Helium-3 production from Pb+Pb collisions at SPS energies with the UrQMD model and the traditional coalescence afterburner

A potential version of the UrQMD （UrQMD/M） transport model and a traditional coalescence model are combined to calculate the production of 3He fragments in central Pb＋Pb collisions at SPS energies 20-80 GeV/nucleon. It is found that the Lorentz transformation in the afterburner influences visibly the 3He yield and should be considered in calculations. The rapidity distribution of 3He multiplicities （including the concave shape） can be described well with UrQMD/M when it stops during tout=（100＋25） fm/c and the coalescence afterburner with one parameter set of （R0,P0）=（3.8 fm, 0.3 GeV/c） is taken into use afterwards.

An explanation of the elliptic flow difference between proton and anti-proton from the UrQMD model with hadron potentials

The time evolution of both proton and anti-proton v2 flows from Au＋Au collisions at √SNN=7.7 GeV are examined by using both pure cascade and mean-field potential versions of the UrQMD model. Due to a stronger repulsion at the early stage introduced by the repulsive potentials and hence much less annihilation probabilities, anti-protons are frozen out earlier with smaller v2 values. Therefore, the experimental data of anti-proton v2 as well as the flow difference between proton and anti-proton can be reasonably described with the potential version of UrQMD.

Rapidity distribution of protons from the potential version of Ur QMD model and the traditional coalescence afterburner

Rapidity distributions of both E895 proton data at AGS energies and NA49 net proton data at SPS energies can be described reasonably well with a potential version of the Ur QMD in which mean-field potentials for both pre-formed hadrons and confined baryons are considered, with the help of a traditional coalescence afterburner in which one parameter set for both relative distance R_0 and relative momentum P_0,(3.8 fm, 0.3 Ge V/c), is used. Because of the large cancellation between the expansion in R_0 and the shrinkage in P_0 through the Lorentz transformation, the relativistic effect in clusters has little effect on the rapidity distribution of free(net) protons. Using a Woods-Saxon-like function instead of a pure logarithmic function as seen by FOPI collaboration at SIS energies, one can fit well both the data at SIS energies and the Ur QMD calculation results at AGS and SPS energies. Further, it is found that for central Au+Au or Pb+Pb collisions at top SIS, SPS and RHIC energies, the proton fractions in clusters are about33%, 10%, and 0.7%, respectively.