  We have constructed an empirical formulae for the fusion and interaction
barriers using experimental values available till date. The fusion barriers so
obtained have been compared with different model predictions based on the
proximity, Woods-Saxon and double folding potentials along with several
empirical formulas, time dependent Hartree-Fock theories, and the experimental
results. The comparison allows us to find the best model, which is nothing but
the present empirical formula only. Most remarkably, the fusion barrier and
radius show excellent consonance with the experimental findings for the
reactions meant for synthesis of the superheavy elements also. Furthermore, it
is seen that substitution of the predicted fusion barrier and radius in classic
Wong formula [C. Wong, Phys. Rev. Lett. {31}, 766 (1973)] for the total fusion
cross sections satisfies very well with the experiments. Similarly, current
interaction barrier predictions have also been compared well with a few
experimental results available and Bass potential model meant for the
interaction barrier predictions. Importantly, the present formulae for the
fusion as well as interaction barrier will have practical implications in
carrying out the physics research near the Coulomb barrier energies.
Furthermore, present fusion barrier and radius provide us a good
nucleus-nucleus potential useful for numerous theoretical applications.
