Renormalized two-body low-energy scattering

Abstract

For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension d ≥ 3, we introduce a stationary scattering theory for Schrodinger operators which is regular at zero energy. In particular, it is well-defined at this energy, and we use it to establish a characterization there of the set of generalized eigenfunctions in an appropriately adapted Besov space, generalizing parts of [DS1]. Principal tools include global solutions of the eikonal equation and strong radiation condition bounds.