A Bayesian analysis of the astrophysical S factor for the ^12C+^12C fusion reaction is presented, based on available experimental information at carbon--carbon relative energies E 2~MeV, including direct measurements, indirect Coulomb-renormalized Trojan Horse Method (THM) results, and recent inverse-kinematics data. The Bayesian inference is performed on the quantity ₁₀S^* (E) rather than on S^* (E) itself, which naturally accommodates the wide dynamic range of the data and leads to approximately Gaussian uncertainties. The logarithm of the astrophysical factor is parametrized by a quadratic polynomial in energy, and the posterior distribution of the fit coefficients is determined using a weighted Bayesian regression. From this posterior, a global median S^* (E) curve is constructed, and the associated covariance matrix is used to define a low/medium/high (LO/MED/HI) band corresponding to a 68\% credible interval. Particular emphasis is placed on the extrapolation below E₂₌=2~MeV, where the fusion reaction rate is most relevant for stellar carbon burning. At E₂₌=1. 5~MeV, the posterior distribution yields S₆₋₎₁₀₋^* (1. 5~MeV) = (2. 13^+0. 01-₀. ₀₁) 10^16\, keV\, b, corresponding to a 68\% credible interval. The extracted result is consistent with recent inverse-kinematics measurements and with Coulomb-corrected Trojan Horse Method constraints, providing a tightly constrained estimate of the ^12C+^12C fusion S factor in the energy region relevant for stellar carbon burning.
A. M. Mukhamedzhanov (Thu,) studied this question.