2009-8-23 IWND2009, Shanghai, China, August 23~25 1/13

Determining the Special Orientations in Deformed 238U +238U Collisions at CSR

Kejun Wu1, Fei Xie1, Feng Liu1, Nu Xu1,2

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

2009-8-23 IWND2009, Shanghai, China, August 23~25 2/13

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:

sphere prolate,9.5,3.8,27.0,238

92 fmrfmrU sl

( Two extreme collision condition )

Motivation : Why UU?

2009-8-23 IWND2009, Shanghai, China, August 23~25 3/13

Motivation: QCD phase diagram

★ Emax =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)

Cro

ss-o

ver

2009-8-23 IWND2009, Shanghai, China, August 23~25 4/13

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 r0=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.

2009-8-23 IWND2009, Shanghai, China, August 23~25 5/13

Central Local Density UU vs. AuAu

The maximal local baryon density can large than 3.2ρ0.

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)

5.2,5.20

max

0

max

Energy and baryonic number conservation

Tlab=500MeV

Zhuang P.F, Nuclear Physics Review, Vol.19,No.3 Sep.,2002

ART 1.0,

2009-8-23 IWND2009, Shanghai, China, August 23~25 6/13

θT,P ： X-Z plane -π/2 ~π/2

φT,P ： X-Y plane 0~2π

Initial Geometry of Random Orientation

tip-tip:

θT =θP=0 ,φT φp random

body-body:

θT=θP= ±π/2, φT=φp±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 ?

),,,,( PTPTb

2009-8-23 IWND2009, Shanghai, China, August 23~25 7/13

Centrality Dependence on Baryon Density

bmax=13fm for tip-tip

bmax=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 1fm3

S>70

t

dvdtS0

)5.2( 0

2009-8-23 IWND2009, Shanghai, China, August 23~25 8/13

Orientation Dependence on Baryon Density

S is independent on φ when θ is fixed. ( Only for central events )

θ <200 if s>70

Φ effect in central collisions θ effect in central collisions

0 pT pT

pT

2/ pT

2009-8-23 IWND2009, Shanghai, China, August 23~25 9/13

What are the central tip-tip like events?

As a rough estimate, those events should be with b<2.6fm (central) and θT ， P <20°(tip-tip like).

How to determine those events in the experiment?

Firstly, find certain measurable (Nn or Nch) 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 θT ， P.

Open Questions

2009-8-23 IWND2009, Shanghai, China, August 23~25 10/13

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.

2009-8-23 IWND2009, Shanghai, China, August 23~25 11/13

Nuclear Stopping Power

When the ratio R is about 1, indicating that the hadronic system might reached thermal equilibrium.

||

||2

iz

it

p

pR

H.Kruse et al.,PRC 31,1770(1985)

R cut for offline analysis is satisfying.

In low energy region,

2009-8-23 IWND2009, Shanghai, China, August 23~25 12/13

The purity of tip-tip like Events

R>1. R>1.05 R>1.1 Nn<=40&& R>1.05

Sample Events 58806 29026 12311 16926

Tip-tip Like events 8724 5960 3471 4190

Body-body like events

138 6 0 1

Percentage 14.84 20.53 28.19 24.75

||

2

z

t

P

PR

(all particles)

Rc>1.1 Rc>1.15 Rc>1.2 Nn<=40&& RC>1.1

Sample Events 32652 15133 6079 14675

Tip-tip like events 5702 3367 1746 3655

Body-body like events

68 13 0 1

Percentage 17.46 22.25 28.72 24.9

||

2

z

tc P

PR

(charge particles with θ<80°)

Rc*>0.9 Rc*>0.95 Rc*>1. Nn<=40&& Rc*>0.95

Sample Events 45172 16869 5001 8200

Tip-tip like events 7208 3690 1453 2404

Body-body like events

164 16 2 0

Percentage 15.96 21.87 29.05 29.32

(charge particles with θ<80°and regarded as nucleons)

||

2*

*

z

tc

P

PR

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

2009-8-23 IWND2009, Shanghai, China, August 23~25 13/13

Summary and Outlook The events with extended high density phase (the central tip-tip like events) are with b<2.6fm and θT,P<20°.

Using the forward neutron multiplicity (e.g. Nn<=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/Rc/Rc*) as offline a

nalysis can select effectively the central tip-tip like events.

We expect the available UU data can be analyzed.

ThanksThanks ！！

2009-8-23 IWND2009, Shanghai, China, August 23~25 14/13

Basic models for heavy-ion collisions

2009-8-23 IWND2009, Shanghai, China, August 23~25 15/13

X

Z

Long axis

T=RZ(Φ)*RY(θ)

X

Z

θ

Long axis

θ2

θ1

Φ1

Φ2

Y

X

Rotation Matrics:

Rotation of colliding nuclei:Y

Beam direction: Z

Y

2009-8-23 IWND2009, Shanghai, China, August 23~25 16/13

(1) tip-tip like collision

(2)body-body like collision

θ1

Z

Y

θ1

(1)(2)

(3)

(4)

Y

X

Φ angle

θ1

Z

Y

(1)(2)

(3)

(4)

θ1

Beam direction: Z