Mean-field study of \(^{12}\)C+\(^{12}\)C fusion

The nuclear mean-field potential arising from the \(^{12}\)C+\(^{12}\)C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the \(^{12}\)C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the \(^{12}\)C+\(^{12}\)C potential. The folded potentials at the different energies were used in the optical model description of the elastic \(^{12}\)C+\(^{12}\)C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical \(S\) factor of the \(^{12}\)C+\(^{12}\)C reactions at the low energies. The obtained results are in good agreement with experimental data over a wide range of energies.