Analysis of elastic and inelastic scattering of 162 MeV pions from C13 by an optical potential and a collective model

Data for elastic scattering of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ from $^{13}\mathrm{C}$ at ${T}_{\ensuremath{\pi}}=162$ MeV between ${\ensuremath{\theta}}_{\mathrm{lab}}=22\ifmmode^\circ\else\textdegree\fi{} \mathrm{and} 105\ifmmode^\circ\else\textdegree\fi{}$ 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 ${\frac{3}{2}}^{\ensuremath{-}}$ (3.68 MeV) and ${\frac{5}{2}}^{\ensuremath{-}}$ (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 $\ensuremath{\gamma}$-ray studies.NUCLEAR REACTIONS $^{13}\mathrm{C}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}\ensuremath{'}}, {\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}})$, ${T}_{\ensuremath{\pi}}=162$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$. Optical model and collective model analysis. $B(\mathrm{EL})$ deduced.