Angular distributions for elastic and inelastic scattering of ${\pi }^{+}$ projectiles from natural carbon and silicon targets at energies of ∼35 and 68 MeV are reported. The elastic data, along with other reported low energy pion scattering data for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, is fitted using the zero-range four-parameter ($b_0,b_1$) Kisslinger optical potential. The best-fit potential is found to be nearly independent of energy between 30 and 68 MeV, the largest energy dependence being in $\mathrm{Re}\left(b_0\right)$ which changes by 30%. Simple distorted-wave impulse approximation calculations which succeed in describing the $2^{+}$ 4.4 MeV cross section at 48.5 MeV do much worse at 67.5 MeV for angles where the $2^{+}$ cross section is comparable to or larger than the elastic cross section. This suggests that a coupled channels calculation is needed. The poor agreement between data and theory for the $0^{+}$ (7.6 MeV) and $3^{-}$ (9.6 MeV) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ transitions found earlier at 48.5 MeV persists at 67.5 MeV. The shape of the pion energy spectra and the energy integrated inelastic angular distribution at 67.5 MeV is poorly described by a quasifree pion-nucleon scattering process.

NUCLEAR REACTIONS Elastic and inelastic scattering of 35 and 68 MeV ${\pi }^{+}$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Angular distributions: $25°<~\theta <~150°$. Optical model and DWIA analysis of cross-section data.

• Received 30 October 1980

DOI:https://doi.org/10.1103/PhysRevC.23.1635