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

TL;DR

This study analyzes existing experimental data on the ${}^{12}$C+${}^{12}$C fusion reaction at sub-barrier energies using a statistical model to reconcile discrepancies and provide updated reaction rates crucial for astrophysics.

Contribution

The paper introduces a systematic correction method for experimental data using statistical model predictions, leading to more consistent S-factor estimates and a new recommended reaction rate.

Findings

Agreement among data sets at energies above 4 MeV after corrections.

Discrepancies remain at energies below 2.6 MeV, indicating need for better measurements.

Recent indirect measurement S* factor is inconsistent with direct data below 2.6 MeV.

Abstract

The $^{12}$C+$^{12}$C fusion reaction plays a crucial role in stellar evolution and explosions. Its open reaction channels mainly include $\alpha$, $p$, $n$, and ${}^{8}$Be. Despite more than a half century of efforts, large discrepancies remain among the experimental data measured using various techniques. In this work, we analyze the existing data using the statistical model. Our calculation shows: 1) the relative systematic uncertainties of the predicted branching ratios get smaller as the predicted ratios increase; 2) the total modified astrophysical S-factors (S$^*$ factors) of the $p$ and $\alpha$ channels can each be obtained by summing the S$^*$ factors of their corresponding ground-state transitions and the characteristic $\gamma$ 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}>$4 MeV, while some discrepancies remain at lower energies suggesting the need for better measurements in the near future. We find that the recent S$^*$ factor obtained from an indirect measurement is inconsistent with the direct measurement at energies below 2.6 MeV. We recommend upper and lower limits for the ${}^{12}$C+${}^{12}$C S$^*$ factor based on the existing models. A new $^{12}$C+$^{12}$C reaction rate is also recommended.