Using the Ultrarelativistic Quantum Molecular Dynamics(UrQMD) model,the balance energies of free neutrons,free protons and Z=1 particles(including free protons,deuterons and tritons) from mass symmetric heavy-ion collisions with isotopes,isobars and isotones are studied.The influence of nuclear symmetry potential energy on the balance energy is emphasized.It is found that the balance energy of free neutrons is sensitive to the nuclear symmetry energy,while that of free protons is not.Particularly,the initial neutron/proton ratio dependence of the balance energy of free neutrons from Sn isotopes can be taken as a useful probe to constrain the stiffness of the nuclear symmetry energy.
The influence of the density-dependent symmetry energy on the balance energy （Ebal） of directed flow from heavy ion collisions （HICs） at incident energies covered by INDRA and MSU experiments is studied, using the updated version of the ultra- relativistic quantum molecular dynamics （UrQMD） model, especially adapted to low-energy heavy ion collisions （HICs）. Four mass-symmetric reactions with total mass numbers between 192 and 394 are chosen for investigating the influence of the symmetry energy on the system-mass dependence of Eual. The results show that the uncertainty in the density dependence of the symmetry potential causes changes of Ebal of the order of several MeV, depending on the type of particle considered. The Ebal of neutrons from HICs is particularly sensitive to the density dependence of the symmetry potential energy, while the system-mass dependence of EbaI of Z = 1 particles is not.
Fusion hindrance in the radial degree of freedom for massive nuclear reactions is known for a long time. However the present work shows that the fusion hindrance also exists in the neck evolution. We calculate the potential at different distances and different neck parameters by the two-center liquid drop model and then check whether fusion hindrance exists in the neck evolution by examing the sign of slope of potential vs. the neck parameter. The area of fusion hindrance in the neck evolution is shown.
In this review article,we first briefty introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies.The developments of improved quantum molecular dynamics model(ImQMD)and ultra-relativistic quantum molecular dynamics model(UrQMD),are reviewed.The reaction mechanism and phenomena related to the fusion,multinucleon transrer,fragmentation,collective flow and particle production are reviewed and discussed within the framework of the two models.The constraints on the isospin asymmetric muclear equation of state and in-medium nucleon nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed,and the uncertainties of these constraints are analyzed as well.Finally,we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism,the descriptions of various observables,the constraint on the nuclear equation of state,as well as for the constraint on in-medium nucleon-nucleon cross sections.
Ying-Xun ZhangNing WangQing-Feng LiLi OuJun-Long TianMin LiuKai ZhaoXi-Zhen WuZhu-Xia Li
