Collective flow in heavy ion collisions at intermediate energies

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Collective flow in heavy ion collisions at intermediate energies

Collective flow

at intermediate energies

INDRA


Excitation functions of flow

elliptic flow v 2

new technique of correcting:

J. Łukasik and W.T., Proc. IWM2005

A. Andronic et al.,

Eur. Phys. J. A 30, 31 (2006)

sidewards flow dv 1 /dy

| midr

0.1

0

in-plane

5.5 – 7.5 fm

INDRA

FOPI

EOS, E895

E877

∂v 1 /∂y | midr

1

0.5

0

Z=1

( )

2 – 5.5 fm

INDRA

FOPI

v 2

-0.1

out-of-plane

1

0 100 200 300 400

Z=2

10 2 10 3 10 4

E beam

(MeV/nucleon)

∂v 1 /∂y | midr

0.5

0

repulsive

attractive

197

Au + 197 Au, data from INDRA, FOPI,

and AGS experiments

0 100 200 300 400

E beam

(MeV/nucleon)


Isospin diffusion

from ISF White Paper (MSU)

stiff stiff

112,124

Sn + 112,124 Sn isotopic cross bombardment at 50 A MeV

data: Tsang et al., PRL 92, 062701 (2004)

analysis: Chen, Ko, Li, Yong et al., arXiv:0704.2340v1[nucl-th]


Inclusive cross section distributions

Xe + Sn @ 100 A MeV

DST_3: Xe+Sn @ 100.00 MeV/n, Z=1, A=1

0.6

0.5

p

DST_3: Xe+Sn @ 100.00 MeV/n, Z=1, A=2

0.6

0.5

d

DST_3: Xe+Sn @ 100.00 MeV/n, Z=1, A=3

0.6

0.5

t

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

DST_3: Xe+Sn @ 100.00 MeV/n, Z=2, A=3

0.6

DST_3: Xe+Sn @ 100.00 MeV/n, Z=2, A=4

0.6

DST_3: Xe+Sn @ 100.00 MeV/n, Z=2, A=6

0.6

0.5

3

He

0.5

4

He

0.5

6

He

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

DST_3: Xe+Sn @ 100.00 MeV/n, Z=3, A=6

DST_3: Xe+Sn @ 100.00 MeV/n, Z=3, A=7

DST_3: Xe+Sn @ 100.00 MeV/n, Z=3, A=8

0.6

0.6

0.6

0.5

6

Li

0.5

7

Li

0.5

8

Li

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

0

-0.4 -0.2 0 0.2 0.4 0.6 0.8

thresholds below mid-rapidity for light fragments

y p

/2 y p


v 1

for extreme N/Z all p t

0.35

0.35

0.35

0.3

0.25

p

0.3

0.25

d

0.3

0.25

t

midr

0.2

midr

0.2

midr

0.2

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

∂v

0.05

∂v

0.05

∂v

0.05

0

0

0

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

0.35

0.3

0.25

3He

0.3

0.25

4He

0.3

0.25

6He

midr

0.2

midr

0.2

midr

0.2

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

∂v

0.05

∂v

0.05

∂v

0.05

0

0

0

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

midr

0.3

0.25

0.2

6Li

midr

0.3

0.25

0.2

7Li

Xe+Sn, AP AT E/A N/Z

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

124 112 100 1.27

∂v

0.05

0

∂v

0.05

0

129 124 100 1.43

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

□ neutron rich ● neutron poor

129+124 124+112

(-17 neutrons)


v 1 for extreme N/Z p t /m > 0.05

0.35

0.35

0.35

0.3

0.25

p

0.3

0.25

d

0.3

0.25

t

midr

0.2

midr

0.2

midr

0.2

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

∂v

0.05

∂v

0.05

∂v

0.05

0

0

0

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

0.35

0.3

0.25

3He

0.3

0.25

4He

0.3

0.25

6He

midr

0.2

midr

0.2

midr

0.2

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

∂v

0.05

∂v

0.05

∂v

0.05

0

0

0

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

midr

0.3

0.25

0.2

6Li

midr

0.3

0.25

0.2

7Li

Xe+Sn, AP AT E/A N/Z

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

124 112 100 1.27

∂v

0.05

0

∂v

0.05

0

129 124 100 1.43

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

□ neutron rich ● neutron poor (-17 neutrons)

