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

A new measurement of fusion reactions down to 10 nb has been performed for the system ⁶⁴Ni + ⁶⁴Ni. Coupled-channels analyses have been carried out for the systems ⁶⁰Ni + ⁸⁹Y and ⁶⁴Ni + ⁶⁴Ni. They demonstrate that coupled-channels calculations are unable to reproduce the unexpected steep falloff of the 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 parameterized with a simple empirical formula. The parameterization, which is derived here for rather stiff heavy-ion systems, provides also an upper limit for reactions involving softer nuclei.