  Recent high precision experimental data for heavy-ion fusion reactions at
subbarrier energies systematically show that a surprisingly large surface
diffuseness parameter for a Woods-Saxon potential is required in order to fit
the data. We point out that experimental data for quasi-elastic scattering at
backward angles also favor a similar large value of surface diffuseness
parameter. Consequently, a double folding approach fails to reproduce the
experimental excitation function of quasielastic scattering for the $^{16}$O +
$^{154}$Sm system at energies around the Coulomb barrier. We also show that the
deviation of the ratio of the quasielastic to the Rutherford cross sections
from unity at deep subbarrier energies offers an unambiguous way to determine
the value of the surface diffuseness parameter in the nucleus-nucleus
potential.
