Re-examination of fusion hindrance in astrophysical $^{12}$C+$^{12}$C and $^{12}$C+$^{13}$C reactions

Abstract

To determine 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. C75, 015803 (2007)], it was concluded that fusion cross sections for the $^{12}$C+$^{12}$C system rapidly drop off as the energy decreases. We here re-examine this hindrance phenomenon. While the previous study fitted the logarithmic slope $L(E)$ of fusion cross sections with a function of $L(E)=A+B/E^n$ and searched the optimum value of $A$ and $B$ with $n=1.5$, we refit the data with the same function for $L(E)$ but by releasing the restriction on $n$. We find that the optimum values of $n$ significantly deviates from $n=1.5$, resulting in the absence of hindrance of fusion cross sections both in the $^{12}$C+$^{12}$C and the $^{12}$C+$^{13}$C systems.