On the isospin effects in flow, its disappearance and other related phenomena

1. On the isospin effects in flow, its disappearance and other related phenomena Sakshi Gautam Department of Physics Panjab University Chandigarh-160014 INDIA

2. Terrestrial labs… In Heaven… EOS for Asymmetric Nuclear Matter Isospin Effects in HIC’s … Neutron Stars … Nuclear Force Structures of Radioactive Nuclei, SHE … Isospin Physics What is the isospin dependence of the in-medium nuclear effective interactions??? HIC’s induced by neutron-rich nuclei Most uncertain property of an asymmetric nuclear matter Density Dependence of the Nuclear Symmetry Energy

3. Equation of State of symmetric nuclear matter is relatively well determined D. H. Youngblood, H. L. Clark and Y. W. Lui PRL 82, 691 (1999) K0=231±5 MeV 2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS EOS of symmetric matter for 1ρ0< ρ < 3ρ0 from K+ production KaoS Collab. P. Danielewicz, R. Lacey and W.G. Lynch Science 298, 1592 (2002) J. Aichelin and C.M. KoPRL55, (1985) 2661

4. Symmetry energy term The Nuclear Symmetry Energy Liquid-drop model EOS of Asymmetric Nuclear Matter Symmetric nuclear matter Symmetry energy term Esym (ρ0)≈ 30 MeV

5. Symmetry Energy Esym and dependence on density, takes some form:Esym()  C(/0) = 1.5 suggests stiff S() = 0.5 suggests soft S() Asy-stiff Using data as input to transport models helps constrain Asy-soft PRL 102, 062502 (2009)

6. Promising Probes of the Esym(ρ) in Nuclear Reactions At sub-saturation densities At supra-saturation densities • Sizes of neutron-skin • n/p ratio of pre-equ. nucleons • Isospin fractionation • Isospin scaling • Isospin diffusion • t/He3 ratio • ……… • π-/π+, K+/K0 ratio • Neutron-proton differential transverse flow • n/p ratio at mid-rapidity • Elliptic flow at high pt • n/p ratio of squeeze out nucleons Esym (ρ)γγ???

7. Isospin-dependent quantum molecular dynamics model • Nucleons of P/T are initialized • Nucleons propagate under the mean field • Nucleons scatter if they come too close Initialization of coordinates and momentum by Monte Carlo method of simulation. Skyrme potential Yukawa potential Coulomb potential Symmetry potential Isospin independent Isospin dependent Momentum –dependent interactions nn cross section C. Hartnack et al., Eur. Phys. J A 1, 151 (1998).

8. Isospin effects in density Not significant isospin effects and effect of symmetry energy Sakshi Gautam, Phys. Rev. C 83, 064604 (2011)

9. Behavior of transverse flow for different forms of symmetry energy Sensitive to symmetry energy Mean field dominance Insensitive to symmetry energy collisions dominance S. Gautam et al., Phys. Rev. C 83, 034606 (2011).

10. At the start larger no. of particles lie in BIN 1 As nuclei overlap particles increases in BIN 2 at midrapidity Attractive mean field will push the particles to participant zone • Expansion phase begins and • Particles increases in BIN 1 • Most of the particles lie in BIN 1

11. In spectator region repulsive symmetry energy will accelerate particles away from overlap zone Behavior of flow for diff. Esym forms Attraction towards Central dense zone Particles entering BIN2 have high +ve value of flow, mean field has to deacc., stop and acc. back towards overlap zone. BIN2 flow behaves similarly for all forms b/w 0-10 fm/c b/w 10-25 fm/c decrease is more for F3 and F4 S. Gautam et al., Phys. Rev. C 83, 034606 (2011).

12. High Energy P T 0 0 <px/A> <px/A> 0 0 Low Energy yc.m./ybeam yc.m./ybeam QP <px/A> 0 QT 0 yc.m./ybeam QP QT Balance Energy

13. Isospin effects in disappearance of flow neutron-rich has higher EVF Coulomb is less Cross-section is less S. Gautam et al, J. Phys. G :Nucl. Part. Phys. 37, 085102 (2010).

14. Isospin effects in mass dependence of balance energy Symmetry energy dominates Coulomb dominates S. Gautam and A. D. Sood, Phys. Rev. C 82, 014604 (2010). S. Gautam et al., Phys. Rev. C 83, 014603 (2011).

