On the universal low energy limit in nonrelativistic scattering theory

Based on a precise formulation of the physical intuition that low momenta correspond to large distances the authors show that scattering quantities have a universal behaviour around the zero energy limit. The methods rely on unitary implementation of scaling x → x/epsilon, p → epsilonp in the Hilbert space L2(R3) and on a corresponding expansion of the scattering matrix and amplitude in powers of epsilon around epsilon = 0. The results are largely independent of the shape of the interaction, and the leading coefficients in these expansions are described in terms of suitable point interactions. (Auth.)