Potential roots of the deep subbarrier heavy-ion fusion hindrance phenomenon within the sudden approximation approach
Abstract
We analyze the origin of the unexpected deep subbarrier heavy-ion fusion hindrance in $^{64}\mathrm{Ni}+^{100}\mathrm{Mo}$, $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$, and $^{28}\mathrm{Si}+^{64}\mathrm{Ni}$ reactions. Our analysis is based on the improved coupled-channels description, 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 within the sudden approximation approach. We found that accounting for the nondiagonal 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 of experimental data. We found as well a good agreement with the general trend of the experimental data for the $S$ factor of the fusion reaction $^{12}\mathrm{C}+^{12}\mathrm{C}$, which has no pronounced maximum for this system.