  We analyze the 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
intersect 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.
