Analysis of elastic and inelastic scattering of 162 MeV pions fromC13by an optical potential and a collective model

Data for elastic scattering of ${\pi }^{+}$ and ${\pi }^{-}$ from ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ at $T_{\pi }=162\mathrm{}$ MeV between ${\theta }_{\mathrm{lab}}=22\mathrm{}° \mathrm{and} 105°$ were analyzed by an optical model. Good fits were obtained with neutron and proton ground state densities of three-parameter Fermi shape having the same rms radius. Inelastic data for the quadrupole transitions to the ${\frac{3}{2}}^{-}$ (3.68 MeV) and ${\frac{5}{2}}^{-}$ (7.55 MeV) states and the octupole transition to a proposed ${\frac{5}{2}}^{+}$, ${\frac{7}{2}}^{+}$ doublet (11.82 MeV) were analyzed using a collective model. The extracted strengths for the neutron and proton parts of the transitions are compared to the results of electron scattering and $\gamma$-ray studies.