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Based on the microscopic transport model UrQMD in which hadronic and string degrees of freedom are employed, the HBT parameters in the longitudinal co-moving system are investigated for charged pion and kaon, and Λ sources in heavy ion collisions (HICs) at SPS and RHIC energies. In the Cascade mode, RO and the RL at high SPS and RHIC energies do not follow the mT-scaling, however, after considering a soft equation of state with momentum dependence (SM-EoS) for formed baryons and a density-dependent Skyrme-like potential for “pre-formed” particles, the HBT radii of pions and kaons and even those of Λs with large transverse momenta follow the mT-scaling function R=3/mT fairly well.
Based on the UrQMD transport model, the transverse momentum and the rapidity dependence of the Hanbury-Brown-Twiss (HBT) radii R_L, R_O, R_S as well as the cross term R_OL at SPS energies are investigated and compared with the experimental NA49 and CERES data. The rapidity dependence of the R_L, R_O, R_S is weak while the R_OL is significantly increased at large rapidities and small transverse momenta. The HBT "life-time" issue (the phenomenon that the calculated sqrt R_O^2-R_S^2 value is larger than the correspondingly extracted experimental data) is also present at SPS energies.
The pion source as seen through HBT correlations at RHIC energies is investigated within the UrQMD approach. We find that the calculated transverse momentum, centrality, and system size dependence of the Pratt-HBT radii R_L and R_S are reasonably well in line with experimental data. The predicted R_O values in central heavy ion collisions are larger as compared to experimental data. The corresponding quantity sqrt R_O^2-R_S^2 of the pion emission source is somewhat larger than experimental estimates.
The nuclear stopping, the elliptic flow, and the HBT interferometry are calculated by the UrQMD transport model, in which potentials for “pre-formed” particles (string fragments) from color fluxtube fragmentation as well as for confined particles are considered. This description provides stronger pressure at the early stage and describes these observables better than the default cascade mode (where the “pre-formed” particles from string fragmentation are treated to be free-streaming). It should be stressed that the inclusion of potential interactions pushes down the calculated HBT radius RO and pulls up the RS so that the HBT time-related puzzle disappears throughout the energies from AGS, SPS, to RHIC.
The N/Z ratio of free nucleons from collisions of neutron-rich nuclei as a function of their momentum is studied by means of Isospin dependent Quantum Molecular Dynamics. We find that this ratio is not only sensitive to the form of the density dependence of the symmetry potential energy but also its strength determined by the symmetry energy coe cient. The uncertainties about the symmetry energy coe cient influence the accuracy of probing the density dependence of the symmetry energy by means of the N/Z ratio of free nucleons of neutron-rich nuclei.
It is shown that the inclusion of hadronic interactions, and in particular nuclear potentials, in simulations of heavy ion collisions at the SPS energy range can lead to obvious correlations of protons. These correlations contribute significantly to an intermittency analysis as performed at the NA61 experiment. The beam energy and system size dependence is studied by comparing the resulting intermittency index for heavy ion collisions of different nuclei at beam energies of 40A, 80A and 150A GeV. The resulting intermittency index from our simulations is similar to the reported values of the NA61 collaboration, if nuclear interactions are included. The observed apparent intermittency signal is the result of the correlated proton pairs with small relative transverse momentum Δpt, which would be enhanced by hadronic potentials, and this correlation between the protons is slightly influenced by the coalescence parameters and the relative invariant four-momentum qinv cut.
The rapidity dependence of the single- and double- neutron to proton ratios of nucleon emission from isospin-asymmetric but mass-symmetric reactions Zr+Ru and Ru+Zr at energy range 100 ~ 800 A MeV and impact parameter range 0 ~ 8 fm is investigated. The reaction system with isospin-asymmetry and mass-symmetry has the advantage of simultaneously showing up the dependence on the symmetry energy and the degree of the isospin equilibrium. We find that the beam energy- and the impact parameter dependence of the slope parameter of the double neutron to proton ratio (F_D) as function of rapidity are quite sensitive to the density dependence of symmetry energy, especially at energies E_b ~ 400 A MeV and reduced impact parameters around 0.5. Here the symmetry energy effect on the F_D is enhanced, as compared to the single neutron to proton ratio. The degree of the equilibrium with respect to isospin (isospin mixing) in terms of the F_D is addressed and its dependence on the symmetry energy is also discussed.
The influence of the isospin-independent, isospin- and momentum-dependent equation of state (EoS), as well as the Coulomb interaction on the pion production in intermediate energy heavy ion collisions (HICs) is studied for both isospin-symmetric and neutron-rich systems. The Coulomb interaction plays an important role in the reaction dynamics, and strongly influences the rapidity and transverse momentum distributions of charged pions. It even leads to the pi- pi+ ratio deviating slightly from unity for isospin-symmetric systems. The Coulomb interaction between mesons and baryons is also crucial for reproducing the proper pion flow since it changes the behavior of the directed and the elliptic flow components of pions visibly. The EoS can be better investigated in neutron-rich system if multiple probes are measured simultaneously. For example, the rapidity and the transverse momentum distributions of the charged pions, the pi- pi+ ratio, the various pion flow components, as well as the difference of pi+-pi- flows. A new sensitive observable is proposed to probe the symmetry potential energy at high densities, namely the transverse momentum distribution of the elliptic flow difference [Delta v_2^pi+ - pi-(p_t rm c.m.].
Probing the density dependence of the symmetry potential in intermediate energy heavy ion collisions
(2005)
Based on the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effects of the density-dependent symmetry potential for baryons and of the Coulomb potential for produced mesons are investigated for neutron-rich heavy ion collisions at intermediate energies. The calculated results of the Delta-/Delta++ and pi -/pi + production ratios show a clear beam-energy dependence on the density-dependent symmetry potential, which is stronger for the pi -/pi + ratio close to the pion production threshold. The Coulomb potential of the mesons changes the transverse momentum distribution of the pi -/pi + ratio significantly, though it alters only slightly the pi- and pi+ total yields. The pi- yields, especially at midrapidity or at low transverse momenta and the p-/pi+ ratios at low transverse momenta, are shown to be sensitive probes of the density-dependent symmetry potential in dense nuclear matter. The effect of the density-dependent symmetry potential on the production of both, K0 and K+ mesons, is also investigated.
We investigate the sensitivity of several observables to the density dependence of the symmetry potential within the microscopic transport model UrQMD (ultrarelativistic quantum molecular dynamics model). The same systems are used to probe the symmetry potential at both low and high densities. The influence of the symmetry potentials on the yields of pi-, pi+, the pi-/pi+ ratio, the n/p ratio of free nucleons and the t/3He ratio are studied for neutron-rich heavy ion collisions (208Pb+208Pb, 132Sn+124Sn, 96Zr+96Zr) at E_b=0.4A GeV. We find that these multiple probes provides comprehensive information on the density dependence of the symmetry potential.