Cuboctahedric Higgs oscillator from the Calogero model

Abstract

We exclude the center of mass of the N-particle rational Calogero model and consider the angular part of the resulting Hamiltonian. We show that it describes the motion of the particle on (N-2)-dimensional sphere interacting with N(N-1)/2 force centers with Higgs oscillator potential. In the case of four-particle system these force centers define the vertexes of an Archimedean solid called cuboctahedron.