OUTLINE OF TALK

1. Exploring the symmetry energy at sub and supra-saturation densities Yu-Gang Ma马余刚Shanghai Institute of Applied Physics, Chinese Academy of Science

2. OUTLINE OF TALK (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights (2) Work Done (i) Symmetry energy or isospin migration at sub-saturation densities by using : (a) Single and double n/p ratio; (b) Concept of quasi-participant and quasi-spectator matter; (c) multiplicity of neutrons from high incident energy (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables (iii) sensitive observable from fragmentation at high incident energy (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments (3) Conclusions

3. Why intermediate energy heavy-ion collisions? • Extreme Conditions Extreme densities and excitation energies Phase Diagram of Nuclear Matter

4. What is Symmetry Energy and isospin? Symmetry energy arises due to the isospin parameter of proton and neutron. Isospin:Isospin is a quantum number related to number of charged states of baryon or meson . Symmetry energy: It is the deviation of the symmetric nuclear matter from pure neutron matter. Bethe Mass Formula How Symmetry energy depend on the density:

5. Symmetric Nuclear Matter (relatively well-determined) The Nuclear Symmetry Energy Symmetry energy term (poorly known) The Symmetry Energy EOS of Isospin Asymmetric Nuclear Matter (Parabolic law) Isospin asymmetry

6. Linear Form of Symmetry Energy Symmetry Energy= Kinetic Symmetry energy + Potential Symmetry energy Symm. Kin. energy comes from fermi statistics: But experimental results at u =1 So, Sym. Pot. Energy is required We choose From S0=30 MeV, CS/2 = 17.5 MeV with F(u)= The final form for Symm. Energy is:

7. IQMD Model Initialization: In real space: the radial position of n and p are sampled by using MC method according to the n and p radial density distribution calculated from SHF (or RMF) theory In momentum space: local Fermi momentum is given by Pauli blocking: the Pauli blocking of n and p is treated separately • NN is isospin dependent np  3nn =3pp

8. Potentials in IQMD Model: • NUCLEON : AsGaussian Wave Packet • Hamiltonian is given as; • New factor in potential is Vsym,Which is called symmetry energy • Where T3i and T3j denote the isospin T3 of the particles i and j, i.e • ½ for protons and -1/2 for neutrons. And Potential is as:

9. Work-Done Realization of symmetry energy in IQMD Symmetry potential per nucleon: Force for the potential is as:

10. Symmetry energy sensitive observables Balance energy, ratio and difference of elliptical flow, pions Ratio, kaon ratio, Sigma Ratio, Transverse flow of IMFs

11. OUTLINE OF TALK • (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights • (2) Work Done • (i) Symmetry energy or isospin migration at sub-saturation densities by using • Single and double n, p ratio (2) Concept of quasi-participant and quasi-spectator matter (3) multiplicity of neutrons from high incident energy • (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables • (iii) sensitive observable from fragmentation at high incident energy • (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments • (3) Conclusions

12. Literature Highlights: Esym at low densities-Clustering Effects Horowitz and Schwenk, Nucl. Phys. A 776 (2006) 55 S. Kowalski, et al., PRC 75 (2007) 014601.

13. Literature Highlights: Esym at low densities-Clustering Effects

14. Esym around saturation densities

16. soft EOS w/o MDI： • gamma is in [0.61 - 1.22] region and L is in [57 -89.4] MeV, • soft EOS with MDI： • gamma is in [0.78 - 1.22] and L is in [66 - 89.4] MeV

17. Catania Group BNV Calc. Literature Highlights Famiano and B. A. Li PRL 97(2006)052701 PRL 78 (1997)1644 Double ratio=

18. Literature highlights at low energy Isospin Diffusion

19. Kinetic Energy Spectra It is very important to see the distribution of protons and neutrons S. Kumar, YGM* et al., Phys. Rev. C 84, 044620 (2011)

20. Single N/Z Ratio Extended the study with impact parameter and more neutron rich system And for the different kind of fragments N/Z ratio at E = 50 MeV/A

