Background: The behavior of fusion excitation functions at deep sub-barrier energies for light systems relevant for astrophysics (e.g., ${}^{12}\mathrm{C} + {}^{12}\mathrm{C}, {}^{12}\mathrm{C} + {}^{16}\mathrm{O}, {}^{16}\mathrm{O} + {}^{16}\mathrm{O}$) is far from being clearly established. This is due to differences between the many data sets, and to the appearance of strong resonance peaks in some cases, as far as the existence and features of fusion hindrance are concerned.

Purpose: To investigate the existence and the threshold of hindrance in the system ${}^{12}\mathrm{C} + {}^{19}\mathrm{F}$, where $Q_{\mathrm{fus}}$ = $+22.95$ MeV, so to clarify the underlying physics by comparing with coupled-channels calculations, and to reliably extrapolate the results to cases of astrophysical relevance such as ${}^{12}\mathrm{C} + {}^{12}\mathrm{C}$ and ${}^{12}\mathrm{C} + {}^{16}\mathrm{O}$.

Methods: ${}^{19}\mathrm{F}$ beams from the XTU Tandem accelerator of LNL were sent onto thin ${}^{12}\mathrm{C}$ targets isotopically enriched to $99.9\%$. The electrostatic beam deflector PISOLO separated the fusion-evaporation residues ER from beam-like particles. Then a $E\text{−}\mathrm{\Delta }E$-time of flight telescope detected and identified the ER.

Results: The fusion cross sections of ${}^{12}\mathrm{C} + {}^{19}\mathrm{F}$ have been measured down to $\approx 76\mu \mathrm{b}$. The logarithmic derivative of the energy-weighted excitation function increases at the lowest energies and reaches the $L_{CS}$ value. Coupled-channels calculations predict significantly lower values, indicating that the hindrance phenomenon shows up in this system. The low-energy cross sections have been fitted using a recently proposed approach.

Conclusions: We compare the low-energy trend of ${}^{12}\mathrm{C} + {}^{19}\mathrm{F}$ with nearby and medium-light systems, using Jiang's phenomenological systematics of the hindrance thresholds, updated with the present data and the behavior of the recent results for ${}^{12}\mathrm{C} + {}^{24,26}\mathrm{Mg}, {}^{28,30}\mathrm{Si}$, and ${}^{16}\mathrm{O} + {}^{48}\mathrm{Ca}$. Overall, we observe that the fit to the measured data, including ${}^{12}\mathrm{C} + {}^{19}\mathrm{F}$ and those systems, leads to an extrapolation to the lighter cases, very close to that obtained from the hindrance model. This is especially true for ${}^{12}\mathrm{C} + {}^{12}\mathrm{C}$, where the several low-energy resonances cause the direct observation of hindrance to be quite challenging.

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• Nuclear reactions