  We carefully compare the one-dimensional WKB barrier tunneling model, and the
one-channel Sch\"odinger equation with a complex optical potential calculation
of heavy-ion fusion, for a light and a heavy system. It is found that the major
difference between the two approaches occurs around the critical energy, above
which the effective potential for the grazing angular momentum ceases to
exhibit a pocket. The value of this critical energy is shown to be strongly
dependent on the nuclear potential at short distances, on the inside region of
the Coulomb barrier, and this dependence is much more important for heavy
systems. Therefore the nuclear fusion process is expected to provide
information on the nuclear potential in this inner region. We compare
calculations with available data to show that the results are consistent with
this expectation.
