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

Abstract

We use an underground counting lab with an extremely low background to perform an activity measurement for the ${}^{12}$C+${}^{13}$C system with energies down to $E{}_{c.m.}$=2.323 MeV, at which the ${}^{12}$C(${}^{13}$C,$p$)${}^{24}$Na cross section is found to be 0.22(7) nb. The ${}^{12}$C+${}^{13}$C fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the ${}^{12}$C+${}^{13}$C 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 ${}^{12}$C+${}^{12}$C fusion cross sections at stellar energies.