Near-barrier heavy-ion fusion: Role of boundary conditions in coupling of channels
Peiwei Wen, О. Чулуунбаатар, А. А. Гусев, R. G. Nazmitdinov, A. K. Nasirov, S. I. Vinitsky, C. J. Lin, H. M. Jia
Abstract
The problem of a quantum-mechanical description of a near-barrier fusion of heavy nuclei, that occurs at strong coupling of their relative motion to surface vibrations, is analyzed. To this end, an efficient finite-element method is proposed for numerically solving coupled Schr\"odinger equations with boundary conditions corresponding to total absorption. The method allows us to eliminate the instabilities in the numerical solutions that appear at a large number of coupled channels in some reactions. To illustrate the validity of our approach, the results of fusion cross section of the $^{64}\mathrm{Ni}+^{100}\mathrm{Mo}$ and $^{36}\mathrm{S}+^{48}\mathrm{Ca}$ reactions have been re-examined. The obtained results demonstrate a remarkable agreement with the available experimental data. It is found that experimental data can be reproduced with the use of the Woods-Saxon potential, without introducing the repulsive cores. It appears that the fusion cross sections at deep sub-barrier energies are sensitive to the potential pocket profile.