Coulomb plus separable potential in coupled channels

The two-potential formalism for long-range forces is generalized to coupled channels. Assuming the short-range potential to be separable we treat the proton-proton interaction in the coupled partial waves ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$. We derive the corresponding Coulomb-modified nuclear transition matrices in closed analytic form and calculate the Coulomb distortion of the phase shifts and of the mixing parameter. The separable parametrization proposed for the p-p interaction in ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$ yields an accurate fit to the experimental data available for these channels. The potential completes the description of the N-N interaction by the Graz-II separable model.