Abstarct: In this thesis, the fusion cross section of the halo nuclei with heavy ions has been studied. We calculated the coefficients of the potential between the projectile and target system using simulation by Monte Carlo Method. In calculating the coefficients of the potential between the projectile and target system, the selection of the effective nucleon-nucleon interaction and the use of the real density distribution of nuclear matter are particular importance. Therefore, we considered two approaches in calculating the coefficients of the potential between the projectile and target system. First, the effective nucleon-nucleon interaction has been analyzed in such a way that the theoretical calculations of the fusion cross section show the expected agreement with the experimental data. For this purpose, the effective nucleon-nucleon interaction of the soft core type has been chosen to calculate the coefficients of the potential between the projectile and target system. The depth parameter of this interaction is such that the theoretical calculations of the fusion cross section show the expected agreement with the experimental data. The results show that, at energies above the fusion barrier, by decreasing the depth parameter of the selected interaction, the expected agreement between the theoretical calculations of the fusion cross section and the experimental data is established. However, at energies below the barrier, this agreement is achieved by increasing the depth parameter of the selected interaction. Furthermore, in order to analyze the real density distribution of the nuclear matter of the 6He and 8He nuclei, we examined four different forms of phenomenological density distribution functions. The parameters of these density distribution functions were obtained from elastic scattering experiments proton with these nuclei. Our findings show that the nuclear density distribution of the GO model, which assumes a better halo structure than the other cases, provides a better spatial arrangement for the distribution of nucleons in the core and halo parts of the mentioned nuclei. Using this spatial arrangement, a better agreement is established between the theoretical calculations of the fusion cross section and the experimental data than the other cases. However, using the nuclear density distribution of then GO model does not establish the expected agreement between the theoretical calculations of the fusion cross section and the experimental data. In this thesis, in order to establish the expected agreement, a generalized function of two-parameter Fermi distribution is proposed for the density of halo nucleons of the 6He and 8He nuclei. For the density of their core nucleons, we chose two-parameter Fermi distribution function, which is more general. The density parameters for each of the halo and core parts of the mentioned nuclei have been analyzed to provide a better agreement between the theoretical results of the fusion cross¬ section and the experimental data. In order to verify both approaches (analysis of the effective nucleon-nucleon interaction and analysis of the density distribution of the core and halo nucleons), we studied the elastic scattering cross-sections of the 4He + 64Zn, 6He + 64Zn and 6He +197Au systems at different energies. In this study, a good agreement was established between the theoretical calculations of the elastic scattering cross¬ section and the experimental data.