The modified astrophysical S-factor of the ${}^{12}$C+${}^{12}$C fusion reaction at sub-barrier energies

The 12C+12C fusion reaction plays a crucial role in stellar evolution and explosions. Its main open reaction channels include , p, n, and 8Be. Despite more than a half century of efforts, large differences remain among the experimental data of this reaction measured using various techniques. In this work, we analyze the existing data using a statistical model. Our calculation shows the following: 1) the relative systematic uncertainties of the predicted branching ratios decrease as the predicted ratios increase; 2) the total modified astrophysical S-factors (S * factors) of the p and channels can be obtained by summing the S * factors of their corresponding ground-state transitions and the characteristic rays, while taking into account the contributions of the missing channels to the latter. After applying corrections based on branching ratios predicted by the statistical model, an agreement is achieved among the different data sets at E cm> 4 MeV, while some discrepancies remain at lower energies, suggesting the need for better measurements in the near future. We find that theS * factor recently obtained from an indirect measurement is inconsistent with the direct measurement value at energies below 2.6 MeV. We recommend upper and lower limits for the 12C+12C S * factor based on the existing models. A new 12C+12C reaction rate is also recommended.