Adiabatic models of the Efimov effect

Elementary demonstrations of the three-body Efimov effect are provided for several models involving a light particle and two heavy ones, and differing by the nature of the two-body (local or nonlocal) 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 Pad{acute e} approximants. {copyright} {ital 1997} {ital The American Physical Society}