Fusion and elastic-scattering cross-section analysis of the 12C + 12C system at low energies

The fusion cross sections of the 12C + 12C system at low energies Ec.m. = 1.5-9 MeV have been analyzed in the optical model. Optical potentials with variable geometry were developed to fit the angular distributions of the 12C + 12C elastic scattering and to reproduce the intermediate resonant structure for the 90o elastic-scattering excitation function in the energy region Ec.m. = 2.5-19 MeV. Calculations showed that the deep optical potential with an energy-dependent adjusted power parameter and an energy-dependent imaginary strength W is valid to give a good description of the individual elastic-scattering angular distributions and to reproduce the most prominent features of the fusion and the elastic scattering excitation functions for the 12C + 12C system at energies above and below the Coulomb barrier, the resonances of some 0.2 to 1.5 MeV in width, which is associated with quasimolecular doorway states. The astrophysical S factor obtained from the fusion experimental data also is reproduced successfully