We demonstrate that when two colliding nuclei approach each other, their quantum vibrations are damped near the touching point. We show that this damping is responsible for the fusion hindrance phenomena measured in the deep sub-barrier fusion reactions. To show those, we, for the first time, apply the random-phase-approximation method to the two-body ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ systems. We calculate the octupole transition strengths for the two nuclei that adiabatically approach each other. The calculated transition strength drastically decreases near the touching point, which strongly suggests the vanishing of the quantum couplings between the relative motion and the vibrational intrinsic degrees of freedom of each nucleus. Based on this picture, we also calculate the fusion cross section for the ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ system by using the coupled-channel method with a damping factor that simulates the vanishing of the couplings. The calculated results reproduce the experimental data well, which indicates that the smooth transition from the sudden to the adiabatic processes indeed occurs in the deep sub-barrier fusion reactions.

• Received 28 February 2013

DOI:https://doi.org/10.1103/PhysRevC.88.011602