Efimov Effect Revisited with Inclusion of Distortions

Abstract

An elementary proof of the 3-body Efimov effect is provided in the case of a separable 2-body potential which binds at zero energy a light particle to a heavy one. The proof proceeds by two steps, namely {\it i)} a projection of the Hamiltonian in a subspace and the observation that the projected Hamiltonian generates an arbitrarily large number of bound states, and {\it ii)} a use of the Hylleraas-Undheim theorem to recover the unprojected Hamiltonian. The definition of the projectors we use can include mean field distortions.