Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

The hindrance in heavy-ion fusion reactions a deep sub-barrier energies is investigated using the double folding model with a hybrid method between the frozen and adiabatic density approximations.In this method,the density distributions of the projectile and the target depend closely on the distance between them.As the distance decreased,the half-density radii of the colliding nucle gradually increased to the half-density radius of the compound nucleus.The total potential based on this non-frozen approximation generates a slightly shallower pocket and becomes more attractive inside the pocket compared to that obtained from the frozen approximation.A damping factor was used to simulate the decline of the coupled channel effects owing to the density rearrangement of the two colliding nuclei.The calculated fusion cross-sections and astrophysical S factors at the deep sub-barrier energies are both in good agreement with the experimental data for the medium-heavyNi+Ni and medium-lightMg+Si mass systems.In addition,it was concluded that the apparent maximum of the S factors most likely appears in fusion systems with strong coupling effects.