Refining the deep sub-barrier 12C+12C excitation function with STELLA
Purpose: We have investigated the cross section around the lowest direct coincident gamma-particle measurements, where previously only limits could be established with the aim of obtaining a detailed description of the excitation function. We have furthermore analysed the ratio of extreme decay branching into the first excited state of daughter nuclei with alpha or proton emission at relative kinetic energies where previous measurements are in disagreement with each other. Conclusions: Our findings in the astrophysics RoI support reaction-rate models with a lower average S-factor trend, that deviates significantly from standard extrapolations between 2.2 MeV and 2.6 MeV, for stellar carbon burning simulations of up to 25 Msol stars. Based on our data, an overall increase of the S-factor at deep subbarrier energy cannot be confirmed. The extremely low ratio of the branching into the first excited state with proton over alpha emission of ~ 2% at 3.23 MeV might indicate the presence of alpha cluster compound states in 24Mg. This highly favours {\alpha} emission with fundamental consequences in possible stellar carbon burning sites.