Limiting Angular Momenta for Light Heavy-Ion Fusion at High Energy

The shapes of angular distributions in reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, $\alpha$) to the $J^{\pi }=0^{+}$ ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ ground state are studied from $E\left({}_{}{}^{16}{}_{}{}^{}\mathrm{O}\right)=28.5\mathrm{} \mathrm{to} 100$ MeV. The position of the first minimum (and maximum) of these oscillatory angular distributions is expected to be sensitive to the presence of a low-angular-momentum cutoff in the compound-nucleus formation cross section. No evidence for a low-$L$ cutoff is found even at energies well beyond the predicted threshold.