Analysis of heavy-ion fusion reactions at extreme sub-barrier energies using the proximity formalism

Abstract

The recent measured values of the fusion excitation functions of the heavy-ion colliding systems ${}^{28}$Si${+}^{100}$Mo, ${}^{58}$Ni${+}^{54}$Fe, and ${}^{64}$Ni${+}^{64}$Ni are investigated using the original version of the proximity formalism. The fusion cross sections are calculated based on the coupled-channels approach, including couplings to the low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in both target and projectile nuclei. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the potential Prox.77 needs to be modified considerably at sub-barrier energies. In the present study, the role of the surface energy coefficient $\ensuremath{\gamma}$ and also the temperature $T$ of the compound nucleus in nuclear potential and fusion cross section has been explored for our colliding systems. Moreover, the mutual and the multiphonon excitations of the lowest ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states are considered in the coupled-channels calculations. It is demonstrated that the potential Prox.77 with these corrective effects can reproduce the experimental data of the fusion cross section, the $S$ factor and the logarithmic derivative for fusion reactions ${}^{28}$Si${+}^{100}$Mo, ${}^{58}$Ni${+}^{54}$Fe, and ${}^{64}$Ni${+}^{64}$Ni with good accuracy especially at below-barrier energies.