The excitation functions have been measured in the energy range $E_{\alpha }$=26–37 MeV for the reaction ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$${(}^4$He${,}^{12}$C${)}^{16}$O at ${\theta }_{\mathrm{lab}=30\mathrm{}}$°, 40°, and 50° and for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$${(}^4$He${,}^4$He’${)}^{24}$Mg at ${\theta }_{\mathrm{lab}=152\mathrm{}}$°–160°. Prominent structures are observed in the excitation functions. The cross sections are compared with the Hauser-Feshbach statistical-model calculations. Probability distributions of the deviations from the average are calculated for all the excitation functions and compared with the statistical-model expectations for the fluctuations. The coherence width is estimated to be 176–214 keV from the observed number of maxima in the excitation functions and it is in agreement with the expected value for the excitation region of 32–42 MeV in the compound nucleus. Cross-channel correlations have been calculated between the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ channel and alpha elastic and inelastic scattering channels. At $E_{\alpha }$=27.8 and 28.6 MeV where large cross-channel correlations have been observed, angular distributions of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured and found to follow the pattern [$P_{11}$(cosθ${\left)\right]}^2$. These results show that the excitation functions are all generally in agreement with the fluctuations expected from the statistical model. However, at $E_{\alpha }$=27.8 and 28.6 MeV where large cross-channel correlations are observed, though there is a small chance of less than 6×${10}^{\mathrm{-}4}$ for these to be due to statistical fluctuations, the possibility that these structures at these two energies are nonstatistical in origin cannot also be ruled out.

• Received 5 December 1988

DOI:https://doi.org/10.1103/PhysRevC.39.1856