We study the fusion reaction of light systems with one-dimensional barrier penetration model using the $\alpha \text{−}\alpha$ double-folding cluster (DFC) potential. We especially analyze the fusion cross sections of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C},{}^{16}\mathrm{O},{}^{24}\mathrm{Mg},{}^{28}\mathrm{Si},{}^{16}\mathrm{O}+{}^{16}\mathrm{O},{}^{24}\mathrm{Mg}+{}^{24}\mathrm{Mg},{}^{28}\mathrm{Si}$, and ${}^{28}\mathrm{Si}+{}^{28}\mathrm{Si}$ reactions. The results are compared with the one obtained with M3Y double folding (DFM) and the Akyüz-Winther (A-W) potentials. It is found that the calculations with DFM and DFC potentials can reproduce the experimental data much better than the calculations using the A-W potential. We also carried out an analysis on the astrophysical aspect of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C},{}^{16}\mathrm{O}$, and ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ reactions. The calculations using DFC and DFM potentials could fit the $S$-factor data reasonably well. However, the calculated reaction rates are lower than the compilation of Caughlan and Fowler at low temperatures. In the important range of temperatures in stellar evolution, the DFC potential reproduces very satisfactory fitting to the experimental cross section and the $S$-factor data and gives a consistent prediction of astrophysical reaction rates. This finding indicates that the DFC potential could be used as an alternative potential to study the fusion reactions in the astrophysical interest.

• Received 6 July 2014
• Revised 2 October 2014

DOI:https://doi.org/10.1103/PhysRevC.91.015811