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 ¹²C+¹³C system with energies down to _{E c . m .} = 2.323 MeV, at which the ¹²C(¹³C,p)²⁴Na cross section is found to be 0.22(7) nb. The ¹²C+¹³C fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the ¹²C+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 ¹²C+¹²C fusion cross sections at stellar energies.