The Nuclear Symmetry Energy And The Collective Flow Of Light Clusters In Heavy-ion Collisions

Nuclear equation of state (EOS), a mathematical relationship between energy and nuclear density, isospin asymmetric and temperature, is one of hot topic in nuclear physics for a long time. Moreover, a number of radioactive beam facilities are being constructed in recent years, the isospin degree of freedom in nuclear EOS has attracted a lot of attention. Although the EOS of isospin symmetric nuclear matter has been limited in a narrow region (its incompressibility Ko is in the range200-260MeV), the EOS of isospin asymmetric nuclear matter is still poorly known, the largest uncertainty comes from the density dependence of the nuclear symmetry energy. Knowledage of the nuclear symmetry energy is important for understanding the properties of exotic nuclei, heavy-ion reactions with radioactive beams and the structure of neutron stars. A large number of theoretical and experimental investigations of the nuclear symmetry energy were carried out. Unitl very recently, the nuclear symmetry energy at subnormal densities are relatively well constrainted, but the high-density behavior of the nuclear symmetry energy is still poorly known.At present, heavy-ion experiments combined with model simulation approaches are among the most important ways to investigate the EOS and/or symmetry energy at high densities. Recently, by using the large acceptance apparatus FOPI at the Schwerionen-Synchrotron (SIS) at GSI, a large amount of data (e.g., stopping power, yield, collective flow) for light charged particles from intermediate energy heavy-ion collisions have been made available. These data offer new opportunities to refine the incompressibility Ko, test theoretical models and extract the information of the symmetry energy.In this work, we update the mean field potential, collision term and cluster recognition criteria of the ultrarelativistic quantum molecular dynamics (UrQMD) model. The Skyrme potential energy density functional is introduced to obtain potential parameters, both the medium modified nucleon-nucleon elastic cross section and Pauli blocking term are updated, an isospin-dependent minimum spanning tree algorithm is considered. The effects of those three parts on collective flow of light clusters are detailed studied, and we found that,(1). it is difficult to get a more exact value of the incompressibility from the present flow data than K0=23O±30MeV,(2) the different choices of medium-modified nucleon-nucleon cross section exhibit a significant influence on the light particle flows and stopping power, and (3) the influence of the cluster recognition method on cluster flows is weak. The experimental data can be reproduced rather well by the updated UrQMD model with one of parameter sets.Within the newly updated UrQMD model, we choose19Skyrme interactions which give quite similar values of isoscalar quantities (e.g., K0) but different values of isovector quantities (e.g., the slope parameter L of symmetry energy), moreover in order to examine the influence of isoscalar quantities on the isospin-sensitive observables, another two Skyrme interaction which give larger K0are also included, the transverse-velocity dependence of the elliptic flow of free neutrons and protons (hydrogen isotopes) within different rapidity windows are studied. It is found that the elliptic flow difference (v2n-V2P) and ratio (v2n/v2p) of neutrons versus protons (hydrogen isotopes) are sensitive to the slope parameter L, especially the ratio at small transverse velocity in the intermediate rapidity intervals, and not sensitive to isoscalar quantities and the medium modified nucleon-nucleon cross section. By comparing both the transverse-momentum dependent (v2n/v2H) and the transverse-momentum-integrated (v2n-v2p, v2n/v2p, v2n-v2H, v2n/v2H) FOPI/LAND data with calculations, the slope parameter L=89±45MeV within a2-σ confidence limit and a (average) central value L≈85MeV are obtained, respectively. A slightly larger slope parameter L≈110MeV is determined from a similar comparison with the transverse-momentum-integrated FOPI/LAND data for which the ERAT has been used for the impact parameter determination instead of the particle multiplicity. The presented results are in full agreement with the previous studies performed with the UrQMD or Tubingen quantum molecular dynamics models, indicating a moderately soft to linear density dependence of the symmetry energy. They contrast to the results obtained with π-/π+yield ratios available in the literature. In addition, it is found that the elliptic flow difference between3H and3He in the intermediate rapidity intervals is also sensitive to the slope parameter L.