  In this theoretical study, we establish an interrelationship between the
nucleon-nucleon interaction potential and the nuclear fusion reaction
cross-sections at low energies. The axially deformed self-consistent
relativistic mean field with non-linear NL3$^*$ force is used to calculate the
density distribution of the projectile and target nuclei for fusion. The Wong
formula is used to estimate the fusion cross-section and barrier distribution
from the nucleus-nucleus optical potential for Ni-based systems, which are
known for fusion hindrance phenomena. The results of the application of the so
obtained nucleus-nucleus optical potential for the fusion cross-section from
the recently developed relativistic $NN-$interaction (R3Y) are compared with
the well-known, phenomenological M3Y effective $NN$ potential. We found a
relatively good results from R3Y interactions below the barrier energies as
compare to the M3Y potential concerning the experimental data. We also observe
the density dependence on the nuclear interaction potential in terms of
nucleon-nucleon optical potentials.
