  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.
