Integrability and exact spectrum of a pairing model for nucleons

Abstract

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the Quantum Inverse Scattering Method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

14 pages, latex, no figures

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• Integrability of the russian doll BCS model
• Isovector pairing in a formalism of quartets for N=Z nuclei
• Integrability and exact solution for coupled BCS systems associated with the $su(4)$ Lie algebra
• Exactly-solvable models of proton and neutron interacting bosons
• SU(3) Richardson-Gaudin models: three level systems
• Band-like structures and quartets in deformed N=Z nuclei
• Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems
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• Integrable Model of Topological SO(5) Superfluidity
• The Oblique Basis Method from an Engineering Point of View
• Richardson-Gaudin Algebras and the Exact Solutions of the Proton-Neutron Pairing
• Challenges for Modeling Nuclear Structure: Are the Proton and Neutron Masses and A-body Interactions Relevant?