Systematic investigations of deep sub-barrier fusion reactions using an adiabatic approach

Background: At extremely low incident energies, unexpected decreases in fusion cross sections, compared to the standard coupled-channels (CC) calculations, have been observed in a wide range of fusion reactions. These significant reductions of the fusion cross sections are often referred to as the fusion hindrance. However, the physical origin of the fusion hindrance is still unclear. Purpose: To describe the fusion hindrance based on an adiabatic approach, I propose a novel extension of the standard CC model by introducing a damping factor that describes a smooth transition from sudden to adiabatic processes, that is, the transition from the separated two-body to the united dinuclear system. I demonstrate the performance of this model by systematically investigating various deep sub-barrier fusion reactions. Method: I extend the standard CC model by introducing a damping factor into the coupling matrix elements in the standard CC model. This avoids double counting of the CC effects, when two colliding nuclei overlap one another. I adopt the Yukawa-plus-exponential (YPE) model as a basic heavy ion-ion potential, which is advantageous for a unified description of the one-and two-body potentials. For the purpose of these systematic investigations, I approximate the one-body potential with a third-order polynomial function based on the YPE model. Results: Calculated fusion cross sections for the medium-heavy mass systems of Ni-64 + Ni-64, Ni-58 + Ni-58, and Ni-58 + Fe-54, the medium-light mass systems of Ca-40 + Ca-40, Ca-48 + Ca-48, and Mg-24 + Si-30, and the mass-asymmetric systems of Ca-48 + Zr-96 and O-16 + Pb-208 are consistent with the experimental data. The astrophysical S factor and logarithmic derivative representations of these are also in good agreement with the experimental data. The values obtained for the individual radius and diffuseness parameters in the damping factor, which reproduce the fusion cross sections well, are nearly equal to the average value for all the systems. Conclusions: Since the results calculated with the damping factor are in excellent agreement with the experimental data in all systems, I conclude that a coordinate-dependent coupling strength is responsible for the fusion hindrance. In all systems, the potential energies at the touching point V-Touch strongly correlate with the incident threshold energies for which the fusion hindrance starts to emerge, except for the medium-light mass systems.