The nuclear mean-field potential built up during the ^(12)C+^(12)C and ^(16)O+^(16)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)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)C+^(12)C and ^(16)O+^(16)O scattering data at energies below 10 MeV/nucleon.These OM results provide a consistently good description of the elastic angular distributions and 90 excitation function. The dinuclear mean-field potential predicted by the DFM is further used to determine the astrophysical S factor of the ^(12)C+^(12)C and ^(16)O+^(16)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)C+^(12)C and ^(16)O+^(16)O fusions very well over a wide range of energies.
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