Systematics of threshold incident energy for deep sub-barrier fusion hindrance

We systematically evaluate the potential energy at the touching configuration for heavy-ion reactions using various potential models. We point out that the energy at the touching point, especially that estimated with the Krappe-Nix-Sierk (KNS) potential, strongly correlates with the threshold incident energy for steep fall-off of fusion cross sections observed recently for several systems at extremely low energies. This clearly indicates that the steep fall-off phenomenon can be attributed to the dynamics after the target and projectile touch with each other, e.g., the tunneling process and the nuclear saturation property in the overlap region.