Collaborators THU: M. Zhang IMP : H. S. Xu, G. C. Yong

1. Pion Emission and its probing to Esym() at suprasaturation densities with HIC at sub-GeV energy regionZhigang XiaoDepartment of Physics, Tsinghua University Collaborators THU: M. Zhang IMP : H. S. Xu, G. C. Yong Texas A&M: B. A. Li SJTU: L. W. Chen GSI： FOPI collaboration

2.  Content  Introduction  An effective probe to Esym()  The most recent pion data  Pion ratio and its indication to Esym()  Softening of Esym()  Suggestions for further experiments near pion threshold  Summary

3. Probe: -/+ ratio B. A. Li PRC71 (2005)014608 Probes to Esym() at high density Charged pion ratio is a sensitive probe to the density dependence of the symmetry energy

4. Recent Pion Data from FOPI

5. Complete set of  multiplicity (I) W. Reisdorf et al. for FOPI collaboration NPA 781(2007) 459 Ca+Ca,Ru+Ru,Zr+Zr from 0.4 to 1.5AGeV, phase space, flow … Charged pion multiplicity consistent with previous data. Data set are largely extended.

6. Complete set of  multiplicity (II) W. Reisdorf et al. for FOPI collaboration NPA 781(2007) 459

7. Complete set of  multiplicity (III) W. Reisdorf et al. for FOPI collaboration NPA 781(2007) 459 IQMD underestimate the ratio At 400 AMeV, the ratio as a function of N/Z differs from that of 1.5 AGeV

8. C. B. Das, S. Das Gupta, C. Gale, B. A. Li PRC67(2003) 034611 Asymmetric energy at high density： little known IBUU04: B. A. Li Phys. Rev. Lett. 88, 192701 (2002) L. W. Chen et al., PRC 76, 054316 G.C.Yong et al., PRC73(2006)034603 B.-A. Li, PRC 69 (2004) 064602

9. Density profile of  production • s are mainly produced at >0

10. Switch x at >0 Switch x at <0 Switch x at <0 Effect of switching x in code • Ratio is sensitive to the change of x at supra-saturation density

11. ? ? A rather soft nuclear symmetry energy is more favored by FOPI data!!! Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502 Circumstantial Evidence for a Soft Nuclear Symmetry Energy at Supra-saturation Densities

12. 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

13. …No experimental confirmation！ Why ??? FOPI collaboration, PRC 75, 011901 (2007) 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； • Not only EOS is unknown; • Dynamics of HIC plays essential role in the determination of EOS (may reduce the sensitivity!)

14. 48Ca+48Ca 1.40 124Sn+124Sn 1.48 197Au+197Au 1.49 Beam Energy and System Size effect S= (-/+ )x=1 /(-/+ )x=0 1. -/+ > Isobar Model 2. Ebeam -/+ 3. Ebeam  S  Asys S 

15. Quantitative Relation between Degree of Isospin Fractionation and Sensitivity Sensitivity : S= (-/+ )x=1 /(-/+ )x=0

16. Summary • Within the framework of IBUU04, the most recent and complete  data set an partial constraint on Esym(). We observed a softening of Esym() at supra-saturation density, which might have many astrophysical indications. More experimental and theoretic work are desirable to reach a confirming Esym(). • It is shown from further simulations, as well as some previous experimental results, that the sensitivity of the  probe on Esym() increases with decreasing the beam energy or increasing the system size. Heavier colliding systems at relatively lower beam energy are preferential for the study of Esym() via pion probe.

17. P.C. Sereno et al. Science, Nov. 13, 1298(1998).(Spinosaurid) Ohm… What will it be 50 years later, 100 years later…? The spinosaurid has been herbivorous for 50 years, now it is supposed to be carnivorous. The fate of Spinosaurid … Thank you!

18. Medium effect on pion ratio Jun Xu, Z. M. Ko et al., arxiv nucl-th: 0906.1602v1

19. Revisit  and its relevance of Esym() Multiplicity Multiplicity reproduced by the model, But shows insignificant sensitivity on the Esym().