The role of inelastic couplings on the ${}^{12}$C+${}^{12}$C fusion at sub-barrier energies

The effect of inelastic couplings on the modified astrophysical S*-factor for ${}^{12}$C+${}^{12}$C fusion reaction at sub-barrier energies is investigated using the Brazilian Nuclear Potential. The ${}^{12}$C excited states (2${}_1^{+}$, 4.44 MeV; 3${}_1^{-}$, 9.64 MeV; 2${}_2^{+}$, 9.84 MeV; 2${}_3^{+}$, 10.3 MeV; 2${}_4^{+}$, 16.1 MeV; 1${}_1^{-}$, 17.2 MeV and 2${}_5^{+}$, 18.8 MeV) are included in the coupling scheme. We have also coupled the 0${}_2^{+}$ Hoyle state (E* = 7.65 MeV) to the 2${}_1^{+}$. In our model, the fusion cross section is associated to the absorption arising from the imaginary potential. Many resonances presented at the sub-barrier data are fairly reproduced by our approach.