Isospin effects inπ±elastic scattering fromC12,C13, andC14at 65 and 80 MeV

Elastic scattering cross sections for ${\pi }^{\pm }$ scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ are presented for pion energies of 65 and 80 MeV and for scattering angles from 20° to 120°. Energy dependent isospin effects are observed. The cross sections were fit with the Kisslinger potential, and the potential strength parameters show an $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$ dependence similar to that predicted by the impulse approximation at 65 MeV, but not at 80 MeV. Calculations using the Siciliano potential, which contains the explicit isospin dependence of the Lorentz-Lorenz-Ericson effect plus isoscalar, isovector, and isotensor terms, indicate the importance and energy dependence of absorption effects. Finally a "model independent" parametrization of the neutron density suggests a neutron excess at the surface of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ but not ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$.