Rigorous derivation of the Efimov effect in a simple model

We consider a system of three identical bosons in R3 with two-body zero-range interactions and a three-body hard-core repulsion of a given radius a > 0. Using a quadratic form approach, we prove that the corresponding Hamiltonian is self-adjoint and bounded from below for any value of a. In particular, this means that the hard-core repulsion is sufficient to prevent the fall to the center phenomenon found by Minlos and Faddeev in their seminal work on the three-body problem in 1961. Furthermore, in the case of infinite two-body scattering length, also known as unitary limit, we prove the Efimov effect, i.e., we show that the Hamiltonian has an infinite sequence of negative eigenvalues En accumulating at zero and fulfilling the asymptotic geometrical law En+1/En → e^{-2 \pi / s_0} for n → +∞ holds, where s_0 ≈ 1.00624.