Study of fusion process of ions with heavy nuclei in the framework of statistical model for synthesis of supper-heavy nuclei

In the present paper, we want to study the nuclear fusion of 48Ca ions with 248Cm nuclei for synthesis of the super heavy nuclei 296Lv located in the island of stability. We estimate the fusion barrier against between 48Ca and 248Cm nuclei in the framework of the theoretical calculations and investigate the influence of the direction of target nuclei on the parameters of the fusion barrier. Furthermore, we show that the minimum energy for synthesis 296Lv is equal to 205.17 MeV which is relevant to the collision between the projectile and target nuclei under orientations (0-0). Finally, in the framework of the statistical model we estimate the evaporation residue cross section for 293Lv and 292Lv nuclei after emission of three and four neutrons from 296Lv nuclei and we show that the results of calculations are in good agreement with the experimental data.