We use the fact that the mass of the pion is much smaller than the mass of the nucleon to derive an expression for the first-order pion-nucleus optical potential that includes the effect of the nuclear Hamiltonian through a single-particle model. We apply this potential to calculate the total and reaction cross sections of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and the charge-exchange cross section to the isobaric analog state in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ for energies between 0 and 300 MeV, obtaining qualitative agreement with experiment.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$(${\pi }^{+}$,${\pi }^0$), ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\pi }^{+}$,${\pi }^{+}$), $E=0-300\mathrm{}$ MeV; calculated ${\sigma }_{\mathrm{tot}}\mathrm{}\left(E\right)\mathrm{}$, ${\sigma }_{\mathrm{reac}}\mathrm{}\left(E\right)\mathrm{}$, and ${\sigma }_{\mathrm{cex}}\mathrm{}\left(E\right)\mathrm{}$.

• Received 6 November 1979

DOI:https://doi.org/10.1103/PhysRevC.21.2094