Analysis of heavy-ion fusion reactions at extreme sub-barrier energies

Abstract

A coupled-channels analysis has been carried out for fusion reactions in the system $^{60}\mathrm{Ni}+^{89}\mathrm{Y}$. It demonstrates that conventional coupled-channels calculations are unable to reproduce the unexpected steep falloff of the recently measured cross sections at extreme sub-barrier energies. Heavy-ion fusion excitation functions are also analyzed in terms of the $S$ factor, as this offers a pragmatic way to study fusion behavior in the energy regime of interest. It is shown that the steep falloff in cross section observed in several heavy-ion systems translates into a maximum of the $S$ factor. The energies where the maximum occurs can be parametrized with a simple empirical formula. The parametrization, which is derived here for rather stiff heavy-ion systems, provides an upper limit for reactions involving softer nuclei.