Threshold resonance effects for $1/R^3$ long-range potentials

We investigate systematically the threshold behavior of scattering cross sections for attractive potentials which have an asymptotic dependence of the type $V(R)\approx-C_3/R^3$. We present numerical results and a theoretical analysis in terms of Jost functions, and we pay close attention to the effects due to near threshold resonances (NTR). Although we restrict our analysis to the single channel case, we show that it is also relevant for the case of weakly coupled many channel problems; in particular, we show that the NTR effects for inelastic scattering can be deduced from the single channel case. Our study could help to identify universal physics in the two-body and three-body systems.