50 MeV ${\mathrm{\pi }}^{+}$ and ${\mathrm{\pi }}^{\mathrm{-}}$ scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$

Differential cross sections were measured for 50 MeV ${\mathrm{\pi }}^{+}$ and ${\mathrm{\pi }}^{\mathrm{-}}$ elastic scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and for 50 MeV ${\mathrm{\pi }}^{+}$ inelastic scattering to the (4.44 MeV, $2^{+}$), (7.65 MeV, $0_2^{+}$), (9.64 MeV, $3^{\mathrm{-}}$), (12.71 MeV, $1^{+}$), and (15.11 MeV, $1^{+}$) levels in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Comparisons of the data obtained in this study to data taken previously for these states resolve discrepancies between the earlier data sets. Using a recently discussed procedure, one-step and coupled-channels calculations using a modified MSU potential were performed. The results of both one-step and coupled-channels calculations describe the data for the ground, first, and third excited states, indicative of the collective isoscalar structure of those states. The one-step analysis fails to describe the excitation of the $0_2^{+}$ state. The coupled-channels calculations are more successful in describing those data, indicating that the failure of the one-step calculations may be attributed to coupled-channels effects.