Mean-field description of heavy-ion scattering at low energies and fusion

The nuclear mean-field potential built up during the ${}^{12}\text{C}+{}^{12}\text{C}$ and ${}^{16}\text{O}+{}^{16}\text{O}$ collisions at low energies relevant for the carbon- and oxygen-burning processes is constructed within the double-folding model (DFM) using the realistic ground-state densities of ${}^{12}\text{C}$ and ${}^{16}$O, and CDM3Yn density-dependent nucleon–nucleon (NN) interaction. The rearrangement term, indicated by the Hugenholtz–van Hove theorem for the single-particle energy in nuclear matter, is properly considered in the DFM calculation. To validate the use of the density-dependent NN interaction at low energies, an adiabatic approximation was suggested for the dinuclear overlap density. The reliability of the nucleus–nucleus potential predicted through this low-energy version of the DFM was tested in the optical model (OM) analysis of the elastic ${}^{12}\text{C}+{}^{12}\text{C}$ and ${}^{16}\text{O}+{}^{16}\text{O}$ scattering data at energies below 10 MeV/nucleon. These OM results provide a consistently good description of the elastic angular distributions and 90${}^{\circ }$ excitation function. The dinuclear mean-field potential predicted by the DFM is further used to determine the astrophysical S factor of the ${}^{12}\text{C}+{}^{12}\text{C}$ and ${}^{16}\text{O}+{}^{16}\text{O}$ fusions in the barrier penetration model. Without any adjustment of the potential strength, our results reproduce the non-resonant behavior of the S factor of the ${}^{12}\text{C}+{}^{12}\text{C}$ and ${}^{16}\text{O}+{}^{16}\text{O}$ fusions very well over a wide range of energies.