Study of Symmetry Energy with Heavy Ion Collision

1. Study of Symmetry Energy with Heavy Ion Collision HIM-KORIA meeting, May 9, 2009 Pusan National University Chang Ho Hyun Daegu University

2. Contents Nuclear physics with radioactive beam facilities Symmetry energy Symmetry energy at sub-nuclear density Symmetry energy at supra-nuclear density Astrophysical application : Neutron star Prospect

3. Nuclear physics with radioactive beam facilities Astrophysics - Origin of heavy elements - Key reactions in supernova explosion - Neutron star EoS and structure Nuclear Structure - Nuclei far from stability valley - Creation of new elements - Synthesis of superheavy elements Symmetry and New physics - Weak nuclear force : parity violation - Permanent electric dipole moment : time reversal breaking

4. Symmetry energy -16 MeV 21 MeV Important in neutron rich heavy nuclei and neutron star Mass formula Mean field model Definition How dependent on density?

5. Modified Gogny force t = 1/2, t ’ = - 1/2, s = 4/3, B = 106.35 MeV x : Mimicvarious predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions

6. Dependence of S(r) on x softer • How to determine the density dependence • r < ro : Isospin diffusion, fragments, np spectra ratios and differential flow • ro < r < 2ro : p-/p+ spectra ratio • 2ro < r < 3ro : np spectra ratio and differential flow

7. Role of symmetry energy in nuclear and astrophysics

8. Symmetry energy at sub-nuclear density Isospin diffusion

9. Probe the symmetry energy at sub-nuclear densities in 124Sn + 112Sn stiff soft Experiment at NSCL stiff EoS  small diffusion; |Ri|≫0 soft EoS  fast equilibrium; Ri0 • NSCL measurement : R ~ 0.46 • Observable in HIC is sensitive to r dependence of S and should provide constraints to symmetry energy

10. Constraints on symmetry energy at saturation density from HIC IBUU IQMD • Uncertainties at nuclear density • IBUU : S(r) ~ 31.6 (r/r0)g ; 0.69 ≤ g ≤ 1.05 • IQMD : S(r) ~ 12.5 (r/r0)2/3 + Csp (r/r0)g ; 0.4≤g≤1.05

11. Reduce uncertainty Require new experiment Density dependence

12. Symmetry energy at supra-nuclear density p-/p+ spectra ratio Production of p- and p+ proportional to the square of n to p ratio at their production site • D(1232) resonance model • Thermal model • Transport model

13. Isospin asymmetry in HIC E/A=800 MeV, b=0, t=10 fm/c

14. Central density π-/ π+ probe of dense matter Soft Stiff Formation of dense, asymmetric nuclear matter

15. N/Z dependence of pion production and effects of the symmetry energy Softer

16. Astrophysical application : Neutron star Sub-nuclear phase : Structure of the NS crust NS EoS : Radius and Mass NS cooling : Direct URCA process Neutron rich nuclei can provide terrestrial laboratory to study the questions : That’s why we need RIBF Density dependence of the symmetry energy plays an important role to the above questions

17. Nucleon matter Example : Mass-radius of NS The softest symmetry energythat the TOV is still stable is x=0.93 giving Mmax=0.1 Msun and R=>40 km

18. Prospect • MSU (2009-2012) : E/A < 100 MeV  measure isospin diffusion, fragments, residues, p,n spectra ratios and differential flow  improve constraints on S(r) at r<ro • MSU (~2013) : E/A > 120 MeV  measure p+, p- spectra ratios  constraints at ro<r <1.7ro • GSI (2011) : E/A ~ 400 – 800 MeV  measure p,n spectra ratios and differential flow  determine constraints S(r) at 2.5ro<r< 3ro

19. MSU Riken GSI • Riken (2011) : E/A > 50 MeV  measure isospin diffusions for fragments and residues  determine S(r) at r< 2ro. 108Sn+112,124Sn – RI beam to increase d • Riken (2013-2017) : E/A = 200-300 MeV measure p+, p- spectra ratios, p,n, t/3He spectra ratios and differential flow  determine S(r) at r~ 2ro