Study On The Distribution Of Neutron-induced ²³⁵U And ²³⁹Pu Fission Yield Based On Five-dimensional Potential Energy Surface Model

Nuclear fission refers to the phenomenon that a heavy nucleus splits into several intermediate mass nuclei.In various motion forms of nuclei,the fission process is very important and contains a lot of research content.Since the discovery of fission,people have made a long-term and in-depth study on the fission phenomenon and made it become an important part of nuclear physics.In addition,nuclear fission will release a lot of energy,which opens up a new field for energy utilization,and then have the development of nuclear engineering.With the development of economy and the progress of science and technology,the research of nuclear fission has also made new progress,people have new requirements for the accuracy and breadth of nuclear fission data.Therefore,it is necessary to conduct more in-depth research on nuclear fission from the perspective of fission mechanism,so as to serve the development of nuclear data and enhance the application of basic research and nuclear technology.The first work of this paper was to calculate the five-dimensional fission potential energy surface of deformed nuclei based on the macroscopic and microscopic models.The nuclear shape was described by the generalized Lawrence shape which contains five geometric parameters:the half length of the nucleus“l”,the radius of the neck“r”,the position of the neck“z”,the curvature of the neck“c”,and the position of the center of gravity“s”.The macroscopic energy was calculated based on the droplet model.This work focused on the surface energy,curvature energy and Coulomb energy which are related to the nuclear deformation by using LSD(Lublin-Strasburg Drop)formula;the microscopic energy included shell correction and pair correction,which are based on the energy level of single particle and calculated by certain theory.The shell correction was calculated by Strutinsky method,and the pair correction was calculated by BCS(Bardeen-Cooper-Schripffer)theory.The total fission potential energy can be obtained by adding the macroscopic energy and the microscopic energy.For all reasonable shapes,the macroscopic and microscopic model was used to calculate the corresponding fission potential energy,and the complete five dimensional potential energy surface for fission can be obtained.The second work of this paper is to study the optimal fission path of deformed nuclei.Based on the idea of watershed in topography,a precipitation simulation algorithm was developed,and a program was written to search the information of catchment basin,watershed and saddle point,so as to obtain the optimal fission path.On this basis,using the knowledge of fluid mechanics for reference,the breakpoint criterion is obtained.It is believed that when the half-length l and the neck radius r of the nucleus meet 2l>11r,the nucleus will break,so as to find the breakpoint position of the nucleus on the optimal fission path and lay the foundation for the next work.The third work of this paper was to introduce Random Neck Rupture model,and the calculation and correction of the mass distribution of fission fragments of ²³⁵U and²³⁹Pu nuclei induced by low energy neutrons have been carried out in the case of the optimal fission path.When calculating the mass distribution of fission fragments,firstly,this work gave the pre-scission shape of the nucleus,and thought that when the deformation of the fission nucleus exceeds the pre-scission shape,the neck will fracture due to the instability of capillary action,and then,the work used the initial conditions such as the continuity of the first derivative at the junction point and the conservation of the volume of the fission nucleus during the deformation process to express the pre-scission shape as a function of the fracture position.Next,according to the Random Neck Rupture model,it was considered that under the influence of random fluctuation effect,the probability of fracture at different positions is different,and different fracture positions correspond to different mass numbers of fragments.Therefore,the probability of occurrence of different fragments can be obtained,and the mass distribution of fission fragments under the optimal fission path can also be obtained.On this basis,the GEF model is adopted to add the modification of other fission channels,and the complete fission fragment mass distribution can be obtained,which can be compared with experimental data for analysis.Generally speaking,in this paper,the fission potential energy surface of actinide nuclei was calculated by using the macro and micro model firstly.Then,the simulated precipitation algorithm was developed to search the optimal fission path of the nuclei.The breakpoint criterion was introduced to find the fracture position of the nuclei.Finally,the Random Neck Rupture model was used to carry out the calculation and correction of the mass distribution of fission fragments of ²³⁵U and ²³⁹Pu nuclei induced by low energy neutrons in the case of the optimal fission path.On the whole,the work of this paper was relatively systematic,which describes the physical process of neutron induced fission of actinide nuclei,that is,the deformation,fracture of composite nuclei and the formation of post physical quantities(this work focused on the mass distribution of fission fragments).The work of this paper can lay a foundation for the study of the physical mechanism of nuclear fission,the distribution data of fission yield,the description of the physical process after fission,and also can make some analysis and prediction of the nuclear data needed in the development of nuclear energy utilization and nuclear engineering.