for nucleons
• Structure of the vacuum states in the presence of isovector and isoscalar pairing correlations

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