Existence of a one-body barrier revealed in deep subbarrier fusion

Based on the adiabatic picture for heavy-ion reactions, in which the neck formation in the one-body system is taken into account, we propose a two-step model for fusion cross sections at deep sub-barrier energies. This model consists of the capture process in the two-body potential pocket, which is followed by the penetration of the adiabatic one-body potential to reach a compound state after the touching configuration. We describe the former process with the coupled-channels framework, while the latter with the Wentzel-Kramers-Brillouin (WKB) approximation by taking into account the coordinate dependent inertia mass. The effect of the one-body barrier is important at incident energies below the potential energy at the touching configuration. We show that this model well accounts for the steep fall-off phenomenon of fusion cross sections at deep sub-barrier energies for the ${}^{64}\mathrm{Ni}$+${}^{64}\mathrm{Ni}$ and ${}^{58}\mathrm{Ni}$+${}^{58}\mathrm{Ni}$ reactions.

Figure 1

One- and two-body potential energies for ${}^{64}\mathrm{Ni}$+${}^{64}\mathrm{Ni}$ obtained with the KNS model as a function of the center-of-mass distance. The shape for the one-body configuration described by the Lemniscatoids parametrization is also shown. The filled circle and square denote the touching configuration and the ground state of the compound system, respectively. The dotted line is the sudden potential taken from Ref. [7].

Figure 2

The internucleus potential used in the two-step model. The solid line in the upper panel denotes the KNS potential for the two-body process, which is cut at the touching configuration, while the dashed line denotes the lowest two-body eigenpotential. The dash-dotted line denotes the position at which the incoming wave boundary condition (IWBC) is imposed in the CC calculation. The solid line in the lower panel denotes the adiabatic one-body potential inside the touching distance.

Figure 3

Fusion cross sections for the ${}^{64}\mathrm{Ni}$+${}^{64}\mathrm{Ni}$ reaction calculated with the two-step model. The filled circles denote the experimental fusion cross section, taken from Ref. [2]. The solid and dotted lines denote the fusion cross section obtained with the normalization factor for the mass inertia of $k=46$ and 0, respectively. The dashed line denotes the corresponding capture cross section. The dash-dotted line is obtained with the Woods-Saxon potential, while the dash-dot-dotted line shows the result in the absence of the channel coupling effect.