Electromagnetic Corrections to the One-Pion-Exchange Potential

Leading-order electromagnetic loop corrections to the one-pion-exchange potential are computed within the framework of chiral perturbation theory. These corrections generate an effective nucleon-nucleon potential, $V_{\pi \gamma }$, which supplements the sum of one-pion-exchange potential and the nucleon-nucleon Coulomb potential. This potential is charge dependent and its construction is demonstrated to be gauge invariant. The potential $V_{\pi \gamma }$ has been included in the Nijmegen partial-wave analysis of $\mathrm{np}$ data. A particular renormalization scheme is chosen that leads to a negligible change in the ${\pi }^{\pm }\mathrm{NN}$ coupling constant and in the $\mathrm{np}$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ scattering length and effective range.