  Using a recently developed effective field theory for the interactions of
nucleons at non-relativistic energies, we calculate non-perturbatively Coulomb
corrections to proton-proton scattering. Including the dimension-eight
derivative interaction in the PDS regularization scheme, we recover a modified
form of the Blatt-Jackson relation between the scattering lengths. The
effective range receives no corrections from the Coulomb interactions to this
order. Also the case of scattering in channels where the Coulomb force is
attractive, is considered. This is of importance for hadronic atoms.
