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arXiv · 1011.5944

Richardson-Gaudin Algebras and the Exact Solutions of the Proton-Neutron Pairing

V. G. Gueorguiev·J. Dukelsky
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Abstract

Many exactly solvable models are based on Lie algebras. The pairing interaction is important in nuclear physics and its exact solution for identical particles in non-degenerate single-particle levels was first given by Richardson in 1963. His solution and its generalization to Richardson-Gaudin quasi-exactly solvable models have attracted the attention of many contemporary researchers and resulted in the exact solution of the isovector pn-pairing within the so(5) RG-model and the equal strength spin-isospin pn-pairing within the so(8) RG-model. Basic properties of the RG-models are summarized and possible applications to nuclear physics are emphasized. MSC2010 Classification: 81U15 Exactly and quasi-solvable systems, 17B81 Applications to physics, 81V35 Nuclear physics, 81R40 Symmetry breaking.

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V. G. Gueorguiev, J. Dukelsky. 2010-11-27. Richardson-Gaudin Algebras and the Exact Solutions of the Proton-Neutron Pairing. https://arxiv.org/abs/1011.5944

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