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 we show that scattering quantities have a universal behaviour around the zero energy limit. Our methods rely on unitary implementation of scaling x x/ε, p → εp in the Hilbert space L2 (R3) and on a corresponding expansion of the scattering matrix and amplitude in powers of ε around ε = 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.
KeywordsEnergy Limit Point Interaction Finite Order Weighted Sobolev Space Scatter Amplitude
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