Correlation between the ¹²C+¹²C, ¹²C+¹³C, and ¹³C+¹³C fusion cross sections

The fusion cross section for ¹²C+¹³C has been measured down to E_c.m.=2.6 MeV, at which the cross section is of the order of 20 nb. By comparing the cross sections for the three carbon isotope systems, ¹²C+¹²C, ¹²C+¹³C, and ¹³C+¹³C, it is found that the cross sections for ¹²C+¹³C and ¹³C+¹³C provide an upper limit for the fusion cross section of ¹²C+¹²C over a wide energy range. After calibrating the effective nuclear potential for ¹²C+¹²C using the ¹²C+¹³C and ¹³C+¹³C fusion cross sections, it is found that a coupled-channels calculation with the ingoing wave boundary condition (IWBC) is capable of predicting the major peak cross sections in ¹²C+¹²C. A qualitative explanation for this upper limit is provided by the Nogami-Imanishi model and by level density differences among the compound nuclei. It is found that the strong resonance found at 2.14 MeV in ¹²C+¹²C exceeds this upper limit by a factor of more than 20. The preliminary result from the most recent measurement shows a much smaller cross section at this energy, which agrees with our predicted upper limit.