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

TL;DR

This study re-examines the fusion hindrance phenomenon in astrophysical carbon reactions by fitting experimental data with a flexible model, finding no evidence of hindrance in the $^{12}$C+$^{12}$C and $^{12}$C+$^{13}$C systems.

Contribution

It introduces a re-analysis of fusion cross section data allowing the model parameter n to vary, challenging previous conclusions of fusion hindrance.

Findings

No fusion hindrance observed in $^{12}$C+$^{12}$C and $^{12}$C+$^{13}$C systems.

Optimal model parameters significantly differ from previous fixed-n assumptions.

Re-analysis suggests fusion cross sections do not drop off rapidly at low energies.

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.