  Recent high precision experimental data for heavy-ion fusion cross sections
at energies in the vicinity of the Coulomb barrier systematically show that a
strikingly large surface diffuseness parameter for a Woods-Saxon potential is
required in order to fit the data. We discuss possible origins for this
anomaly, including the effects of dissipation and the sensitivity of fusion
cross sections to the choice of inter-nuclear potential. Our study suggests
that the frozen density approximation, which is often used in analyses of
heavy-ion reactions, may have to be re-examined for heavy-ion fusion.
