Virtual Pion Scattering

We propose a theory which exploits the charge-exchange reactions ($^3$He,$^3$H$\pi^+$) and (p,n$\pi^+$) as effective sources of virtual pions. We consider processes in which the creation of virtual pions is followed by conventional coupled-channel pion scattering to discrete nuclear states. This picture allows us to incorporate successful theories of pion scattering and utilize virtual pions as probes of the nuclear matter. For coherent pion production we clearly demonstrate that the shift of the coherent peak position in the excitation function of $^3$He-A relative to $^3$He-N scattering is determined entirely by the pion nucleus rescattering.