Report

The sensitivity of probes to DDSP at high densities Qingfeng Li * DDSP: Density dependent symmetry potential Outline Brief introduction to the DDSP. Predicted sensitive probes to DDSP at high densities. However, too many (huge) uncertainties from other potentials, from collision term, from models and from experiments, etc are awaiting us to solve. Several examples. No conclusions, only remarks. 2015/7/17 ASY-EOS Workshop 2008,Catania 2 SP is relatively small Binding energy from Liquid-drop mass formula: = Isospin-dependent EoS (energy density as a function of and ): E(, ) E(,0) Esym ( ) 2 O( 4 ), (n p ) / Initial 2: Au: 0.0392; Pb:0.0447 Zr96:0.0278;Ru96:0.0069 Sn132:0.0587;Sn124:0.0375 2015/7/17 It would not be a big deal if the uncertainty in Esym was not big ASY-EOS Workshop 2008,Catania 3 The origin of the DDSP ---From the RBUU point of view. L LF LI i 1 1 LF x x M N x x F F 2 2 4 1 1 L L U U U U 2 4 1 Lint g g g g 2 p p X X , p , t Re X , p , t X HF F p * M Re X X Re F X , p, t p p Re F X , p, t H X M* * f X, p E p 1 dp2 dp3 dp4 4 2 p p p 2 3 p4 E p E p2 E p3 E p4 2 2 3 2 3 2 3 Wel ,in p, p2 , p3 , p4 Fel2,in Fel1,in ~ d 3 p2 v 2015/7/17 d el ,in s, t d d ASY-EOS Workshop 2008,Catania 4 The isospin effects in RBUU ESym 2 2 g2 1 K f 1 g { 2 2( 6 E f 2 4m m M *2 )} B g EF2 [1 2 A( K f , M * )] m 2 Hartree Term A( K f , M ) * pp ,nn ,np d d pp ,nn ,np d 1 2 d cos 1 d pp ,nn ,np d 4 (2 )3 d k (k k2 3 2 2 M * )3 / 2 2i Fi t 2 i t Interaction 2015/7/17 Direct Term ASY-EOS Workshop 2008,Catania Exchange Term 5 Density dependence of symmetry potential at low and high densities Phenomenological Skyrme parameter sets 18 sets From B. Alex Brown, PRL 85, 5296 (2000) Uncertainty comes mainly from high density region 2015/7/17 ASY-EOS Workshop 2008,Catania 6 Is the DDSP at high densities mainly important to neutron star? It might impact on nuclear physics when one investigates the HICs induced by radioactive beam at intermediate energies. Now, the community tries to find the effect of DDSP on observables from HICs at intermediate energies (~0.252.0A GeV) 2015/7/17 ASY-EOS Workshop 2008,Catania 7 Predicted probes of DDSP at high densities from the HICs The (double) ratio of multiplicities of charged nucleons, s, s, pions, kaons and hard photons as functions of Eb, b, N/Z; pt, y, Ekin, etc. The (double) flow, flow difference, differential flow of nucleons, pions as functions of Eb,b,N/Z,pt, y, Ekin, etc. 2015/7/17 ASY-EOS Workshop 2008,Catania 8 Difficulties and Uncertainties With the increase of beam energy (to ~A GeV): ① the compression stage is shorter The effect of nucelar MF on dynamics is weaker The isospin asymmetry during dynamic evolution is reduced ② ③ 2015/7/17 The dynamics is dominated by CT rather than the nuclear MF. In addition to and , other resonances and mesons produce which makes the situation much more complicated Large medium modification on the collision term The relativistic effects in kinetic or dynamic transports ……(from experimental sides?) Not easy to achieve our goal ASY-EOS Workshop 2008,Catania 9 Meson multiplicity ratio and double ratio New “puzzles” Eb=1.528A GeV INM Au+Au (N/Z=1.494) HIC 132Sn+124Sn From W. Reisdorf etal, NPA781,459(2007) 2015/7/17 From X. Lopez etal PRC75, 011901(R) (2007) ASY-EOS Workshop 2008,Catania 10 The update of UrQMD for heavy ion reactions at Eb~0.1-2A GeV SP for all baryons. (for some non-nucleonic particles, C-G coefficients of isospin coupling are employed. MD for all baryons. (isospin independent) Coulomb interaction between two mesons or MesonBaryon. More EoS parameter sets. (H, S, HM, SM), which describe the ground state properties of finite nuclei equally well (KNM ranges from 200 to 400 MeV). The medium modified N-N elastic cross section (optional). Relativistic effect on relative distances in phase space of two particles (Lorentz transformation). See, e.g., JPG32,151(2006) and PLB659,525(2008) 2015/7/17 ASY-EOS Workshop 2008,Catania 11 Example I uncertainty from Afterburner program 1. 2. 2015/7/17 To construct clusters of nucleons, one Afterburner analyzing program is usually used to couple to the transport model. But, usually, it is paid less attention. There exist two types: In QMD-like models, the phase-space coalescence model is employed. In BUU-like models, a density cut (in coordinate space) is often used to find out free nucleons. Due to the smallness of DDSP effect, one should check the effect from the difference of the two types. ASY-EOS Workshop 2008,Catania 12 Cluster freeze-out “Coalescence Model” 2015/7/17 ASY-EOS Workshop 2008,Catania “Density-cut” 13 pt dependence of the N/Z ratio c=0/10 Sensitive to SP at both low and high densities n/p (double) ratios at small pt are influenced by the freeze-out criteria The ratios at large pt are not influenced by the freeze-out criteria. Argument: one needs to investigate the isospin dependent momentum dependent term 2015/7/17 ASY-EOS Workshop 2008,Catania 14 Example II: contamination in reconstruction at freeze-out “contaminated reconstruction” mode 2015/7/17 “clean reconstruction” mode ASY-EOS Workshop 2008,Catania 15 pt dependence of 0/++ ratio “contamination” effect is huge at small Ekin due to the rescattering of nucleons. Two modes give two different ratios (L) and scaled ratios (R) vs Ekin in both low and high regions. The reconstruction should be analyzed with care. 2015/7/17 ASY-EOS Workshop 2008,Catania 16 Example III: Mesonic Coulomb Potential and reduction of N channel on Pion flows (v1 and v2) 0.05 1.5A GeV FOPI data, from W.Reisdorf etal, NPA781,459(2007) - v1 - + 0 =<px/pt> + 0.04 -v2 =<(px2-py2)/pt2> 0 b0:0.25-0.45 2015/7/17 ASY-EOS Workshop 2008,Catania 17 Several remarks The isospin-independent terms are also needed to check carefully when investigating the symmetry potential at high densities. Nucleon-related quantities should be paid much more attention. Higher beam energy HIC is not always better. HICs at beam energies ~100-800A MeV are recommended at this time. Better Afterburner program is needed Detailed comparison between transport models is urgently needed. I call for closer cooperation between theoretical and experimental physicists. 2015/7/17 ASY-EOS Workshop 2008,Catania 18 As were done before We will be the next, yes? 2015/7/17 ASY-EOS Workshop 2008,Catania 19 Thanks Contact me? [email protected] [email protected] 2015/7/17 ASY-EOS Workshop 2008,Catania 20