  The averaged effective two-body interaction (\textit{AEI}) which can be
generated through the lowest order constrained variational (\textit{LOCV})
method for symmetric nuclear matter (\textit{SNM}) with the input
\textit{Reid}68 nucleon-nucleon potential, is used as the effective
nucleon-nucleon potential in the folding model to describe the heavy-ion
(\textit{HI}) elastic scattering cross sections. The elastic scattering cross
sections of $^{12}C-^{12}C$ and $^{16}O-^{16}O$ systems are calculated in the
above frameworks. The results are compared with the corresponding calculations
coming from the fitting procedures with the input finite range
\textit{DDM3Y1-Reid} potential and the available experimental data at different
incident energies. It is shown that a reasonable description of the elastic
$^{12}C-^{12}C$ and $^{16}O-^{16}O$ scattering data at the low and the medium
energies can be obtained by using the above \textit{ LOCV AEI}, without any
need to define a parameterize density dependent function in the effective
nucleon-nucleon potential, which is formally considered in the typical
\textit{DDM3Y1-Reid} interactions.
