The sub-barrier fusion hindrance has been observed in the domain of very low
energies of astrophysical relevance. This phenomenon can be analyzed
effectively using an uncomplicated straightforward elegant mathematical formula
gleaned presuming diffused barrier with a Gaussian distribution. The
mathematical formula for cross section of nuclear fusion reaction has been
obtained by folding together a Gaussian function representing the fusion
barrier height distribution and the expression for classical cross section of
fusion assuming a fixed barrier. The variation of fusion cross section as a
function of energy, thus obtained, describes well the existing data on
sub-barrier heavy-ion fusion for lighter systems of astrophysical interest.
Employing this elegant formula, cross sections of interacting nuclei from
${}^{16}$ O + ${}^{18}$ O to ${}^{12}$ C + ${}^{198}$ Pt, all of which were measured down
to $<$ 10 $\mu $ b have been analyzed. The agreement of the present analysis with
the measured values is comparable, if not better, than those calculated from
more sophisticated calculations. The three parameters of this formula varies
rather smoothly implying its usage in estimating the excitation function or
extrapolating cross sections for pairs of interacting nuclei which are yet to
be measured. Possible effects of neutron transfers on the hindrance in
heavy-ion fusion have been explored.