The modified astrophysical S-factor of the ${}^{12}$C+${}^{12}$C fusion reaction at sub-barrier energies

Abstract

The ${}^{12}$C+${}^{12}$C fusion reaction plays a crucial role in stellar evolution and explosions. Its open reaction channels mainly include $\alpha$, $p$, $n$, and ${}^8$Be. Despite more than a half century of efforts, large discrepancies remain among the experimental data measured using various techniques. In this work, we analyze the existing data using the statistical model. Our calculation shows: 1) the relative systematic uncertainties of the predicted branching ratios get smaller as the predicted ratios increase; 2) the total modified astrophysical S-factors (S${}^{\ast }$ factors) of the $p$ and $\alpha$ channels can each be obtained by summing the S${}^{\ast }$ factors of their corresponding ground-state transitions and the characteristic $\gamma$ rays while taking into account the contributions of the missing channels to the latter. After applying corrections based on branching ratios predicted by the statistical model, an agreement is achieved among the different data sets at $E_{cm}>$4 MeV, while some discrepancies remain at lower energies suggesting the need for better measurements in the near future. We find that the recent S${}^{\ast }$ factor obtained from an indirect measurement is inconsistent with the direct measurement at energies below 2.6 MeV. We recommend upper and lower limits for the ${}^{12}$C+${}^{12}$C S${}^{\ast }$ factor based on the existing models. A new ${}^{12}$C+${}^{12}$C reaction rate is also recommended.

References in corpus (18)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Production, properties and potential of graphene
• A program for coupled-channels calculations with all order couplings for heavy-ion fusion reactions
• Study of the 12C+12C fusion reactions near the Gamow energy
• Nuclear fusion in dense matter: Reaction rate and carbon burning
• The 12C + 12C reaction and the impact on nucleosynthesis in massive stars
• Possible Resonances in the 12C + 12C Fusion Rate and Superburst Ignition
• New measurement of ${}^{12}$C+${}^{12}$C fusion reaction at astrophysical energies
• Effects of mutual excitations in the fusion of carbon isotopes
• Theory of deuteron stripping. From surface integrals to generalized $R$-matrix approach
• Astrophysical factors of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion from Trojan horse method
• Constraining the ${}^{12}$C+${}^{12}$C astrophysical S-factors with the ${}^{12}$C+${}^{13}$C measurements at very low energies
• Status on ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion at deep subbarrier energies: impact of resonances on astrophysical $S^{\ast }$ factors
• The first direct measurement of 12C(12C,n)23Mg at stellar energies
• Absence of hindrance in microscopic ${}^{12}$C+${}^{12}$C fusion study
• Impacts of the New Carbon Fusion Cross Sections on Type Ia Supernovae
• An efficient method for mapping the 12C+12C molecular resonances at low energies
• Subbarrier fusion of carbon isotopes: from resonance structure to fusion oscillations

Cited by in corpus (5)

• A new ${}^{12}$C + ${}^{12}$C nuclear reaction rate: impact on stellar evolution
• Potential roots of the deep sub-barrier heavy-ion fusion hindrance phenomenon
• Progress in Nuclear Astrophysics of East and Southeast Asia
• ${\mathrm{S}}^{\ast }(\mathrm{E})$ measurement of the ${}^{12}\mathrm{C}({}^{12}\mathrm{C},\alpha ){}^{20}\mathrm{Ne}$ reaction at astrophysical energies via the Trojan horse method with ${}^{16}\mathrm{O}$ quasi-free breakup
• Indirect Measurement of the ${\mathrm{S}}^{\ast }(\mathrm{E})$ Factor for ${}^{12}\mathrm{C}({}^{12}\mathrm{C},p){}^{23}\mathrm{Na}$ at Gamow Energies via the Trojan Horse Method with Near-0 degree Spectator Detection