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

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.