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Integrability and exact spectrum of a pairing model for nucleons

Jon Links, Huan-Qiang Zhou, Mark D Gould and Ross H McKenzie

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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.


PACS

02.30.Ik Integrable systems

03.65.Nk Scattering theory

02.10.Ud Linear algebra

MSC

81U40 Inverse scattering problems

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 30 (2 August 2002)

Received 14 May 2002

Published 19 July 2002



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