Constraining the 12C+12C astrophysical S-factors with the 12C+13C measurements at very low energies

We use an underground counting lab with an extremely low background to perform an activity measurement for the C12+13C system with energies down to Ec.m.=2.323 MeV, at which the 12C(13C,p)24Na cross section is found to be 0.22(7) nb. The C12+13C fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the C12+13C fusion cross section is the first decisive evidence in the carbon isotope systems which rules out the existence of the astrophysical S-factor maximum predicted by the phenomenological hindrance model, while confirming the rising trend of the S-factor towards lower energies predicted by other models, such as CC-M3Y+Rep, DC-TDHF, KNS, SPP and ESW. After normalizing the model predictions with our data, a more reliable upper limit is established for the C12+12C fusion cross sections at stellar energies. Keywords: Fusion cross section, Astrophysical S-factor, Extrapolation models, Hindrance