Two-nucleon processes in a coupled-channel approach to pion-nucleus single-charge-exchange reactions

A momentum space coupled-channel formalism is proposed for the study of pion-nucleus single-charge-exchange reactions at medium energies. Formal elimination of certain reaction channels leads to a reduced set of coupled equations with a complex and energy-dependent interaction. A nonperturbative method based upon unitarity considerations is then used to construct each order of this effective pion-nucleus interaction. Our analysis thus leads to a second-order pion-nucleus interaction with analytical properties very different from those obtained from multiple-scattering theory. The theory is applied to the study of pion-${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ elastic scattering and the single-charge-exchange reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{+},{\pi }^0){}_{}{}^{13}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s})$. Included in our calculations are the first- and second-order pion-nucleus strong interactions, and the pion-nucleus Coulomb interaction. We have calculated the first-order interaction using a covariant, nonstatic theory and have evaluated contributions to the second-order interaction arising from two-nucleon processes related to true pion absorption and to the scattering of pions from a nucleon pair. We present a general relation connecting the second-order pion-nucleus strong interaction potentials of nuclei whose structure do not differ appreciably. Theoretical results for $\pi {}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ elastic scattering predicted by our theory are found to be in good agreement with the data. The calculated excitation function of the single-charge-exchange reaction exhibits a high sensitivity to the type of two-nucleon processes considered. Pion-nucleus single-charge-exchange reactions therefore have promise as a tool for investigating pion-nucleus reaction mechanisms.