  For a single potential barrier, the barrier penetrability can be inverted
based on the WKB approximation to yield the barrier thickness. We apply this
method to heavy-ion fusion reactions at energies well below the Coulomb barrier
and directly determine the inter-nucleus potential between the colliding
nuclei. To this end, we assume that fusion cross sections at deep subbarrier
energies are governed by the lowest barrier in the barrier distribution. The
inverted inter-nucleus potentials for the $^{16}$O +$^{144}$Sm and $^{16}$O
+$^{208}$Pb reactions show that they are much thicker than phenomenological
potentials. We discuss a consequence of such thick potential by fitting the
inverted potentials with the Bass function.
