Existence of conventional fusion hindrance in carbon fusion

Determine whether the $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reaction exhibits the conventional fusion-hindrance signature, characterized by an increasing logarithmic slope of the excitation function and a possible maximum in the astrophysical $S$ factor, at deep-sub-barrier energies.

Background

Fusion hindrance refers to a stronger-than-expected decrease of the fusion cross section at deep-sub-barrier energies. In heavier-ion systems, it has been associated with an increasing logarithmic slope of the excitation function and the possible development of a maximum in the astrophysical SS factor.

For 12C+12C^{12}\mathrm{C}+^{12}\mathrm{C} fusion, the relevant experimental energy region is sparsely constrained and contains pronounced resonance structure. Different extrapolations of the logarithmic slope lead to different conclusions: some analyses predict a crossing associated with hindrance, whereas others find that the crossing disappears when the extrapolation form is relaxed. The paper’s calculations do not produce such a crossing over the calculated energy range, but the broader existence of the conventional hindrance phenomenon remains unresolved.

References

Thus, the existence of a conventional fusion-hindrance signature in ${12}\mathrm{C}+{12}\mathrm{C}$ remains unsettled, and suppression of the low-energy cross section alone does not establish the occurrence of hindrance.

— Systematic study of macroscopic interaction models and short-range effects in $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion  (2609.25996 - Aziz et al., 22 Sep 2026) in Introduction, paragraph 3; see also Section III.E, “Logarithmic-slope analysis and fusion hindrance”