  For a class of long-range potentials, including ultra-strong perturbations of
the attractive Coulomb potential in dimension $d\geq3$, we introduce a
stationary scattering theory for Schr\"odinger 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 \cite{DS3}.
Principal tools include global solutions to the eikonal equation and strong
radiation condition bounds.
