Does deep sub-barrier fusion hindrance set in for 12C+12C?
In plain words
In many pairs of nuclei, fusion far below the Coulomb barrier (the electric repulsion the nuclei must tunnel through) drops faster than standard models predict, an effect called hindrance. Whether this also happens for two carbon nuclei changes the carbon-burning rate by large factors.
Precise statement
For $12\mathrm{C}+12\mathrm{C}$, determine whether the non-resonant part of the fusion $S*$-factor reaches a maximum and decreases with falling energy below $E_{\mathrm{cm}} \sim 3 \text{ to } 4\,\mathrm{MeV}$, as hindrance systematics of heavier systems and shallow potentials with a repulsive core (Misicu and Esbensen 2006) predict, or keeps rising, as standard coupled-channels calculations with deep Woods-Saxon-type potentials predict. The answer is yes or no together with the energy dependence of the averaged $S*(E)$ between $1.5 \text{ and } 3\,\mathrm{MeV}$.
What would settle it
Direct cross sections below 2 MeV that separate a smooth non-resonant trend from resonances, together with a microscopic fusion calculation that reproduces the measured trend in 12C+12C and neighbouring systems such as 12C+13C.
Status in the literature
Unverified note
Microscopic descriptions at stellar energies continue to appear (2026), but the low-energy trend is still not fixed experimentally.