The elastic scattering of ${\pi }^{+}$ on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the $P33\mathrm{}$ channel is examined for two different two-body interaction theories. A modified Chew-Low interaction and an energy dependent separable potential, both of which are solved as inverse problems to fit the on-shell two-body data exactly, are used to construct a first order optical potential. Differential cross sections are calculated in the impulse approximation at three energies; below, at, and above the energy of the $\pi$-nucleon resonance in the (3,3) channel. The differences between cross sections of the two models are compared to the differences made by varying the high energy phase shifts in the region where they are not well known experimentally ($E_{\mathrm{c}.\mathrm{m}.\mathrm{}}>1900\mathrm{}$ MeV) and found to be of the same order of magnitude.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\pi ,\pi )$, $E=75, 150, 250$ MeV; calculated $\sigma \left(\theta \right)$ with potential and field theoretic model of $\pi$-nucleon interaction.

• Received 6 August 1975

DOI:https://doi.org/10.1103/PhysRevC.14.204