Average Cross Sections for theC12(C12, α)Ne20Reactions

Measurements of the integrated cross sections and angular distributions of the ${\mathrm{C}}^{12}({\mathrm{C}}^{12}, \alpha ){\mathrm{Ne}}^{20}$ reactions, for alpha particles leaving ${\mathrm{Ne}}^{20}$ in the ground state and first excited state, are averaged over the energy interval of 10.15 to 12.8 MeV (in the center-of-mass frame) and compared with calculations based on the statistical theory of nuclear reactions. The calculations employ optical-model transmission functions of the correct energy for each of the channels open to the compound nucleus. The applicability of the statistical theory to heavy-ion reactions is discussed. Quantitative estimates are made of the random error in calculated cross sections arising from the finite size of the averaging interval and the cross-section fluctuations in the interval. Generally good agreement is obtained between calculated and measured average cross sections for both the magnitude of integrated cross sections and the shape of angular distributions. The statistical theory calculations are combined with experimental values of total level widths (found in a parallel paper discussing the cross-section fluctuations underlying our average cross sections) to yield level spacings in ${\mathrm{Mg}}^{24}$, at excitation energies of 20-25 MeV. Individual level spacings for states with $J\Pi =2^{+}, 4^{+}, 8^{+}$ lead to estimates of the spin cutoff parameter. The corresponding value of the moment of inertia for the highly excited states of ${\mathrm{Mg}}^{24}$ is considerably larger than that of the ground-state band.