Study Of Heavy And Super-heavy Nuclear Reactions Based On ImQMD Model And Two-Step Model

The dynamical nucleus-nucleus potential and multidimensional potential energy surface are studied with the improved quantum molecular dynamics model (ImQMD), including the fusion reactions induced with 48Ca and 50Ti nuclei-In addition, the extended Thomas-Fermi approximation is applied for the kinetic energy of nuclei, so that the energies of the nuclei can be expressed as a function of nuclear densities. The obtained fusion barrier for the light nuclear system is in good with the extracted fusion barrier from the measured fusion excitation function, and the depths of the fusion pockets are close to the results of time-dependent Hartree-Fock calculations. Because the fusion barrier depends on the incident energy, so the influence of the incident energy on the nucleus-nucleus potential and potential energy surface is also investigated. For heavy fusion systems, the fusion pocket becomes shallow and almost disappears for symmetric system and the obtained potential at short distance is higher than the adiabatic potential. The entrance channel potential containing one degree-of-freedom is expressed as the function of two nucleus's distance. Potential energy surface contains two degrees of freedom, the distance between two nuclei and mass asymmetry. We investigate the entrance channel potential and potential surfaces at different kinetic energies. The calculations show that the entrance channel potential and potential energy surface of heavy fusion systems change slightly with the increase of the incident energies.The two-step model is a macroscopic model. It describes two stages of the nuclear reaction, the overcoming of the Coulomb potential before touching point which is called sticking process and the evolution of the amalgamated system after touching point which is called formation process. The sticking process can be described with an empirical formula and the formation process can be described by multi-dimensional Langevin equation. Multiplying of the two probabilities for description of the two processes mentioned previously, we can obtain the fusion probability of compound nucleus. The formation probability of compound nucleus depends on the excitation energy, the nuclear interaction potential of nuclear system, the total angular momentum of the system and other factors. The formation probability contributes a lot to the fusion probability. Therefore, it is very important to accurately calculate the nuclear interaction potential. We use the two-step model to calculate the approaching, the formation, and the fusion probability for heavy systems with compound nuclei Z=119,120. Finally, combining the statistical evaporation model, we obtain the residue cross section of super-heavy nuclei.It is known that the nucleus is a many-body interacting system of fermions. It is difficult to use a unified model for describing the whole formation process of the super-heavy nuclei. Before we combine the ImQMD model and Two-Step model to analysis the formation process of super-heavy nuclei, three points should be considered. First, the liquid drop potential surfaces contain three degrees of freedom, namely the mass asymmetry, the neck and the distance of two nuclei which can be evolved to zero. But potential surfaces in ImQMD model are the function of the mass asymmetry and the distance of two nuclei which can not be evolved to zero. In order to combine two different models, we set the neck parameter to 0.1. There may be two ways to make the distance to zero, the first method is to strengthen incident energy, and the other method is to extend fusion time. These two methods give the consequences as follows. The compound nucleus excitation energy becomes big, which leads that the compound nucleus' temperature is more than 50MeV and it is hard to accurately calculate the residue cross section at low excitation energy, also the programming must take too long time to calculate the potential surfaces. So the combination of these two models is great trouble. Second, using ImQMD model to calculate 48Ca series and 50Ti series of fusion reactions, we test the relationship between nuclear interaction potential and the system's incident energy and choose an suitable incident energy for the 48Ca and 50Ti series of fusion reactions. Third, we assume that random force strength and mass tensor are not heavily dependent on system temperature. In these two hypothesis, ImQMD interaction potential with the impact parameter b=0 is instead of the total angular momentum L=0 interaction potential in two-step model. In this work, we apply the semi-classical quantum molecular dynamics model (ImQMD) to describe the formation process of the compound nuclei and study the fusion of heavy nuclei into the reaction mechanism and the possibility of superheavy nuclei.