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 m<m∗=(13.607)−1, 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 m>m∗ the number of negative eigenvalues of H is finite and
for m<m∗ the number N(z) of negative eigenvalues of H below z<0 has
the asymptotic behavior N(z)∼C(m)∣log∣z∣∣ for z→0−. Moreover, we give an upper and a lower bound for the positive constant
C(m).Comment: 26 page