Systematics of directed and elliptic flow of light particles in heavy ion collisions in the 1A GeV

regime

王永佳兰州大学核科学与技术学院

合作者：郭琛琛 ( 北京师范大学 )导师：李庆峰 ( 湖州师范学院理学院 ) 张鸿飞 ( 兰州大学核科学与技术学院 ) [Ref.] W. Reisdorf et al. FOPI Collaboration NPA(2012)876.1-60

Outline

Ultrarelativistic Quantum-Molecular-Dynamics (UrQMD) model Initializationpotential updates--Skyrme potentialscross section---medium effectcluster construction

Results yieldcollective flow of proton, deuteron, mass 3 (triton and 3

He) and 4He comparison of directed flow of 3H with 3He

Ultrarelativistic Quantum-Molecular-Dynamics (UrQMD) model

• study collisions of p+p, p+A and A+A systems at incident energies covered by INDRA/GSI experiments up to highest energies presently available at LHC/CERN.

• recently updates:various Skyrme interactions have been introduced,

like ImQMD, LQMDmomentum-modified density-dependent nucleon n

ucleon elastic cross section (NNECS)isospin denpendence in cluster recognition, iso-MS

T (minimum spanning tree )

UrQMD Model: Initialization

0 2 4 6 8 10 120.00

0.04

0.08

0.12

0.16

0.20

2 4 6 8 10 12

n p all

197AuWoods-Saxon

r (fm)

n p all

197AuHard-sphere

• Woods-Saxon (WS)• Hard-sphere (HS)

0 30 60 90 120 150-0.010

-0.008

-0.006

-0.004

-0.002

0.000

bind

ing

ener

gy (G

eV)

t (fm/c)

197Au5 random eventsx

(fm

)

Initialization ： Hard-sphere

Potential updates

like ImQMD,LQMD

mdCoulloc UUUTH

potential energy density functional:

Change the symmetry potential by varying the η

momentun dependent term:

22 /GeV500c

1.57MeV,

2

,,

2

0

1ln2

ijji

jiij

md ppU

2211

3/22

3/50

2/3221

,02211,

,02221

03,00

5432

3

24

1

)2

3()45(3

80

3

)12()12(364

1

2

45964

1

2

,16

1

18

3

2

xtxtC

txtg

xtxtg

txttg

tt

s

isosur

sur

2

03/5

0

3/82

0

,2

00

1

0

2

)(2

)]([212

spn

isosursurloc

Cg

ggu

1

SkP (K=200MeV)

Cross section

2 3 4

20

100

UrQMD-np-total UrQMD-pp-total Expt.-pp-tot Expt.-np-tot

cros

s se

ctio

n (m

b)

sNN

(GeV)

0.1 1 10 100 1000

10

100

UrQMD-pp-inel UrQMD-pp-el Expt.-pp-el Expt.-pp-inel

cros

s se

ctio

n (m

b)

Elab

(GeV)

0.1 1 10 100

10

100

UrQMD-np-inel UrQMD-np-el Expt.-np-el Expt.-np-inel

cross

sect

ion (m

b)

Elab(GeV)

[Ref] S.A. Bass et al. Prog.Part. Nucl. Phys. 41, 255 (1998)

Momentum-modified density-dependent nucleon nucleon elastic cross section (NNECS)

0 1 20.0

0.5

1.0

0.5 1.0

f

u

FU1 FU2 FU3 FU4

p (GeV/c)

FU3FP1 FU4FP14 FU4FP15 FU3FP16

[Ref] Qingfeng Li et al. PRC 83.044617

Cluster construction• minimum spanning tree (MST)

relative distances : dr<2.8 fm

relative momenta : dp<0.2 GeV/c

• isospin dependent minimum spanning tree (Iso-MST)

relative distances :

1. proton-proton, dr<2.5 fm

2. neutron-neutron, neutron-proton, dr<4.5 fm

relative momenta : dp<0.2 GeV/c

ImQMD: Yingxun Zhang and Zhuxia Li, et al. PRC 85, 051602(R) (2012)

relative momenta: dp<0.25 GeV/c

0 5 10 15 201E-3

0.01

0.1

1

10

100

yield

charge (Z)

MST FOPI Iso-MST

E=150A MeV

Resluts: yield

0 5 10 151E-4

1E-3

0.01

0.1

1

10

100

1000

yield

charge (Z)

MST FOPI Iso-MST

FU4FP15E=250A MeVAu+Au

Au+Au,b=0-2fm, SkP-FU3FP16,Hard-sphere

Resluts: proton and deuteron yield

100 100010

100

deuteron

FOPI-p FOPI-d MST-p MST-d iso-MST-p iso-MST-d

yiel

d

Elab (A MeV)