21. Double Ratio Extended the study with impact parameter and more neutron rich system DR(N/Z) ratio at E = 50 MeV/A

22. Conclusions-1 • Comparison with Single and double ratio leads to the prediction of Soft symmetry energy: means that asymmetric matter is soft. • Different fragments are sensitivite to the symmetry energy, but the symmetry energy is found to be weakly affected by the geometry of reaction systems or impact parameter at sub normal densities. • At higher Ek, the exchange between the symmetry energies is observed for the Liquid phase or fragments, but not for the gas state or free particles. • S. Kumar, YGM* et al., Phys. Rev. C 84, 044620 (2011)

23. OUTLINE OF TALK • (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights • (2) Work Done • (i) Symmetry energy or isospin migration at sub-saturation densities by using • Single and double n, p ratio (2) Concept of quasi-participant and quasi-spectator matter (3) multiplicity of neutrons from high incident energy • (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables • (iii) sensitive observable from fragmentation at high incident energy • (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments • (3) Conclusions

24. Isospin equilibration Long τint Esym vs ρ Asy-Stiff Short τint Asy-Soft Isospin translucency Isospin drift Isospin diffusion ρ/ρ0 1 n drift N/Z Proj Targ TLF Neck PLF n/p diffusion TLF Neck PLF Isospin drift & diffusion ρ~ρ0 PLF PLF PLF Targ Proj ρ~1/8ρ0 ρ~ρ0 TLF TLF TLF Low ρ<ρ0 Colonna et al.; Danielewicz et al.

25. Participant-Spectator Matter: Symmetry energy and isospin migration

26. Search Observable for Isospin Migration

27. 2. Activities….. Conclusions-2 • The neutrons to protons difference from participant/spectator matter is highly sensitive towards the isospin of the system along the whole geometry of the reaction • participant to spectator matter difference from neutrons/protons is particularly, sensitive towards the density dependence of symmetry energy at semi-peripheral geometry, which can act as a probe for isospin migration. • S. Kumar, YGM* et al., Phys. Rev. C 86, 044616 (2012)

28. OUTLINE OF TALK • (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights • (2) Work Done • (i) Symmetry energy or isospin migration at sub-saturation densities by using • Single and double n, p ratio (2) Concept of quasi-participant and quasi-spectator matter (3) multiplicity of neutrons from high incident energy • (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables • (iii) sensitive observable from fragmentation at high incident energy • (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments • (3) Conclusions

29. Experimental data from ALADIN 2000 Collaboration for Projectile spectator fragmentation at 600 MeV/nucleon

30. Defining the cut for projectile spectator fragmentation and Comparison with data

31. Checking the sensitivity with other Observables at PSF at 600 MeV/nucleon

32. 2. Activities….. Conclusions-3 • soft symmetry energy from projectile spectator fragmentation (means Sub-saturation density), Which took place at 600 MeV/nucleon or high density zone. • Single ratio is more sensitive compared to multiplicity as well as double ratio, when isobars are studied, however, for isotopes, it was Double ratio. • Single ratio obtained the maxima or minima trend like multiplicity, But not from double ratio study. • S. Kumar, YGM, Phys. Rev. C 86, 051601R (2012)

33. OUTLINE OF TALK • (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights • (2) Work Done • (i) Symmetry energy or isospin migration at sub-saturation densities by using • Single and double n, p ratio (2) Concept of quasi-participant and quasi-spectator matter (3) multiplicity of neutrons from high incident energy • (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables • (iii) sensitive observable from fragmentation at high incident energy • (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments • (3) Conclusions

34. K_asy is poorly known till date at Sub as well as supra saturation density, some Clue near -550 MeV from diffusion study K_0 is well known near the saturation Density235+14, while varies vastly at high Densities from the study of collective flow, Multifragmentation, KAOS Collaboration, neutron star studies Review is available in Kumar and Ma, NPA 898, 57 (2013)

