Pion scattering to $4^{\mathrm{-}}$ states in ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$

Angular distributions and excitation functions for inelastic scattering of ${\pi }^{+}$ and ${\pi }^{\mathrm{-}}$ from ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ were measured at incident pion energies near the ${\Delta }_{33}$ resonance. Three states at excitation energies 11.7, 15.2, and 17.3 MeV were identified as $4^{\mathrm{-}}$ states. Isovector and isoscalar spectroscopic amplitudes $Z_0$ and $Z_1$, and equivalently, neutron and proton amplitudes $Z_{\mathrm{n}}$ and $Z_{\mathrm{p}}$ were deduced by comparison with microscopic distorted wave impulse approximation calculations. The 11.7-MeV state was found to be excited with a $Z_{\mathrm{n}/Z_{\mathrm{p}}}$ amplitude ratio of -1/3, resulting in a complete cancellation of the ${\pi }^{+}$ cross section. A nearly pure proton excitation was observed for the transition to the 17.3-MeV state. Both results are in qualitative agreement with the presented shell-model calculations. A poor correspondence with theory is found for the 15.2-MeV state. Data and distorted-wave impulse approximation calculations using shell-model wave functions are presented for the first $3^{\mathrm{-}}$ state at 6.73 MeV as an example of a transition dominated by ΔS=0 (no spin transfer). Its excitation function and angular-distribution shape contrast sharply with the transitions to the $4^{\mathrm{-}}$ states that proceed by ΔS=1.