Transition from subbarrier to deep-subbarrier regimes in heavy-ion fusion reactions

We analyze recent experimental data of heavy-ion fusion cross sections available up to deep-subbarrier energies in order to discuss the threshold incident energy for a deep-subbarrier fusion hindrance phenomenon. To this end, we employ a one-dimensional potential model with a Woods-Saxon internuclear potential. Fitting the experimental data in two different energy regions with different Woods-Saxon potentials, we define the threshold energy as an intersection of the two fusion excitation functions. We show that the threshold energies so extracted are in good agreement with the empirical systematics as well as with the values of the Krappe-Nix-Sierk (KNS) potential at the touching point. We also discuss the asymptotic energy shift of fusion cross sections with respect to the potential model calculations, and show that it decreases with decreasing energies in the deep-subbarrier region, although it takes a constant value at subbarrier energies.