Nucleon flow in the process of evolution from dinucleus to mononucleus investigated with a dynamic model

Abstract

Nucleon flow in the process of evolution from dinucleus to mononucleus is studied by means of the coupled Langevin equations in the three-dimensional collective space of the radial, neck, and asymmetry degrees of freedom for the systems ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$. For a comparison, the dynamic evolution of the neck is also investigated with the Langevin equations in the two-dimensional collective space of the radial and neck for these two reaction systems. The results show that nucleon flow is strongly damped in the stage of the dinuclear system due to the large dissipation associated with the mass asymmetry degree of freedom. The evaporation residue (ER) cross sections for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$ reactions are evaluated by means of the modified fusion-by-diffusion (FBD) model, in which the injection distance distributions in the asymmetric fission valley obtained from the dynamic calculations are integrated. The theoretical excitation functions of the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ reaction are in good agreement with the experimental data. For the ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$ reaction, the maximum ER cross sections in 3$n$- and 4$n$-evaporation channels calculated with the three-dimensional Langevin equations are, respectively, $0.008$ and $0.020$ fb. We have demonstrated that the effect of drift and diffusion towards a more symmetric configuration on the ER cross sections is counterbalanced by that of diffusion towards a more asymmetric one. The ER excitation functions calculated with the two approaches are similar, which means that the impact of the nucleon flow during the process of neck evolution on the formation probability of superheavy nuclei is small in the framework of the dynamic model. In this sense, the frozen approximation of mass asymmetry in the FBD model should be reasonable in the hot fusion reactions.