Medium modification of meson propagation between two nucleons in finite nuclei

We derive simple expressions for the effect of medium modifications (or distortions) on the propagation of a pion between two nucleons in a nucleus. Our results are applicable to pion reactions in a variety of situations, but we are particularly interested in the influence of distortions on pion double charge exchange at low energy. We are able to calculate these distortions for a finite nucleus using a realistic choice of optical potential. We represent their effect as a modification of the S- and P-wave pion-nucleon scattering amplitudes that occur at the location of the first (or last) nucleon to be struck. We illustrate our method by showing numerical results for a shematic optical potential