Based on the semi-classical Thomas-Fermi approximation together with the Skyrme energy-density functional, we study the deformation dependence of symmetry energy coefficients of finite nuclei. The symmetry energy coefficients of nuclei with mass number A = 40, 100, 150, 208 are extracted from two-parameter parabola fitting to the calculated energy per particle. We find that the symmetry energy coefficients decrease with the increase of nuclear quadrupole deformations, which is mainly due to the isospin dependence of the difference between the proton and neutron surface diffuseness. Large deformations of nuclei can cause the change of the symmetry energy coefficient by about 0.5 Me V and the influence of nuclear deformations on the symmetry energy coefficients is more evident for light and intermediate nuclei.
A new version of improved quantum molecular dynamics model that includes standard Skyrme interactions has been developed.Based on the new code,four commonly used parameter sets,SLy4,SkI2,SkM*and Gs are adopted in the improved quantum molecular dynamics model and the isospin sensitive observables,namely isospin transport ratios,single and double ratios of the yields of neutrons and protons are investigated.The isospin transport ratios are strongly sensitive to the slope of symmetry energy,and are not very sensitive to the nucleon effective mass splitting.On the other hand,the high energy neutrons and protons yields ratios from reactions at different incident energies provide a good observable to the momentum dependence of nucleon effective mass splitting.By comparing our calculations with the data,we find that the constrained L value(the slope of density dependence of symmetry energy) is about ~46 MeV when the Skyrme type interaction is considered in transport models,and the isospin diffusion data prefer to mn*>mp*,but it is not a strong constraint with deep χ2minimum.
Some nearly-symmetric fusion reactions are systematically investigated with the improved quantum molecular dynamics(Im QMD)model. By introducing two-body inelastic scattering in the Fermi constraint procedure, the stability of an individual nucleus and the description of fusion cross sections at energies near the Coulomb barrier can be further improved. Simultaneously, the quasifission process in154Sm+160Gd is also investigated with the microscopic dynamics model for the first time. We find that at energies above the Bass barrier, the fusion probability is smaller than 10-5for this reaction, and the nuclear contact time is generally smaller than 1500 fm/c. From the central collisions of Sm+Gd, the neutron-rich fragments such as164,165 Gd,192W can be produced in the Im QMD simulations, which implies that the quasi-fission reaction could be an alternative way to synthesize new neutron-rich heavy nuclei.
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
The nucleon-nucleon interaction is investigated by using the improved quantum molecular dynamic （ImQMD） model with three sets of parameters IQ1, IQ2 and IQ3, in which the corresponding incompressibility coefficients of nuclear matter are different. The charge distributions of fragments are calculated for various reaction systems at different incident energies. The parameters strongly affect the charge distributions and the fragment multiplicity spectrum below the threshold energy of nuclear multifragmentation. The fragment multiplicity spectrum for 238U＋197Au at 15 A MeV and the charge distributions for 129Xe＋12~Sn at 32 and 45 A MeV, and 197Au＋197Au at 35 A MeV are reproduced by the ImQMD model with the set of parameter IQ3. It is found that： 1） The charge distribution of the fragments and the fragment multiplicity spectrum are good observables for testing the model and the parameters. 2） The Fermi energy region is a sensitive energy region for studying nucleon-nucleon interaction.
The nuclear symmetry energy coefficient（including the coefficient asym^（4） of the I^4 term） of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei.It is found that the extracted symmetry energy coefficient asym^＊（A,I） decreases with increasing isospin asymmetry I,which is mainly caused by Wigner correction,since esym^＊ is the summation of the traditional symmetry energy esym and the Wigner energy ew.We obtain the optimal values J = 30.25±0.10 MeV,ass=56.18±1.25 MeV,asym^（4） = 8.33±1.21 MeV and the Wigner parameter x= 2.38 ±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with20 ≤ A ≤ 261 with an rms deviation of 23.42 keV.We also find that the volume symmetry coefficient J≌ 30 MeV is insensitive to the value x,whereas the surface symmetry coefficient ass and the coefficient asym^（4） are very sensitive to the value of x in the range 1≤x≤4.The contribution of the asym^（4） term increases rapidly with increasing isospin asymmetry I.For very neutron-rich nuclei,the contribution of the asym^（4） term will play an important role.
