Substate Populations and Nuclear Polarization Produced by Inelastic Alpha-Particle Scattering on Carbon-12

We have measured the normalized $\alpha -\gamma$ angular correlation in the reaction plane for excitation of the 4.44-MeV, $2^{+}$ state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 22.750 MeV. These data yield the relative populations ${\left(a_m\right)}^2$ of the three magnetic substates referred to the normal to the reaction plane. The ambiguity between ${\left(a_{+2\mathrm{}}\right)}^2$ and ${\left(a_{-2\mathrm{}}\right)}^2$ was resolved by coincidence measurements of the circular polarization of deexcitation $\gamma$ rays emitted near the normal to the reaction plane. The inelastic scattering process can then be dissected into partial differential cross sections ${\sigma }_m$ to the substates. The results show that each ${\sigma }_m$ has a different angular dependence. ${\sigma }_0$ has the most regular and pronounced diffractionlike structure, ${\sigma }_{-2\mathrm{}}$ dominates out to 75°, and ${\sigma }_{+2\mathrm{}}$ dominates thereafter. Thus, the excited nuclei spin in the sense of classical hard-sphere scattering with friction out to ≈ 75°, and in the reverse sense from ≈ 75° to ≈ 170°. The nuclear polarization exhibits an oscillatory character as a function of angle. Comparison of the results with diffraction-model calculations, and with distorted-wave Born-approximation calculations, is poor. In principle, the experimental method, though difficult, could be applied to nuclei which are more accurately described by nuclear models than is ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.