  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.
