Integrable system connected with the Coulomb three-body problem near two-particle thresholds

Abstract

The problem of mixing of degenerated sublevels of a hydrogen-like system by a charged particle is reconsidered from the point of view of the theory of integrable systems on Lie algebras. The Lax representation is constructed both in classical and quantum mechanics. The corresponding dynamical system is a special limit case of a four-sites xxx magnet considered by Gaudin (1976).