Pion-nucleus charge exchange reactions in the isobar-doorway model

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Abstract
The isobar-doorway model, previously applied to the study of pion-nucleus elastic scatterings, is generalized to the treatment of single and double charge exchange reactions. The charge exchange amplitudes are calculated within the framework of distorted-wave Born approximation, where the resonant distortion of the elastic scattering wave functions in the initial and final channels as well as the resonant part of the charge exchange interaction are explicitly taken into account. In the isobar-doorway model, it is shown that the transition amplitude depends upon quantities related to the elastic scattering and to a charge exchange amplitude which contains nonresonant initial and final pion wave functions. The strong energy dependence in various components of single and double charge exchange amplitudes is clearly displayed in the model; this energy dependence due to the (3,3) isobar in the reaction mechanism (including initial- and final-state interactions) may also be separated out from the nuclear structure information as contained in the nuclear form factors. This separation is obtained through the static and the closure approximations which are in the isobar-doorway model.