  The hindrance in fusion of heavy-ion reactions crops up in the region of
extreme sub-barrier energies. This phenomenon can be effectively analyzed using
a simple diffused barrier formula derived assuming a Gaussian distribution of
fusion barrier heights. Folding the Gaussian barrier distribution with the
classical expression for the fusion cross section for a fixed barrier, the
fusion cross section is obtained. The energy dependence of the fusion cross
section provides good description to the existing data on sub-barrier heavy-ion
fusion for lighter systems of astrophysical interest. Using this simple
formula, an analysis has been presented from $^{16}$O + $^{18}$O to $^{12}$C +
$^{198}$Pt, all of which were measured down to $<$ 10 $\mu$b. The agreement of
the present analysis with the measured values is better than those calculated
even from the sophisticated coupled channels calculations. The relatively
smooth variation of the three parameters of this formula implies that it may be
exploited to estimate the excitation function or to extrapolate cross sections
for pairs of interacting nuclei which are yet to be measured. Possible
extensions of the present methodology and its limitations have also been
discussed.
