Characterizing the astrophysical S-factor for $^{12}$C+$^{12}$C with wave-packet dynamics

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