Abstract
We simplify a treatment of pion distortions using a separable expansion of optical potential in momentum space. We use this method to gain insight into the role of distortions in isoelastic pion charge-exchange scattering within the framework of the isospin-invariant optical model. The method provides an analytic procedure for calculating external distortions for single- and double-charge-exchange scattering. This allows us to analyze separately the role of on- and off-shell pions in distortions for each partial wave. Results for sequential scattering at 50 MeV for the reaction $^{14}\mathrm{C}$(${\mathrm{\ensuremath{\pi}}}^{+}$,${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$${)}^{14}$ O are presented. It is shown that the external distortions give a small enhancement in forward directions and reduce the differential cross sections at large angles.