Entrance channel limit on the fusion of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at high energy

Cross sections for the fusion of ${}_{}{}^{28}{}_{}{}^{}\mathrm{C}$ have been measured at center of mass bombarding energies of 39, 43.5, 48, and 54 MeV. Velocity and energy spectra of reaction products having charge Z≥12 and mass number A≥24 were studied at several angles between ${\mathrm{theta}}_{\mathrm{lab}=2\mathrm{}\mathrm{°}}$ and 13°. Separation of fusion from other processes was made by comparison of kinematic calculations to measured spectra. The extracted critical angular momentum ($l_{\mathrm{cr}{}^{\mathrm{fus})}}$ of 22ħ indicates the existence of an entrance-channel-imposed limit on the high energy fusion cross section. More symmetric systems forming the same compound nucleus, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, have considerably larger limiting angular momenta. This result is consistent with the previous observation of a maximum angular momentum of 22ħ (relative to the entrance channel) for the orbiting dinuclear complex found in studies of back-angle deeply inelastic scattering of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.