Results from FOPI on nuclear collective flow in heavy

ion collisions at SIS energies

N. Bastid

To cite this version:

N. Bastid. Results from FOPI on nuclear collective flow in heavy ion collisions at SIS energies.International Nuclear Physics Conferences (INPC 2004) 1, Jun 2004, Goteborg, Sweden. pp.1-12, 2004.

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Submitted on 9 Sep 2004

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%N. Bastid for the FOPI Collaboration, LPC Clermont-Ferrand Göteborg, June 27 - July 2

Results from FOPI

on Nuclear Collective Flow

in Heavy Ion Collisions at SIS energies

1 Motivations

2 FOPI detector overview

3 Experimental systematics

• Directed flow

• Elliptic flow

4 Data versus IQMD

• Sensitivity to σnn?

• Sensitivity to EoS?

5 Anisotropic flow from Lee-Yang Zeroes

6 Conclusion

Ca + Ca, Ni + Ni, Ru + Ru, Xe + CsI, Au + Au

90A MeV - 2A GeV

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Motivations & Observables

Probing hot & dense hadronic matter

↪→ Nuclear Equation of State

� Collision dynamics

� In-medium effects: σnn, MDI

bounce off

bounce off

OFF plane emission

OFF plane emission

reaction plane

impact parameter b

Ru (400 AMeV) + Ru - Z = 2

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-1 -0.5 0 0.5 1

l = 1.1 fmn = 2.9 fmM = 4.7 fm

(pz)cm0

Au+Au E=250 AMeV A=4 |y(0)|

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FOPI detector @ GSI

x

y

z

inner plastic wallouter plastic wall

CDC

Helitron

solenoid

plastic barrel 1 m

beam

target

10-1

1

0 5 10 15 20 25 30 35

Velocity [cm/ns]

PLa

b [G

eV]

π+K+

P

D

T

1

10

10 2

10 3

10 4

10 5

-0.5 0 0.5 1

P

π+

K+

π-

K-

Mass [GeV/c2]

Yie

ld

0

500

1000

0.2 0.4 0.6 0.8

Yie

ld

MK

KS → π+π- (69%)0

0

500

1000

1.05 1.1 1.15 1.2

MΛ

Λ → pπ- (64%)

0

10

20

30

1 1.2

MΦ

Φ → K+K- (49%)

0

500

1000

0.2 0.4 0.6 0.80

500

1000

1.05 1.1 1.15 1.2

0

10

20

0.9 1 1.1 1.2 1.3

MINV (GeV/c2)

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Systematics ofDirected Flow & Stopping

Sideflow

Au+Au

Ca+Ca

hydro

Excitation Functions

10-1 100

beam energy (GeV/A)

0.1

0.2

max

[ p x

dir(

0) ]

Au+Au

Ca+Ca

Stopping

0.4

0.5

0.6

0.7

0.8

0.9

vart

l

Sideflown 0.4A GeV∆ 1.5A GeV

CaNi

RuXe

Au

Size dependence

40 80 120 160

Z system

Stoppingn 0.4A GeV∆ 1.5A MeV

CaNi

RuXe

Au

Size dependence

Stopping:

b/bmax < 0.15

vartl =σ2(yt)

σ2(yz)

Sideflow:

b/bmax ' 0.3 - 0.4

max [(pdirx )(0)]

W. Reisdorf et al., (FOPI), PRL 92 (2004) 232301

• Correlation between stopping & flow & pressure

• Evidence for incomplete stopping

• Stopping: maximum ∼ 400A MeV

decreasing towards higher beam energies

rising with system size, no saturation

below expectations from hydrodynamics

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Systematics of Elliptic Flow

-0.1

-0.05

0

0.05

0.1

10-1

1

v 2

Z=1, all pt(0)

M2M3M4

-0.2

-0.1

0

0.1

10-1

1

Ebeam /A (GeV)

A≤4, xApt(0) > 0.8

• Transition from in-plane to

out-of-plane preferred

emission at low energies

• Maximum ∼ 400A MeV

(depending on Pt)

• v2 decreasing toward higher

beam energies

A. Andronic et al., (FOPI), GSI Report 2004-1 (2004) 54

• Interplay between fireball expansion & spectator

shadowing

• Passing time decreasing at high beam energies

• Influence of collision dynamics

• Information on different stages of the collision

⇒ High pt particles messengers of high density phase

T. Gaitanos et al., Eur. Phys. J. A 12 (2001) 421

Au + Au, | y(0) |< 0.1

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Shape parameters:Sensitivity to in-medium σnn?

• θF → Directed flow

• λ31 = f23/f

21 → Directed flow &

Stopping

• λ21 = f22/f

21 → Elliptic flow

J. Gosset et al., (DIOGENE), Phys. Lett. B 247 (1990) 233

10

20

30

40

50

60

70

0 2 4 6

σnn/σfreenn

θ F (

deg

.)

IQMD - HM

IQMD - SM

FOPI Data

1

1.25

1.5

1.75

2

0 2 4 6

σnn/σfreenn

λ 31

1

1.2

1.4

1.6

1.8

2

0 2 4 6

σnn/σfreenn

λ 21

Ru (400 AMeV) + Ru - Proton-likes - < bgeo > = 1.1 fm

N. Bastid et al., (FOPI), Nucl. Phys. A (2004), in press

Data favour in-medium σnn close or

slightly higher than σfreenn

⇒ Consistent with results on nuclear stopping

F. Rami et al., (FOPI), Phys. Rev. Lett. 84 (2000) 1120B. Hong et al., (FOPI), Phys. Rev C 66 (2002) 034901

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EoS from Directed Flow?

