Analysis of Fusion Reactions with Carbon Isotopes

Fusion data for $^{13}$C+$^{13}$C are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. Quadrupole and octupole transitions to low-lying states in projectile and target are included, as well as mutual excitations of these states. The one-neutron transfer to the $^{12}$C+$^{14}$C mass partition is also considered. By adjusting the parameters of the M3Y+repulsion interaction it is possible to obtain an excellent fit to the data. This requires, however, that the absolute normalization of the calculation is adjusted, and justifications for doing that are discussed. The calibrated M3Y+repulsion interaction is applied to predict the fusion cross section for $^{12}$C+$^{13}$C and good agreement with the data is achieved. The prediction for $^{12}$C+$^{12}$C is in reasonable agreement with the maximum peak cross sections that have been measured, and provides an upper limit for the extrapolation to the low energies that are of interest to astrophysics.