A statistical optical potential has been used to analyze andevaluate the neutron interaction with heavy nuclei 197Au at theneutron energy range (1-20 MeV). Empirical formulae of the opticalpotentials parameters are predicted by using ABAREX Code withminimize accuracy compared with experimental bench work data.The total elastic, absorption, shape elastic and total compound crosssections are calculated for different target nuclei and differentincident neutron energies to predict the appropriate opticalparameters that suit the present interaction. Also the dispersionrelation linking between real and imaginary potential is analyzedwith more accuracy. The results indicate the behavior of thedispersion contribution in imaginary potential has a parabolic changeabout the Fermi surface energy while in the real potential it fall withincreasing the neutron energy. Good agreements have been achievedwith the available experimental data

A spherical-statistical optical model (SOM) has been used to calculate and evaluate the neutron interaction with medium nuclei (40). Empirical formulae of the optical potentials parameters are predicted with minimize accuracy compared with experimental bench work data. With these optical formulae an evaluation of the shape and compound elastic scattering cross-section of interaction neutrons with 56 Fe nuclei at different energy range (1-20) MeV has been calculated and compared with experimental results. Also, volume integrals for real and imaginary potential energies have been evaluated and matched with the standard ABAREX code. Good agreements with have been achieved with the available experimental data.