Angular-momentum-dependent level density limitation to fusion

Fusion cross sections for the reaction pairs ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (leading to ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$) and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ (leading to ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$) are examined to extract critical angular momenta. At low energies entrance channel effects are present, whereas at higher energies the results are qualitatively consistent with a common limiting angular momentum characteristic of the compound nucleus. Comparison with angular-momentum-dependent level densities suggests that the fusion cross sections at intermediate energy are sensitive to the availability of a sufficient level density in the compound nucleus. A model calculation employing the criterion that the level spacing of a particular angular momentum be comparable to or smaller than the level widths is used to calculate fusion cross sections. The results are in qualitative agreement with experiment, accounting for both the magnitude of the cross sections and the periodicity of the gross structure in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.