  A quantitative study of the astrophysically important sub-barrier fusion of
$^{12}$C+$^{12}$C is presented. Low-energy collisions are described in the
body-fixed reference frame using wave-packet dynamics within a nuclear
molecular picture. A collective Hamiltonian drives the time propagation of the
wave-packet through the collective potential-energy landscape. The fusion
imaginary potential for specific dinuclear configurations is crucial for
understanding the appearance of resonances in the fusion cross section. The
theoretical sub-barrier fusion cross sections explain some observed resonant
structures in the astrophysical S-factor. These cross sections monotonically
decline towards stellar energies. The structures in the data that are not
explained are possibly due to cluster effects in the nuclear molecule, which
are to be included in the present approach.
