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Towards a microscopic description of 12C+12C fusion at stellar energies

P. Descouvemont

Abstract

I present a fully microscopic description of the 12C+12C fusion reaction at stellar energies. Utilizing the multichannel Resonating Group Method (RGM), my model explicitly includes 12C+12C and alpha+20Ne reaction channels (with excited states). This approach provides a consistent, simultaneous, description of fusion, elastic scattering, and 24Mg spectroscopy. Results for 12C+12C elastic scattering show excellent agreement with experimental data, significantly improving the single-channel approximations. Spectroscopic analysis reveals that 24Mg states and resonances are highly mixed configurations, contradicting the concept of pure "molecular states." The calculated fusion S-factor is consistent with available experimental data and predicts both narrow and broad resonances near the Coulomb barrier. Main resonance widths originate primarily from the alpha+20Ne exit channels. The S-factor exhibits a decrease at low energies, providing a microscopic support for the hypothesis of fusion hindrance. This work is a first step towards a reliable theoretical extrapolation of the 12C+12C reaction to deep stellar burning temperatures. Future works should include the neutron and proton channels to provide a complete description of the 12C+12C fusion.

Towards a microscopic description of 12C+12C fusion at stellar energies

Abstract

I present a fully microscopic description of the 12C+12C fusion reaction at stellar energies. Utilizing the multichannel Resonating Group Method (RGM), my model explicitly includes 12C+12C and alpha+20Ne reaction channels (with excited states). This approach provides a consistent, simultaneous, description of fusion, elastic scattering, and 24Mg spectroscopy. Results for 12C+12C elastic scattering show excellent agreement with experimental data, significantly improving the single-channel approximations. Spectroscopic analysis reveals that 24Mg states and resonances are highly mixed configurations, contradicting the concept of pure "molecular states." The calculated fusion S-factor is consistent with available experimental data and predicts both narrow and broad resonances near the Coulomb barrier. Main resonance widths originate primarily from the alpha+20Ne exit channels. The S-factor exhibits a decrease at low energies, providing a microscopic support for the hypothesis of fusion hindrance. This work is a first step towards a reliable theoretical extrapolation of the 12C+12C reaction to deep stellar burning temperatures. Future works should include the neutron and proton channels to provide a complete description of the 12C+12C fusion.
Paper Structure (12 sections, 18 equations, 5 figures, 3 tables)

This paper contains 12 sections, 18 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Microscopic Model
  3. $^{12}\mathrm{C}$ and $^{20}\mathrm{Ne}$ shell-model wave functions
  4. GCM wave functions
  5. GCM kernels
  6. Relative functions
  7. Tests of the model: $^{24}\text{Mg}$ spectroscopy and $\hbox{$^{12}$C+$^{12}$C}$ elastic scattering
  8. Conditions of the calculation
  9. $^{24}$Mg bound states and resonances
  10. $\hbox{$^{12}$C+$^{12}$C}$ elastic scattering
  11. Fusion cross section
  12. Conclusion and outlook

Figures (5)

  • Figure 1: Shell-model $^{12}$C and $^{20}$Ne states up to 35 MeV. The Volkov V2 interaction is used (see Sec. \ref{['sec5']}).
  • Figure 2: $^{24}$Mg lowest states for increasing number of $^{12}$C and $^{20}$Ne basis states. The zero energy is the $\hbox{$^{12}$C+$^{12}$C}$ threshold.
  • Figure 3: $^{24}$Mg states in the multichannel calculation (filled symbols) compared to experiment (open symbols). The red marks (also indicated by arrows) correspond to the resonances present in the GCM fusion cross section (see Sec. \ref{['sec6']}).
  • Figure 4: Ratios of the elastic and Mott cross sections at 3 c.m. energies around the Coulomb barrier. The solid lines correspond to the multichannel calculation, and the dotted lines to the single-channel approximation. The experimental data are taken from Ref. TFG80.
  • Figure 5: Fusion $S$-factor in the $\alpha$ channel. The experimental data are taken from Refs. SRR07TBD20FCH20TGL24NCH25.