Determining the energy dependence of fusion cross sections at extremely low energies is crucial for various astrophysical processes. In the previous study by Jiang et al. [Phys. Rev. C 75, 015803 (2007)], it was concluded that fusion cross sections for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ system rapidly drop off as the energy decreases. We here reexamine this hindrance phenomenon. While the previous study fitted the logarithmic slope $L\left(E\right)$ of fusion cross sections with a function of $L\left(E\right)=A+B/E^n$ and sought the optimum value of $A$ and $B$ with $n=1.5$, we refit the data with the same function for $L\left(E\right)$ but by releasing the restriction on $n$. We find that the optimum values of $n$ significantly deviate from $n=1.5$. For the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ system, the presence or the absence of the hindrance phenomenon depends on a fitting procedure and a selection of data sets. On the other hand, for the ${}^{12}\mathrm{C}+{}^{13}\mathrm{C}$ system, we show that the optimum values of $n$ are smaller than $n=1.5$ regardless of the details of the fitting procedure, indicating the absence of hindrance in the fusion cross sections.

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• Nuclear astrophysics
• Nuclear fusion