Study of the reaction ${\pi }^{-}+{}_{}{}^{12}{}_{}{}^{}\mathrm{C}\to {\pi }^{-}+{}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ (4.44 MeV) at 4.5 GeV/c

Characteristic 4.44-MeV $\gamma$ rays from the first excited state of carbon were observed in coincidence with scattered 4.5-GeV/c ${\pi }^{-}$ mesons in counters and wire spark chambers. The $\gamma$-ray angular distribution in the momentum-transfer frame confirms the electric quadrupole nature of the transition and reveals the polarization of the recoiling ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}*$ nucleus so that density matrix elements can be determined. A simple model with no adjustable parameters, which employs the distorted-wave impulse approximation and uses electron scattering data to obtain the nuclear transition matrix elements, predicts the angular distribution of the pions and the polarization of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}*$ recoils very well. However, the absolute values of the measured cross sections are only half as large as the predicted ones.