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

TL;DR

This paper discusses the use of Richardson-Gaudin algebras to obtain exact solutions for proton-neutron pairing models in nuclear physics, highlighting their mathematical properties and potential applications.

Contribution

It extends Richardson-Gaudin models to describe proton-neutron pairing interactions, providing exact solutions for complex nuclear systems.

Findings

Exact solutions for isovector pn-pairing within the so(5) RG-model.

Exact solutions for spin-isospin pn-pairing within the so(8) RG-model.

Summarizes properties and applications of RG-models in nuclear physics.

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.