Au+Aub

0<0.15

SkP-FU3FP16 proton

100 1000

1

10

FOPI-t FOPI-He3 iso-MST-t iso-MST-He3 MST-t MST-He3

yiel

d

Elab

(A MeV)

triton

He3

Au+Au,b=0-2fm, SkP-FU3FP16,Hard-sphere

Resluts: directed flow of proton

100 10000.0

0.2

0.4

0.6

0.8

1.0

FU4FP14-p FU4FP14-p FOPI-b0<0.25

FOPI-0.25<b0<0.45

FU4FP15-pu

t0>0.8

V1 s

lope

of p

roto

n

Elab

(A MeV)

Resluts: directed flow of proton

400 600 800 1000 1200 1400 16000.0

0.2

0.4

0.6

0.8

1.0

FOPI-b0<0.25 FOPI-0.25<b0<0.45

FU3FP16-b0<0.25 FU3FP16-0.25<b0<0.45

FU4FP14-b0<0.25 FU4FP14-0.25<b0<0.45

FU4FP15-0.25<b0<0.45

ut0>0.4

V1 s

lope o

f pro

ton

Elab

(A MeV)

Resluts: directed flow of deuteron

100 10000.0

0.3

0.6

0.9

1.2

FOPI-b0<0.25

FOPI-0.25<b0<0.45

FU4FP14-d FU4FP14-d FU4FP15-d

ut0>0.8

V1 s

lope o

f deute

ron

Elab

(A MeV)

Resluts: directed flow of deuteron

400 600 800 1000 1200 1400 16000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

FOPI-b0<0.25

FOPI-0.25<b0<0.45

FU3FP16-d FU3FP16-d FU4FP14-d FU4FP14-d FU4FP15-d

V1 s

lope o

f deute

ron

Elab

(A MeV)

Au+Au,ut0>0.4

Comparison with experimental data

[Ref] W.Reisdorf et al. NPA876.1-60 (2012)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

V1

y0

p d FOPI-p FOPI-d

Au+AuE=1000A MeV0.25<b

0<0.45

ut0>0.4

FU3FP16

Comparison with experimental data

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

V1

y0

A3 He4 FOPI-A3 FOPI-He4

Au+AuE=1000A MeV0.25<b

0<0.45

ut0>0.4

FU3FP16

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

V1

y0

A3 He4 FOPI-He4 FOPI-A3

Au+AuE=250A MeV0.25<b

0<0.45

ut0>0.8

FU3FP16

Comparison with experimental data

Resluts: elliptic flow of proton

100 1000-0.125

-0.100

-0.075

-0.050

-0.025

0.000

0.025

0.050

FOPI-p FU3FP16 FU4FP15

Au+Au0.25<b

0<0.45

ut0>0.8

V2 o

f pro

ton

Elab

(A MeV)

Resluts: elliptic flow of deuteron

100 1000-0.20

-0.15

-0.10

-0.05

0.00

0.05

FOPI-d FU3FP16 FU4FP15

Au+Au0.25<b

0<0.45

ut0>0.8

V2 of

deu

tero

n

Elab

(A MeV)

Elliptic flow of A3 (triton and He3)

100 1000

-0.2

-0.1

0.0

FOPI-A3 FU3FP16 FU4FP15

Au+Au0.25<b

0<0.45

ut0>0.8

V2 o

f mass

3

Elab

(A MeV)

p d A3 He40.25

0.50

0.75

1.00

1.25

1.50

V1 sl

ope

Iso-MST MST FOPI

E=1500A MeV0.25<b

0<0.45

ut0>0.4

Influence of Iso-MST on directed flow

Result from FOPI experimentV

1 slo

pe

Elab=400A MeV

impact parameter b0

Comparison of directed flow of 3H with 3He

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

H3 He3

E=1500A MeVAu+Au0.25<b

0<0.45

FU3FP16ut

0>0.4

V1

y0

3H: slope: 1.1120.0203He: slope: 1.0460.021

Comparison of directed flow of 3H with 3He

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

H3 He3

FU3FP16E=1000A MeV0.25<b

0<0.45

ut0>0.4

V1

y0

3H: slope: 1.0990.0183He: slope: 1.0420.016

Comparison of directed flow of 3H with 3He

0.00

0.25

0.50

0.75

0.0 0.2 0.4 0.6 0.8

0.00

0.25

0.50

0.75

H3 He3

E=400A MeV0.25<b

0<0.45

ut0>0.4

V1

MST

H3: slope: 0.6320.024He3: slope: 0.6030.019

H3: slope: 0.5650.019He3: slope: 0.5360.014

Iso-MST

V1

y0

Summary

UrQMD model InitializationSkyrme potentialCross section-- nuclear medium effectCluster recognition-MST, Iso-MST

Study of collective flow of p, d, A3, He4 in heavy ion collisions in the 1A GeV regimeIso-MST influence on directed flowComparison of directed flow of 3H with 3He