Universal damping mechanism of quantum vibrations in deep sub-barrier fusion reactions

I demonstrate that the coordinate dependence of the coupling strengths of colliding nuclei is important for describing the deep sub-barrier fusion hindrance. To this end, I firstly show the performance of an extended coupled-channel model by phenomenologically introducing a damping factor in the coupling potential. The damping factor stimulates the damping of quantum vibrations occurring near the touching point of colliding nuclei and introduce a coordinate dependence in the coupling strengths. Next, I directly show the coordinate dependence of the transition strengths of colliding nuclei by microscopically calculating excited states using the random phase approximation method. The obtained transition strengths of colliding nuclei as a function of the center-of-mass distance strongly correlate with the damping factor that reproduces very well the fusion hindrance. This is a direct justification for the concept of the coordinate-dependent coupling strengths. Finally, I conclude that the damping of quantum vibrations near the touching point is the universal mechanism for the deep sub-barrier fusion hindrance.