Dynamical explanation for the anomaly in the diffuseness parameter of the nucleus-nucleus potential in heavy-ion fusion reactions

The abnormally large diffuseness parameter of the Woods-Saxon (WS) potential in heavy-ion fusion reactions is explained for the first time based on the microscopic dynamics simulations. With the improved quantum molecular dynamic (ImQMD) model, we systematically explore the dynamical processes in the fusion reactions ${}^{12}\mathrm{C}+{}^{92}\mathrm{Zr}$, ${}^{16}\mathrm{O}+{}^{92}\mathrm{Zr}$, ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$, ${}^{35}\mathrm{Cl}+{}^{92}\mathrm{Zr}$, ${}^{40}\mathrm{Ca}+{}^{46}\mathrm{Ti}$, and ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$. Without introducing any free model parameters or additional assumptions, the microscopic ImQMD model can reproduce the measured fusion cross sections of all selected colliding systems with good accuracy. Due to the dynamical evolutions of the density distributions in the fusion processes, the energy dependence of nucleus-nucleus potential can be clearly observed. Based on the dynamical nucleus-nucleus potential of the ImQMD simulations, we extract the corresponding diffuseness parameters of the WS potential. The obtained values locate in a range between $\mathit{a}=0.83$ and $1.17\mathrm{fm}$ at different incident energies. In addition, the regular decreasing trend for the diffuseness parameter with the increase of the incident energies is also observed.

Figure 1

Time evolution of density distribution for head-on collisions of ${}^{40}\mathrm{Ca}+{}^{46}\mathrm{Ti}$ at two incident energies: (a) $E_{\mathrm{c}.\mathrm{m}.}=65$ MeV and (b) $E_{\mathrm{c}.\mathrm{m}.}=75$ MeV.

Figure 2

Dynamical nucleus-nucleus potentials for the fusion reactions ${}^{16}\mathrm{O}+{}^{92}\mathrm{Zr}$ and ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$ at different incident energies $E_{\mathrm{c}.\mathrm{m}.}$. Solid curve denotes the static proximity potential [15].

Figure 3

Fusion excitation functions for the fusion reactions (a) ${}^{12}\mathrm{C}+{}^{92}\mathrm{Zr}$, (b) ${}^{16}\mathrm{O}+{}^{92}\mathrm{Zr}$, (c) ${}^{28}\mathrm{Si}+{}^{92}\mathrm{Zr}$, (d) ${}^{35}\mathrm{Cl}+{}^{92}\mathrm{Zr}$, (e) ${}^{40}\mathrm{Ca}+{}^{46}\mathrm{Ti}$, and (f) ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$. The open and solid circles denote the experimental data and the results of the ImQMD model, respectively. The experimental data are taken from Refs. [19, 58, 59].

Figure 4

Extracted diffuseness parameter as a function of incident energy. In panels (a) and (b), the solid curves denote the results of M. Singh et al. [29], for example. The estimation error of fitting the WS potential to the dynamical potentials is less than ${10}^{-7}$.