Bayesian analysis on non-resonant behavior of 12C + 12C fusion reaction at sub-barrier energies

Controversies exist among experiments and theories on the begin{document}$ S^star$end{document} factor of the astrophysical important reaction ¹²C + ¹²C for energies below 3 MeV. Only frequentist approaches have been used so far for data analysis, and the confidence levels or theoretical errors are not available from previous theoretical predictions. In this study, the Bayesian method is employed to provide theoretical predictions and its 1σ confidence level based on all the currently available experimental data for the first time. The improved coupled-channels model CCFULL-FEM implemented with the finite element method as well as the Markov chain Monte Carlo approach emcee are adopted to analyze the non-resonant behavior of this reaction. The posterior distribution of the Woods-Saxon potential parameters is investigated. Compared with the widely used frequentist method MIGRAD within the Minuit minimization program, the Bayesian method has a significant advantage for exploring the potential parameter space. When the existing experimental data measured down to subbarrier energies are considered, the potential parameters are constrained to a very narrow range, and the predictions of the begin{document}$ S^star$end{document} factor showed no sharp decrease in the low-energy region.