Separable Potentials and Coulomb Interactions

The scattering of two nonrelativistic charged particles interacting via a short-range separable potential and a repulsive Coulomb potential is studied. The "nuclear" phase shift is given by an explicit formula, identical to that for the neutral-particle case except that the separable potential functions are replaced by their Coulomb-modified counterparts. A simple one-term $S$-wave separable potential of the Yamaguchi type is used to illustrate this result. A perturbation theory is developed and used to relate the proton-proton scattering length and effective range and the corresponding neutron-neutron parameters. The result is in resonable agreement with experiment and with previous calculations using local potentials.