35. Determination of K_asy

36. Z_bound dependence for LCPs and IMFs including neutrons and protons between them IMFs LCPs

37. Z_bound dependence for free nucleons and LCPs including neutrons and protons between them LCPs free nucleons

38. Determination of K_0 IMFs: HMD

39. 2. Activities….. Conclusions-4 • Soft symmetry energy from isospin sensitive observable M_n with the Isospin part isobaric compressibility K_asy=-372 to -530 MeV from projectile spectator fragmentation region. • Hard momentum dependent equation of state with K= 380 MeV from Isospin insensitive observable M_imfs from projectile fragmentation region. • In projectile spectator fragmentation region, universal Z_bound dependence for free, LCPS and IMFs, while from projectile fragmentation region, no universality is maintained. In projectile spectator fragmentation region, M_n are most sensitive to symmetry energy, while in PF region, LCPS are most sensitive. Correlation is maintained between the free M_n from PSF with soft EOS and soft Symmetry energy with M_n within IMFs with Hard EOS and any symmetry energy. • S. Kumar, YGM*, Nucl. Phys. A 898, 57 (2013).

40. OUTLINE OF TALK • (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights • (2) Work Done • (i) Symmetry energy or isospin migration at sub-saturation densities by using • Single and double n, p ratio (2) Concept of quasi-participant and quasi-spectator matter (3) multiplicity of neutrons from high incident energy • (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables • (iii) sensitive observable from fragmentation at high incident energy • (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments • (3) Conclusions

41. Pions ratio at high incident energies

42. Elliptical flow at high energy

43. Specifying Observable for Supra-saturation density region during Fragmentation

44. Beam energy dependence of Single and Double Ratio

45. Power law dependence of double ratio study

46. 2. Activities….. Conclusions-5 • The double neutron-to-proton ratio from free nucleons is highly sensitive to the symmetry energy, incident energy, and isospin asymmetry of the system. • The sensitivity of the neutron-to-proton double ratio from LCPs to the nuclear symmetry energy is almost beam-energy independent above 200 MeV/nucleon. The same trend is observed for the single Pionsratio above 1 GeV/nucleon. • The sensitivity of the soft symmetry energy to the ratio parameter is strongly affected by the choice of times, which is not true for the stiff symmetry energy. • neutron-to-proton double ratio from free nucleons can act as a useful probe to constrain the high-density behavior of the symmetry energy. Experiments are planned at MSU, GSI, RIKEN, and FRIB to determine the high-density behavior of the symmetry energy by using the neutron-to-proton ratio. • S. Kumar, YGM* et al., Phys. Rev. C 85, 024620 (2012)

47. OUTLINE OF TALK • (1)Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights • (2) Work Done • (i) Symmetry energy or isospin migration at sub-saturation densities by using • Single and double n, p ratio (2) Concept of quasi-participant and quasi-spectator matter (3) multiplicity of neutrons from high incident energy • (ii) Hint for compressibilities with symmetry energy sensitive and insensitive observables • (iii) sensitive observable from fragmentation at high incident energy • (iv) Impact of binding energy clusterization towards isospin physics and stability of fragments • (3) Conclusions

48. Literature review with different clusterization methods • In order to study the NEOS of symmetric nuclear matter: • Spatial Coelesence Method (famous as MST)-Most commonly used • Spatial Coelsence method with Binding energy cut (MSTB) PRC 83, 047601 (2011) • Energy Minimization technique (SACA). J. of Comp. Phys. 162, 245 (2000) • Early cluster recognization Algorithm (ECRA). PLB 301, 328 (1993)

49. Effect on the symmetric matter NEOS PRC 83, 047601 (2011) JPG 37, 015105 (2010) PRC 83, 047601 (2011) Different calescence method found to affect drastically the symmetric Matter equation of state. The binding energy effects were found Uniquely important

50. Literature review with different clusterization methods • In order to study the NEOS of asymmetric nuclear matter: • Spatial Coelesence Method (famous as MST)-Most commonly used • Isospin_MST Method is used. PRC 85, 051602 (2012). In Iso-MST, the relative difference was nn,pp, pn dependent: