Adiabatic Models of the Efimov Effect

Elementary demonstrations of the 3-body Efimov effect are provided for several models involving a light particle and two heavy ones, and differing by the nature of the 2-body (local or non-local) potentials which bind at zero energy the light particle to each of the heavy ones. The proofs rely on Born-Oppenheimer approximations, which are actually projections of the Hamiltonian into suitable subspaces, and they use the correct reduced mass. A numerical estimate of the long range potential responsible for the accumulation of Efimov bound states is obtained through Padé approximants.