The angular correlation between inelastically scattered $\alpha$ particles and the subsequent deexcitation $\gamma$ ray has been measured at an $\alpha$ energy of 42 MeV. Measurements have been carried out in the reaction plane for $\gamma$ rays resulting from the decay of the first excited ($2^{+}$) state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$. The results are reported in terms of the $\gamma$-ray symmetry angle, ${\theta }_0$, and the ratio $\frac{A}{B}$. Qualitatively the behavior of the symmetry angle is found to be the same for all four isotopes, rotating continuously at forward $\alpha$-scattering angles and oscillating about the plane-wave and adiabatic predictions at larger $\alpha$-scattering angles. For the three isotopes for which $\frac{A}{B}$ measurements were possible, the ratio was clearly not identically zero. Both the angular-correlation and cross-section data are compared with the results of distorted-wave-Born-approximation calculations using a wide range of optical-model parameters. The optical-model ambiguities encountered here are similar to those found in fitting cross-section data alone.

• Received 12 March 1971

DOI:https://doi.org/10.1103/PhysRevC.4.1159