15. N/Z dependence of EVF Different forms of symmetry energy and nn cross section Insensitive to isospin dependence of nn cross-section Sensitive to density dependence of symmetry energy

16. N/Z dependence of participant matter Participant matter decreases slightly with neutron content of the colliding pairs

17. MDI Esym = 0 Participant matter becomes almost constant of the neutron content of the colliding pair Participant matter decreases with the neutron content of the colliding pair Repulsive in nature Throw the matter away from the central dense zone during the initial stage of the reaction Symmetry energy effects are dominating the mass effects Sakshi Gautam, Eur. Phys. J A 48, 3 (2012)

18. System size dependence of participant/spectator matter Power law behaviour is observed with system mass Mass independent behaviour of participant/spectator matter Sakshi Gautam and R. K. Puri, Phys. Rev. C (communicated)

19. Conclusive remarks… • Transverse directed flow- sensitive to symmetry energy and its density dependence. • Dominance of Coulomb potential in isospin effects in EVF of isobaric pairs • N/Z dependence of EVF– a probe of symmetry energy and its density dependence. • Participant/spectator matter behaves in a similar way for n-rich colliding pairs as for stable systems.

20. and to my collaborators Dr. Aman D. Sood, P.U. India Prof. Rajeev K. Puri, P.U. India Prof. C. Hartnack, SUBATECH, France Prof. J. Aichelin, SUBATECH, France

21. Equilibrium Anisotropy ratio Relative momentum Indicator of global equilibrium as doesn’t depend on local positions Indicator of local equilibrium as it depend on local positions 21

22. Saturates after high dense phase indicating nn collisions after high density phase don’t change p-space much Better thermalization 22

23. Directed Transverse flow Types of flows .…. X b Z Squeeze out Elliptic flow 23

24. Thank You

25. Role of colliding geometry in isospin effects forISOTOPIC PAIRS n-rich has lower Ebal No isospin effects throughout b System size effects dominate throughout colliding geometry

26. Role of colliding geometry in isospin effects forISOBARIC PAIRS Without A = 48 With A = 48 Coul. Red. n-rich has higher Ebal Isospin effects enhance at higher b n-rich has lower Ebal Symmetry energy role is uniform Decrease in EVF is much steeper Coulomb is responsible for steep decrease

27. Variation of tau τ1 increases more sharply No diff. with and without A =48 Steep rise without A =48 Role of isospin-dependent cross section and symm. energy is independent of N/Z on mass dep. of Ebal throughout colliding geom. τ1 and τ1.4 almost same.

28. Effect of collisions Ebal increases on switching off the collisions Role of Coulomb Magnitude of rise in Ebal is almost same for both the masses Significant rise in Ebal shows importance of collisions at peripheral geometry S. Gautam, A. D. Sood, R. K. Puri, and J. Aichelin, Phys. Rev. C 83, 014603 (2011).

29. Impact parameter dependence of Ebal Coulomb full N/Z =1 N/Z =1.4 Lighter: Ebal Heavier: Ebal All: Ebal Coulomb reduced N/Z =1,1.4 Ebal diff. constant Symm. energy: uniform in mass, geometry

30. Effect of Coulomb on collision rate Peripheral Coulomb reduces Collision Rate !!! Effects is strong for • heavy masses Central Effects is strong for medium and heavy masses

31. N/Z dependence of EVF • Ebal decreases with N/Z: • Increase in mass • Increased role • of symmetry energy Relative importance not clear

32. Insensitive to isospin dependence of nn cross-section Sensitive to symmetry energy

33. Mean field and collisions contribution to the transverse flow • The difference is reflected in flow due to mean field

34. Time evolution of spectator/participant matter at balance energies Transition from spectator to participant matter is swift and sudden for lighter systems At the end of the reaction, nearly same participant matter indicating universality in balancing attractive and repulsive forces. Lighter systems react at higher incident energies

35. MDI Esym Increase in density of neutron-rich systems Density decreases with inclusion of MDI because of repulsive nature Repulsive nature of symmetry energy Sakshi Gautam, Eur. Phys. J A 48, 3 (2012)

36. Isospin effects in disappearance of flow neutron-rich has higher EVF Coulomb is less Cross-section is less S. Gautam et al, J. Phys. G :Nucl. Part. Phys. 37, 085102 (2010).