A Treatment Of Initialization And Mean-field Potential In The Improved Quantum Molecular Dynamics Model

Quantum molecular dynamics model is an important branch of transport model.In the quantum molecular dynamics model,the method of initialization of projectile nucleus and target nucleus,the density distribution of initial nucleus,the stability of initial nucleus and so on all have important influence on the description of the reaction process of heavy ion collision and the theoretical prediction of observables.However,due to the complexity of transport theory,most quantum molecular dynamics models still have shortcomings in the accurate description of initialization and the correlation between initialization and potential field.For example,most quantum molecular dynamics can not perfectly reproduce the den-sity distribution of initial nucleus.Even the simplest two-parameter Woods-Saxon density distribution can not be reproduced,the density distribution given by quantum molecular dynamics is still far from it.In addition,many models deal with the relationship between the density distribution of the initial nucleus and the potential field independently.This independent treatment increases the uncertainty of the isospin sensitive observations given by the model.Furthermore,it also increases the uncertainty of constraints such as the equa-tion of state of nuclear matter,symmetry energy and nucleon-nucleon cross section in the medium.Therefore,we urgently need to theoretically answer such a theoretical question,namely,can the quantum molecular dynamics model reproduce the simplest Woods-Saxon distribution?What are the conditions?Do we have a suitable approximation scheme to correlate the initial nuclear density distribution with the potential field?In this paper,we have explored the above questions1)Through the inverse Weierstrass transformation,the paper theoretically explores how to re-produce the conditions of Woods-Saxon distribution by using Gaussian distribution particles The relationship between the width of Gaussian wave packet and Woods-Saxon dispersion parameters is established.The width of the wave packet required by this relation is smaller than that commonly used in QMD models.However,the small wave packets will affect the stability of the nucleus,so how to balance the width of wave packets required to reproduce the density distribution while ensuring the stability of the nucleus is a rather tricky prob-lem,and there is no perfect solution so far.Only in view of the specific research problems in these two aspects to make the corresponding trade-off,by balancing the contradictions and differences between the two to achieve the goal to achieve.2)an approximate method is established to deal with the relationship between the nuclear density distribution and the potential field during initialization.Firstly,by means of the restricted density variational method,a set of interaction parameters which are the same as those calculated by the potential field are input to obtain the corresponding initial nucleus density distribution,and the corresponding neutron half-density radius Rn,proton half-density radius Rp,and the binding energy of the system are given.Then,in the ImQMD model,the neutron and proton density distributions are sampled within Rn and Rp radii.Thus,the relationship between the initialization of the nucleus and the potential field is approximately established.3)The isospin sensitive observations are studied and discussed.We have reanalyzed the neu-tron to proton yield ratios for emitted free nucleons and for coalescence invariant nucleon yield for 112,124,132Sn+112Sn at the beam energy of 200 MeV per nucleon.The new calculation results show that the neutron to proton yield ratios can be used as a probe to investigate the behavior of symmetry energy in the high density region when the kinetic energy of the nucleon is higher than 100MeV.In addition,it is also proposed that the reaction cross sec-tions of primary fragments with mass numbers greater than 100 along the beam direction have a strong correlation with the slope of the symmetry energy,which can be used as a probe to constraining the symmetry energy.Under the condition of y/yproj c.m.?0.8,the sym-metry energy slope effect can be enhanced by the ratio of the average number of neutrons and protons of all emitted nucleons and fragments,and can also be used to determine the neutron skin of unstable neutron-rich nucleiThrough the above research work,we have theoretically answered the problem of model initialization.Through the improvement and perfection of the model initialization process,the uncertainty of the observation results caused by the model initialization process can be effectively reduced and the reliability of the model can be increased.Our calculations show that the neutron to proton yield ratios at high kinetic energy region and the reaction cross section of the primary heavy nucleus fragments with mass number greater than 100 along the beam direction can be used to probe the symmetry.