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 C-12+C-13 system with energies down to E-c.m. = 2.323 MeV, at which the C-12(C-13, p)Na-24 cross section is found to be 0.22(7) nb. The C-12+C-13 fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the C-12+C-13 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 C-12+C-12 fusion cross sections at stellar energies. (C) 2019 The Author(s). Published by Elsevier B.V.