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

v 1

y(0)=0.5-0.7

Z=1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2

y(0)=0.7-0.9

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

Z=2

Data

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

HMHSMS

IQMD

pt(0)

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2

v1

y(0)=0.5-0.7

all,xZ

Data

M4

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2

HMHSMS

IQMD

y(0)=0.7-0.9

pt(0)

Au + Au @ 400A MeV, M4400A MeV

Pt(0)

Au (90A MeV) + Au

A. Andronic et al., (FOPI), Phys. Rev C 67 (2003) 034907

• Sensitivity to the EoS parametrization

• Soft EoS (with MDI & σfreenn ) in best agreement with

directed flow data for Au + Au & Xe + CsI at 400 AMeV

• Difficulties of the model to reproduce directed flow versus

system size & low Ebeam (90A MeV)

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EoS from Elliptic Flow?

-0.2

-0.15

-0.1

-0.05

0

0 0.5 1 1.5 2p⊥(o)

v 2 DatenIQMD SMIQMD HM

dN/dp⊥IQMD

Au 600AMeV mul4 Proton

-0.15

-0.1

-0.05

0

500 1000 1500Eb [AMeV]

v 2

Au mul4 Proton |y(0)|

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Flow from Lee-Yang Zeroes method

Genuine flow directly from correlation between many

particles

⇒ Non-flow correlations due to quantum statistics,

resonance decays, momentum conservation effects, ...,

not neglected

� Generating function:

G(ir) =〈∏

j

[

1 + irωjcos(n(ϕj − θ))]〉

events

where ln G(ir) =∑+∞

k=1 ck(ir)k

k!, ck = cumulant

� Find first zeroe (minimum), rθ0, of | G(ir) |

rθ0

→ Asymptotic behaviour of ck in the expansion of ln G(ir)

� “Integrated” flow: Vθn{∞} =j01

rθ0(& averaged over θ)

� Resolution parameter: χ=Vn{∞}

σ→ χ > 1: Lee-Yang zeroes should be used

→ 0.5 < χ < 1: Important to optimize weights

→ χ < 0.5: Large statistical errors, better to use cumulants

� Differential flow:

→ Deduced from Vθn{∞} in harmonics multiples of n

Detailed description in:

R.S. Bhalerao et al., Phys. Lett. B 580 (2004) 157 & Nucl. Phys. A 727 (2003) 373;N. Borghini et al., nucl-th/0402053 (2004

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First application of Lee-Yang theoryto FOPI data: Ru + Ru @ 1.69A GeV

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

< bgeo > = 2.9 fm

|Gθ (

ir)|

θ = 0 n = 1

r

|Gθ (

ir)|

0

0.05

0.1

0.15

0.2

0.25

0.3

0.16 0.18 0.2 0.22

r

|Gθ (

ir)|

Generating function

↑r0

• χ = 1.45 ⇒ Lee-Yang Zeroes

theory can be used

• Clear indication of collective

effects

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Protons

-0.9 < y(0) < -0.7

< bgeo> = 2.9 fm

Lee-Yang zeroes

Standard method

Standard method (w/o recoil correction)

Cumulants 2nd order

Cumulants 4th order

Pt (GeV/c)

v 1

PRELIM

INARY

• Non-flow effects from 4-particle correlations negligible

• Evidence for (small) momentum conservation effects on v1

• Non-flow effects negligible for higher harmonics

Ongoing development → π± flow & influence of ∆ decay?

(110 Millions central Ni + Ni @ 1.93A GeV)

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Conclusion

Complete set of data at SIS energies measured with FOPI:

• Variation of beam energy from 90A MeV to 2A GeV

• Variation of system size from Ca to Au

• Variation of asymmetry in isospin (Ru/Zr)

• Variation of asymmetry in system size (Au/Ca & Pb/Ni)

• Main dependences of directed & elliptic flow are available

• New procedure of Lee-Yang Zeroes (& cumulants at SIS)

successfully used for first time to analyze flow

• Correlations from non-flow effects negligible for protons &

composite particles

• Most features of flow data reproduced qualitatively well

by IQMD model but not in detail

• EoS is influencing different observables

• EoS is linked to in-medium NN interaction

⇒ momentum dependence, cross sections

• Non-equilibrium effects important

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FOPI

FOPI Collaboration

A. Andronic, V. Barret, Z. Basrak, N. Bastid,M.L. Benabderrahmane, R. Čaplar, E. Cordier, P. Crochet, P. Dupieux,

M. Dželalija, Z. Fodor, I. Gasparić, Y. Grishkin, O. Hartmann, N. Herrmann,K.D. Hildenbrand, B. Hong, D. Kang, J. Kecskemeti, Y.J. Kim,

M. Kirejczyk, P. Koczon, M. Korolija, R. Kotte, M. Kowalczyk, T. Kress,

A. Lebedev, Y. Leifels, X. Lopez, A. Mangiarotti, V. Manko, T. Matulewicz,M. Merschmeyer, D. Moisa, D. Pelte, M. Petrovici, F. Rami, W. Reisdorf,

A. Schuettauf, Z. Seres, B. Sikora, K.S. Sim, V. Simion,K. Siwek-Wilczyńska, M. Smolarkiewicz, V. Smolyankin,

J. Soliwoda-Poddany, M. Stockmeier, G. Stoicea, Z. Tyminski,K. Wísniewski, D. Wohlfarth, Z. Xiao, I. Yushmanov, A. Zhilin

NIPNE Bucharest, RomaniaKFKI Budapest, Hungary

LPC Clermont-Ferrand, FranceGSI Darmstadt, Germany

Univ. of Heidelberg, GermanyIKH Rossendorf/Dresden, Germany

ITEP Moscow, Russia

Kurchatov Institute, Moscow, RussiaKorea University Seoul, Korea

IReS Strasbourg, FranceRBI Zagreb, Croatia

Univ. of Warsaw, Poland