Investigation of Diffusion Process in Deep Sub-barrier Fusion Reactions

We introduce a new diffusion factor to describe the hindrance phenomenon in fusion reactions at deep sub-barrier energies based on the Pauli blocking effect after the projectile and target overlap. In this approach, the fusion cross sections are assumed to be the product of two parts: the tunneling factor to overcome the Coulomb barrier and the diffusion factor after two colliding nuclei contact. The former is described by coupled-channels approach and the latter depends on the colliding energies as well as the temperature of system. In total, 21 fusion systems with hindrance phenomenon are analyzed in details and it is found that the diffusion factor plays an important role near the experimental threshold energies of fusion hindrance. In addition, taking negative-Q-value system ⁶⁴Ni+⁶⁴Ni and positive-Q-value system ²⁴Mg+³⁰Si as examples, not only fusion cross sections but also two important representations, namely, astrophysical S factor and logarithmic derivative, are found to be in good agreement with experimental data.