In the present work, the detailed calculations of a nuclear collision (deuteron + gold) (D+Au) using the sharp surface density profile as a function of collision impact parameter at center of mass energy (√s_NN = 200 GeV) are presented. The number of nucleons that participate in the collisions, in addition to the differential elastic cross-section, at different energies was calculated. The study of the effect of various energies on the outcome of intranuclear nucleon collisions can be carried out by varying the energy of each collision. Thus, properties of the particles resulting from the collision are observed by the different high energies, √s = 200, 56, 200, 2760, and 5440  GeV . The nuclear overlapping function of the D+Au collision, as the probability of depth penetrating the potential, was different from that of the thickness function calculations. The main results of the ¹⁹⁷AuN_part at these energies are different as energy affects the outcoming nucleons. It was found that the elastic differential cross-section is larger for smaller impact parameters, and it decreases with increasing collision energy.