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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 $Erm_{c.m.}$=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.
Carbon and oxygen burning reactions, in particular, $^{12}$C+$^{12}$C fusion, are important for the understanding and interpretation of the late phases of stellar evolution as well as the ignition and nucleosynthesis in cataclysmic binary systems suc
The $^{12}$C+$^{12}$C fusion reaction plays a crucial role in stellar evolution and explosions. Its open reaction channels mainly include $alpha$, $p$, $n$, and ${}^{8}$Be. Despite more than a half century of efforts, large discrepancies remain among
A quantitative study of the astrophysically important sub-barrier fusion of $^{12}$C+$^{12}$C is presented. Low-energy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. A collect
The neutron yield in $^{12}$C(d,n)$^{13}$N and the proton yield in $^{12}C(d,p)^{13}$C have been measured by deuteron beam from 0.6 MeV to 3 MeV which is delivered from a 4-MeV electro static accelerator bombarding on the thick carbon target. The neu
The ${}^{12}mathrm{C} + {}^{12}mathrm{C}$ fusion reaction plays a vital role in the explosive phenomena of the universe. The resonances in the Gamow window rule its reaction rate and products. Hence, the determination of the resonance parameters by n