Potential roots of the deep sub-barrier heavy-ion fusion hindrance phenomenon

We analyse the origin of the unexpected deep sub-barrier heavy-ion fusion hindrance in 64Ni+100Mo and 28Si+64Ni recations. Our analysis is based on the improved coupled-channels approach, implemented by means of the finite element method. With the aid of the Woods-Saxon potential the experimental cross sections and the S-factors of these reactions are remarkably well reproduced. We found that the account on the non-diagonal matrix elements of the coupling matrix, traditionally neglected in the conventional coupled-channels approaches in setting the left boundary conditions inside the potential pocket, and its minimal value are crucially important for the interpretation experimental data. Within our approach we found a good agreement with the experimental data for the S-factor of the fusion reaction 12C+12C, which has no a pronounced maximum for this system.