  Based on the adiabatic picture for heavy-ion reactions, in which the neck
formation in the one-body system is taken into account, we propose a two-step
model for fusion cross sections at deep subbarrier energies. This model
consists of the capture process in the two-body potential pocket, which is
followed by the penetration of the adiabatic one-body potential to reach a
compound state after the touching configuration. We describe the former process
with the coupled-channels framework, while the latter with the WKB
approximation by taking into account the coordinate dependent inertia mass. The
effect of the one-body barrier is important at incident energies below the
potential energy at the touching configuration. We show that this model well
accounts for the steep fall-off phenomenon of fusion cross sections at deep
subbarrier energies for the $^{64}$Ni+$^{64}$Ni and $^{58}$Ni+$^{58}$Ni
reactions.
