Angular distributions for elastic and inelastic scattering of ∼ 50 MeV ${\pi }^{+}$ projectiles from targets of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, Si, and Fe are reported. Systematic differences between the experimental results and predictions of some first-order theories constructed from free $\pi -N$ amplitudes are observed for all cases studied. These discrepancies are similar to those reported earlier. Although several improved optical models exist which take into account better treatments of the first-order potential as well as some second-order effects such as $\pi$ absorption and the Lorentz-Lorentz effect, good agreement with the data cannot be achieved without a phenomenological adjustment of the potential parameters. A purely phenomenological Kisslinger potential when used to fit the data yields potential parameters which are independent of mass number over the $A$ region studied. The resulting $p$-wave parameter $b_1$ is close to the value predicted from free $\pi N$ models, while the $s$-wave parameter $b_0$ requires severe adjustment of both real and imaginary parts from the value predicted from free $\pi N$ models. The inelastic results are compared to distorted-wave Born-approximation calculations, which are seen to manifest characteristics similar to those seen in the elastic channel. A common optical potential is found to provide a good description of both elastic and inelastic scattering.

NUCLEAR REACTIONS Elastic and inelastic scattering of 50 MeV ${\pi }^{+}$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, Si and Fe. Angular distributions: $25°<{\ominus }_L<145\mathrm{}°$. Optical model and DWBA of cross-section data.

• Received 12 June 1978

DOI:https://doi.org/10.1103/PhysRevC.19.971