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 falloff 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.

Figure 1

Schematic picture for heavy-ion sub-barrier fusion reactions. The filled circle denotes the energy at the touching point, $V_{\mathrm{touch}}$.

Figure 2

Potential energy at the touching point calculated by various theoretical models. The open circles, triangles, diamonds and squares denote the results of the Krappe-Nix-Sierk, the Bass, the proximity, and the Akyüz-Winther models, respectively. The solid line denotes the systematics proposed by Jiang et al. [5]. The filled circles, squares, triangles, and the horizontal lines show the experimental energy taken from Ref. [5] at which the astrophysical S-factor has the maximum value.

Figure 3

Same as Fig. 2, but as a function of the effective fissility parameter defined in Ref. [11]. The upper panel shows the difference between $E_s$ and $V_{\mathrm{KNS}}$.