Study of fusion hindrance in the system $^{12}$C+$^{24}$Mg

The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behaviour of heavy-ion fusion at extreme sub-barrier energies, including reactions involving lighter systems, e.g. reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the S-factor vs. energy. Whether there is an S-factor maximum at very low energies for systems with a positive fusion Q-value is an experimentally challenging question. Our aim has been to search evidence for fusion hindrance in 12C + 24Mg which is a medium-light systems with positive Q-value for fusion, besides the heavier cases where hindrance is recognised to be a general phenomenon. The experiment has been performed at the XTU Tandem accelerator of LNL by directly detecting the fusion evaporation residues at very forward angles. The excitation function has been extended down to sime10μb, i.e. 4 orders of magnitude lower than previous measurements and we observe that the S-factor develops a clear maximum vs. energy. Coupled-Channels calculations using a Woods-Saxon potential give a good account of the data near and above the barrier but over predict the cross sections at very low energies. Therefore the hindrance phenomenon is clearly recognised in 12 C + 24 Mg with an energy threshold that nicely fits the systematics in several medium-light systems. The fusion cross sections at the hindrance threshold show that the highest value (as=1.6mb) is indeed found for this system. It may be possible to extend the measurements further down in energy.