1. 2009-8-23IWND2009, Shanghai, China, August 23~251/13 Determining the Special Orientations in Deformed 238 U + 238 U Collisions at CSR Kejun Wu 1, Fei Xie 1, Feng Liu 1, Nu Xu 1,2 1) Institute of Particle Physics, Huazhong Normal University, China 2) Nuclear Science Division, LBNL, Berkeley, CA 94720, USA Outline  Motivation  Results and discussions  Summary and Outlook --- Orientation Effect on High Density Matter --- Selecting those Events with High Density

2. 2009-8-23IWND2009, Shanghai, China, August 23~252/13 tip-tip PRC 61,021903 (2002) PRC 61,034905 (2003) PRL 94,132301 (2005) PRC 72, 037901 (2005) PRC 73,034911 (2006) PRC 76, 051902(R) (2007) … Two most special geometry orientations ★ Besides large atomic weight, Uranium is the most deformed stable nucleus. ★ Longer duration for central tip-tip --- Higher local baryon density and easier thermalization ★ Large initial eccentricity for central body-body --- Strong anisotropy flow Advantages and Suggestions: ( Two extreme collision condition ) Motivation : Why UU?

3. 2009-8-23IWND2009, Shanghai, China, August 23~253/13 Motivation: QCD phase diagram ★ E max =520MeV for U in CSR. ★ For tip-tip UU, medium has high temperature and density, partonic phase may be achieved. ★ CSR could make significant contribution in searching for the possible phase boundary. ★ Find a proper probe to study EoS and Chiral symmetry restoration. CSR The Heavy Ion Research Facility in Lanzhou (HIRFL) - Cooler Storage Ring (CSR) Cross-over

4. 2009-8-23IWND2009, Shanghai, China, August 23~254/13 ART (a Relativistic Transport) Model The ART model was developed from the Boltzmann-Uehling-Uhlenbeck (BUU) model. More baryon/meson resonances and their interactions are included. The maximum beam energy is 15 GeV/nucleon. 1) B.A.Li and W.Bauer,Phys.Lett.B 254,335(1991);Phys.Rev.C 44,450(1991) 。 2) B.A.Li and W.Bauer,and G.F.Bertsch,Phys.Rev.C 44,2095(1991) 。 The particle-in-cell method of hydrodynamics Divide the phase space into cells and set suitable test particles. Evolving the test particle by Newton mechanics. The initial condition the particle are distributed uniformly with a radius parameter of r 0 =1.12 fm. the momentum distribution is given by local Fermi gas approximation. The collision integral is treated by dividing the ensemble of test particles into individual INC( intra-nuclear cascade ) simulations. G.F.Bertsch and S.Das Gupta,Phys.Rep.160,189(1988). BUU equation describes the time evolution of single particle in phase space.

5. 2009-8-23IWND2009, Shanghai, China, August 23~255/13 Central Local Density UU vs. AuAu  The maximal local baryon density can large than 3.2 ρ 0.  Longer duration in tip-tip UU than AuAu, even 2 times of body- body.  Baryon and energy density profile are similar. b=0 fm ( Full stopping for pp) Energy and baryonic number conservation T lab =500MeV Zhuang P.F, Nuclear Physics Review, Vol.19,No.3 Sep.,2002 ART 1.0,

6. 2009-8-23IWND2009, Shanghai, China, August 23~256/13 θ T,P ： X-Z plane - π /2 ~ π /2 φ T,P ： X-Y plane 0~2 π Initial Geometry of Random Orientation tip-tip: θ T =θ P =0,φ T φ p random body-body: θ T =θ P = ± π/2, φ T =φ p ± π  Non-polarized U  random orientation  Ideal tip-tip and body-body events are quite unusual.  Our goal is to select central tip-tip like events. What are the tip-tip like events? How to get the tip-tip like events ?

7. 2009-8-23IWND2009, Shanghai, China, August 23~257/13 Centrality Dependence on Baryon Density b max =13fm for tip-tip b max =19fm for body-body The most interesting events are tip-tip collision with b<2.6 fm, which might be selected by measuring distinctively the forward neutron multiplicity. Define: is central cube with 1fm 3 S>70

8. 2009-8-23IWND2009, Shanghai, China, August 23~258/13 Orientation Dependence on Baryon Density  S is independent on φ when θ is fixed. ( Only for central events )  θ 70 Φ effect in central collisions θ effect in central collisions

9. 2009-8-23IWND2009, Shanghai, China, August 23~259/13 What are the central tip-tip like events? As a rough estimate, those events should be with b<2.6fm (central) and θ T ， P <20° ( tip-tip like). How to determine those events in the experiment? Firstly, find certain measurable (N n or N ch ) as online analysis to scale centrality and gain the sub-sample with small b. Secondly, find some special observables as offline analysis to select those events with small θ T ， P. Open Questions

10. 2009-8-23IWND2009, Shanghai, China, August 23~2510/13 Determining the Central Events b<=2.6fm 2.6fm<b<=4fm 4fm<b<=6fm  Nn cut for online analysis is satisfying.  In order to further enhance those events, offline analysis is needed.

11. 2009-8-23IWND2009, Shanghai, China, August 23~2511/13 Nuclear Stopping Power When the ratio R is about 1, indicating that the hadronic system might reached thermal equilibrium. H.Kruse et al.,PRC 31,1770(1985)  R cut for offline analysis is satisfying. In low energy region,

12. 2009-8-23IWND2009, Shanghai, China, August 23~2512/13 The purity of tip-tip like Events R>1.R>1.05R>1.1N n 1.05 Sample Events58806290261231116926 Tip-tip Like events8724596034714190 Body-body like events138601 Percentage14.8420.5328.1924.75 (all particles) R c >1.1R c >1.15R c >1.2Nn 1.1 Sample Events3265215133607914675 Tip-tip like events5702336717463655 Body-body like events681301 Percentage17.4622.2528.7224.9 (charge particles with θ<80°) Rc*>0.9Rc*>0.95Rc*>1.Nn 0.95 Sample Events451721686950018200 Tip-tip like events7208369014532404 Body-body like events1641620 Percentage15.9621.8729.05 29.32 (charge particles with θ<80°and regarded as nucleons)  The purity can be improved when R and Nn cut are used together. TOF acceptance No PID Total 402K, b<2.6fm 20K,tip-tip like

13. 2009-8-23IWND2009, Shanghai, China, August 23~2513/13 Summary and Outlook The events with extended high density phase (the central tip-tip like events) are with b<2.6fm and θ T,P <20°. Using the forward neutron multiplicity (e.g. N n <=40) as online analysis in CSR experiment is recommended. This can hold the central events effectively. As an additional result, the body-body like events can be rejected effectively by cutting Nn. Using nuclear stopping power (e.g. R/R c /R c * ) as offline analysis can select effectively the central tip-tip like events. We expect the available UU data can be analyzed. Thanks ！

14. 2009-8-23IWND2009, Shanghai, China, August 23~2514/13 Basic models for heavy-ion collisions

15. 2009-8-23IWND2009, Shanghai, China, August 23~2515/13 X Z Long axis T=R Z (Φ)*R Y (θ) X Z θ Long axis θ2θ2 θ1θ1 Φ1Φ1 Φ2Φ2 Y X Rotation Matrics: Rotation of colliding nuclei: Y Beam direction: Z Y

16. 2009-8-23IWND2009, Shanghai, China, August 23~2516/13 (1) tip-tip like collision (2)body-body like collision θ1θ1 Z Y θ1θ1 (1) (2) (3) (4) Y X Φ angle θ1θ1 Z Y (1) (2) (3) (4) θ1θ1 Beam direction: Z