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

TL;DR

This study measures the $^{12}$C+$^{13}$C fusion cross section at very low energies using an underground lab, providing new constraints on astrophysical S-factors and refining models relevant to stellar nucleosynthesis.

Contribution

It offers the first decisive experimental evidence against the S-factor maximum prediction in $^{12}$C+$^{13}$C fusion, and refines the upper limits for $^{12}$C+$^{12}$C fusion at stellar energies.

Findings

$^{12}$C+$^{13}$C fusion cross section measured down to 2.323 MeV.

Evidence against the S-factor maximum predicted by hindrance models.

Normalized models to establish upper limits for $^{12}$C+$^{12}$C fusion.

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 $E\rm_{c.m.}$=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.