Efimov Effect for a Three-Particle System with Two Identical Fermions

We consider a three-particle quantum system in dimension three composed of two identical fermions of mass one and a different particle of mass m. The particles interact via two-body short range potentials. We assume that the Hamiltonians of all the two-particle subsystems do not have bound states with negative energy and, moreover, that the Hamiltonians of the two subsystems made of a fermion and the different particle have a zero-energy resonance. Under these conditions and for , we give a rigorous proof of the occurrence of the Efimov effect, i.e., the existence of infinitely many negative eigenvalues for the three-particle Hamiltonian H. More precisely, we prove that for the number of negative eigenvalues of H is finite and for the number N(z) of negative eigenvalues of H below has the asymptotic behavior for . Moreover, we give an upper and a lower bound for the positive constant .