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

Abstract

The nuclear mean-field potential built up during the $${}^{12}\hbox {C}+{}^{12}\hbox {C}$$ and $${}^{16}\hbox {O}+{}^{16}\hbox {O}$$ 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 $$^{12}\hbox {C}$$ 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 $${}^{12}\hbox {C}+{}^{12}\hbox {C}$$ and $${}^{16}\hbox {O}+{}^{16}\hbox {O}$$ 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 $${}^{12}\hbox {C}+{}^{12}\hbox {C}$$ and $${}^{16}\hbox {O}+{}^{16}\hbox {O}$$ 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 $${}^{12}\hbox {C}+{}^{12}\hbox {C}$$ and $${}^{16}\hbox {O}+{}^{16}\hbox {O}$$ fusions very well over a wide range of energies.