Using a recently developed effective field theory for the interactions of n
ucleons at non-relativistic energies, we calculate non-perturbatively Coulo
mb corrections to proton-proton scattering. Including the dimension-eight d
erivative interaction in the PDS regularization scheme, we recover a modifi
ed form of the Blatt-Jackson relation between the scattering lengths. The e
ffective range receives no corrections from the Coulomb interactions to thi
s order. Also the case of scattering in channels where the Coulomb force is
attractive, is considered. This is of importance for hadronic atoms. (C) 2
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