Pion Single-Charge Exchange in the Isobar Doorway Model

The isobar doorway model of Kisslinger and Wang is extended to include the pion single-charge-exchange channel in addition to the elastic one. By use of this model, the integrated charge-exchange cross section to the isospin analog state is calculated and compared with the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{+}, {\pi }^0){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ measurements. Good agreement with experiment is achieved. The connection between elastic scattering and charge exchange is discussed.