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The nuclear mean-field potential built up by the $^{12}$C+$^{12}$C interaction at energies relevant for the carbon burning process is calculated in the double-folding model (DFM) using the realistic ground-state density of $^{12}$C and the CDM3Y3 density dependent nucleon-nucleon (NN) interaction, with the rearrangement term properly included. To validate the use of a density dependent NN interaction in the DFM calculation in the low-energy regime, an adiabatic approximation is suggested for the nucleus-nucleus overlap density. The reliability of the nuclear mean-field potential predicted by this low-energy version of the DFM is tested in a detailed optical model analysis of the elastic $^{12}$C+$^{12}$C scattering data at energies below 10 MeV/nucleon. The folded mean-field potential is then used to study the astrophysical $S$ factor of the $^{12}$C+$^{12}$C fusion in the barrier penetration model. Without any adjustment of the potential strength, our results reproduce very well the non-resonant behavior of the $S$ factor of the $^{12}$C+$^{12}$C fusion over a wide range of energies.

physical review. c

Consistent mean-field description of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo> </mml:mo><mml:mo>+</mml:mo><mml:mo> </mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>optical potential at low energies and …

Consistent mean-field description of theC12 + C12optical potential at low energies and …