Workshop on relativistic heavy ion collisions May 21

Workshop on relativistic heavy ion collisions May 21 -24, 2008, Wu han Nuclear EOS from heavy ion collisions at Ge. V/u regime Zhigang XIAO Department of physics, Tsinghua University Collaborators Ming Zhang, Pengfei Zhuang … Tsinghua University, Beijing, China Fen Fu, Zhaoqing Feng, Gaochan Yong Institute of Modern Physics, CAS, Lanzhou, China & FOPI collaboration GSI, Darmstadt

Content Introduction Probes to the EOS Dynamic Effects on the EOS determination Summary

EOS representation : Compressibility Esym • Consistence Maintained at low density • Sensitive on and . T. Klaehn et al. , Phys. Rev. C 74, 035802 (2006)

How via HIC? Nucl. EOS Flow H I C: Initial conditions Transport Process Freeze K, … Out Cluster …… • EOS used as input, tested by exp. /model. consistency.

The fate of Spinosaurid … P. C. Sereno et al. Science, Nov. 13, 1298(1998). (Spinosaurid) For about 50 years Spinosaurid has been vegetarian, now it is a carnivore. Imagine what it’ll be in the next 50 years, 100 years, …?

Introduction Probes to the EOS Compressibility of symmetrical nuclear matter Symmetry energy at high densities Dynamic effects on the EOS determination Summary

Compressibility of symmetric nuclear matter: K+ and More compressed Less compressed C. Fuchs et al. , Phys. Rev. Lett 86, 1974 (2001) • NOTICE 1: Insensitive in light system C+C • NOTICE 2: Higher sensitivity found at low energies

Compressibility of symmetric nuclear matter P. Danielewicz, R. Lacey and W. G. Lynch, Science, 298 (2002), 1592 A. Andronic et al. , Phys. Lett. B 612 (2005) 173. • V 1 Soft ，V 2 Stiff； • constrained roughly (167, 380) • Model and ion dependent

EOS of asymmetric nuclear matter： Esym ~1 Ge. V/u B. A. Li Phys. Rev. Lett. 88, 192701 (2002) L. W. Chen et al. , ar. Xiv: 0709. 0900 v 2 [nucl/th]

Probes to Esym A lots of probes proposed, few experiments Solidity of the probes Experimental precision 、K Esym

Probe 1：Isospin diffusion B. A. Li et al. , PRC 72, 064611 (2005) L. W. Chen et al. , PRL 94, 032701(2005)

Probe 2 : K 0/K＋ ， －/ ＋ ~4% ~7% G. Ferini et al. , PRL 97(2006), 202301 G. C. Yong et al. , PRC 73(2006), 034603 • K＋、K 0 produced at early stage without strong absorption. • K 0/K＋ sensitively rely on Esym. • Sensitivity increases with system N/Z asymmetry. • NOTICE 2 again: Higher sensitivity found at low energies

…No experimental confirmation！ Why ? ? ? Collision dynamic effect reduces the sensitivity Experimental precision not high enough to pin down Esym nn p - cancels out part of the N/Z asymmetry； • NOTICE 3: Much less sensitive in HIC than in infinite nuclear matter FOPI collaboration, PRC 75, 011901 (2007)

Introduction Probes to the EOS Dynamic effects on the EOS determination Nuclear Transparency Correlation to the Compression Revisit to the determination of Esym( ) from pion probes Summary

Introduction to FOPI device • • • Operating at ~ Ge. V/u Full phase coverage, azimuthally symmetric Charged particle measurement

Stopping Transverse/Longitudinal symmetry • Longitudinal distribution broader than transverse Partly transparent FOPI collaboration et al. , In progress

Stopping hierarchy: Pb+Pb vs. Ni+Ni Higher Ebeam less stopping; Lighter system less stopping; Heavier mass less stopping; FOPI collaboration et al. , In progress

Stopping vs. compression/pressure F. Fu, Z. G. Xiao et al. , In progress More Stopping More Compressed Larger signal FOPI collaboration. , PRL 92(2004), 232301 More sensitive on EOS

Stopping vs Density gain • Less Stopping • Less compression • Lower gain for density F. Fu, Z. G. Xiao et al. , In progress

Revisit to the Esym from probe

Introduction to IBUU 04 References: G. C. Yong et al. , PRC 73(2006)034603 B. -A. Li, PRC 69 (2004) 064602

Multiplicity reproduced by the model, But shows insignificant sensitivity on the Esym( ).

Stopping probed by pions With increasing the beam energy, Stopping decreases. Tendency repeated. “Temperature” and Stopping overestimated.

R( -/ +) vs Ebeam Eb>0. 6 Ge. V/u: Undistinguishable Eb<0. 6 Ge. V/u: Soft Esym seems favored. Unlike the result at 50 Me. V/u?

<pt( +)>/<pt( -)> vs Ebeam Bend-off with decreasing Ebeam, seems to be sensitive to the x at lower beam energy Measure excitation function at lower energy helps!

Sensitivity vs Ebeam energy stopping sensitivity Measurement of pion emissions at lower energy may helps to resolve the Esym( )!

Summary Nuclear stopping is systematically studied by varying the system size, beam energy and species. A hierarchy is established. Correlation between the stopping and the compression is demonstrated. As a global mechanism, it may hinder the gaining of high baryon density in HIC at Ge. V/u regime, and thus reduce the sensitivity of determining the asymmetric nuclear EOS. With IBUU 04, we compare the ratio of the yield and of the mean transverse momentum of - and + to the data. Rather consistence between the data and the model is obtained. From the comparison it seems that a softer Esym( ) (x=1 to 0) is favored by the data, which is at variance with the conclusion drawn at low energy (x=0 to -1). } The sensitivity of the observables on Esym( ) is found clearly correlated to the degree of stopping or beam energy, being significant near the threshold of pion production. Beam energy less than 0. 5 Ge. V/u is favorable for Esym( ) study.

Thank you!