The Time Evolution Of Elliptic Flow In Heavy Ion Collisions At Intermediate Energy

The nuclear equation of state（EoS）is a macroscopic manifestation of the interaction between microscopic nucleons.It describes the relationship between the binding energy,pressure,density and isospin asymmetry of nuclear matter.The heavy ion collisions（HICs）experiment provides a unique condition for us to study the properties of different high-temperature and high-density nuclear matter.The elliptic flow（v₂）is one of the most important sensitive observations for exploring the properties of nuclear matter by HICs,andv₂ is affected by the dynamic process.From theoretical point of view,v₂ is highly sensitive to the mean field potential and nucleon-nucleon（NN）collisions.However,a quantitative attribution of these effects to v₂ is a few,so we quantitatively analyze the factors that affect v₂ in this thesis（for master’s degree）.Based on the Ultra-relativistic Quantum Molecular Dynamics（UrQMD）model,the free nucleons in the rapidity range of the final state of the reaction are selected,and then the time evolution of v₂ of these tracked（or labeled）nucleons is studied by reversely tracing the free nucleons in the entire HICs process.The results obtained by using the above transport models and methods are as follows:（1）By reversely tracing free nucleons that are finally emitted at mid-rapidity（|y₀|<0.1）in HICs process,the time evolution of v₂ of these traced nucleons is studied in gold-gold（Au+Au）collisions at beam energy of 0.4 GeV/nucleon with different impact parameters.The calculation results show that the initial value of v₂ is positive and increases with impact parameter it is positive at the beginning and increases with the increase of collision parameters,then decreases with time and tends to be saturated at negative values.In addition,nucleon-nucleon collisions will suppress the value of v₂（enhance the out-of-plane emission）,while the effect of the nucleon mean field potential is more complex,which depends on both collision parameters and reaction time.At the same time,the most relevant density probed by v₂ of nucleons at mid-rapidity is found to be～60%of the maximum density reached during the collisions.（2）The influence of the（with or without）Fermi momentum on the time evolution ofv₂ in the initial state is analyzed.The results show that the value of v₂ is related to the Fermi momentum of the initial nucleons.The yield of free nucleons in the mid-rapidity with considering the Fermi momentum is much larger than that obtained without the Fermi momentum,due to the reduction in the yield of NN collisions.However,v₂ shows the opposite effect,it obtained with considering the Fermi momentum is much smaller than without considering the Fermi momentum,because the spectator nucleons have the stronger blocking effect in the transport model.（3）The influence of different mid-rapidity and transverse momentum window on the time evolution of v₂ is further explored.The calculation results show that with different mid-rapidity of free nucleons,there is no influence of v₂ at the initial time;as the reaction proceeds（t（29）10 fm/c）,for the larger mid-rapidity,the smaller the value of v₂,which is due to the weaker blocking effect caused by the more tracked free nucleons.For different transverse momentum（p_t）windows,for the larger p_t,indicating that the window for the tracked free nucleons becomes smaller,the value v₂ is relatively larger,due to the fewer tracked nucleons are susceptible to the stronger blocking effects.Therefore,when analyzing the time evolution of the v₂ as an observation at intermediate energies HICs,it is necessary to consider the influence of the impact parameters,the Fermi momentum of the initial nucleus,rapidity and transverse momentum.Only through such detailed quantitative analysis can we determine the influence of each factor,and then better study the nuclear equation of state.