129+124 124+112


v 1 for extreme N/Z p t /m > 0.10

0.35

0.35

0.35

0.3

0.25

p

0.3

0.25

d

0.3

0.25

t

midr

0.2

midr

0.2

midr

0.2

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

∂v

0.05

∂v

0.05

∂v

0.05

0

0

0

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

0.35

0.3

0.25

3He

0.3

0.25

4He

0.3

0.25

6He

midr

0.2

midr

0.2

midr

0.2

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

∂v

0.05

∂v

0.05

∂v

0.05

0

0

0

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

midr

0.3

0.25

0.2

6Li

midr

0.3

0.25

0.2

7Li

Xe+Sn, AP AT E/A N/Z

/ ∂y |

1

0.15

0.1

/ ∂y |

1

0.15

0.1

124 112 100 1.27

∂v

0.05

0

∂v

0.05

0

129 124 100 1.43

-0.05

8-6 6-4 4-2 2-0

centrality

-0.05

8-6 6-4 4-2 2-0

centrality

□ neutron rich ● neutron poor (-17 neutrons)

129+124 124+112


v 2

for extreme N/Z all p t

0.06

0.06

0.06

0.05

0.04

p

0.05

0.04

d

0.05

0.04

t

0.03

0.03

0.03

|

midr

0.02

0.01

|

midr

0.02

0.01

|

midr

0.02

0.01

v 2

0

v 2

0

v 2

0

-0.01

-0.01

-0.01

-0.02

-0.02

-0.02

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

0.06

0.06

0.06

0.05

0.04

3He

0.05

0.04

4He

0.05

0.04

6He

0.03

0.03

0.03

|

midr

0.02

0.01

|

midr

0.02

0.01

|

midr

0.02

0.01

v 2

0

v 2

0

v 2

0

-0.01

-0.01

-0.01

-0.02

-0.02

-0.02

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

0.06

0.06

0.05

0.04

6Li

0.05

0.04

7Li

0.03

0.03

Xe+Sn, AP AT E/A N/Z

|

v 2

midr

0.02

0.01

0

|

v 2

midr

0.02

0.01

0

124 112 100 1.27

-0.01

-0.02

-0.01

-0.02

129 124 100 1.43

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

□ neutron rich ● neutron poor (-17 neutrons)

129+124 124+112


v 2 for extreme N/Z p t /m > 0.05

0.06

0.06

0.06

0.05

0.04

p

0.05

0.04

d

0.05

0.04

t

0.03

0.03

0.03

|

midr

0.02

0.01

|

midr

0.02

0.01

|

midr

0.02

0.01

v 2

0

v 2

0

v 2

0

-0.01

-0.01

-0.01

-0.02

-0.02

-0.02

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

0.06

0.06

0.06

0.05

0.04

3He

0.05

0.04

4He

0.05

0.04

6He

0.03

0.03

0.03

|

midr

0.02

0.01

|

midr

0.02

0.01

|

midr

0.02

0.01

v 2

0

v 2

0

v 2

0

-0.01

-0.01

-0.01

-0.02

-0.02

-0.02

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

0.06

0.06

0.05

0.04

6Li

0.05

0.04

7Li

0.03

0.03

Xe+Sn, AP AT E/A N/Z

|

v 2

midr

0.02

0.01

0

|

v 2

midr

0.02

0.01

0

124 112 100 1.27

-0.01

-0.02

-0.01

-0.02

129 124 100 1.43

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

□ neutron rich ● neutron poor (-17 neutrons)

129+124 124+112


v 2 for extreme N/Z p t /m > 0.10

0.06

0.06

0.06

0.05

0.04

p

0.05

0.04

d

0.05

0.04

t

0.03

0.03

0.03

|

midr

0.02

0.01

|

midr

0.02

0.01

|

midr

0.02

0.01

v 2

0

v 2

0

v 2

0

-0.01

-0.01

-0.01

-0.02

-0.02

-0.02

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

0.06

0.06

0.06

0.05

0.04

3He

0.05

0.04

4He

0.05

0.04

6He

0.03

0.03

0.03

|

midr

0.02

0.01

|

midr

0.02

0.01

|

midr

0.02

0.01

v 2

0

v 2

0

v 2

0

-0.01

-0.01

-0.01

-0.02

-0.02

-0.02

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

0.06

0.06

0.05

0.04

6Li

0.05

0.04

7Li

0.03

0.03

Xe+Sn, AP AT E/A N/Z

|

v 2

midr

0.02

0.01

0

|

v 2

midr

0.02

0.01

0

124 112 100 1.27

-0.01

-0.02

-0.01

-0.02

129 124 100 1.43

-0.03

8-6 6-4 4-2 2-0

centrality

-0.03

8-6 6-4 4-2 2-0

centrality

□ neutron rich ● neutron poor (-17 neutrons)

129+124 124+112


v 1

100 and 150 A MeV same N/Z

0.7

0.7

0.7

0.6

p

0.6

d

0.6

t

0.5

0.5

0.5

midr

0.4

midr

0.4

midr

0.4

/ ∂y |

0.3

/ ∂y |

0.3

/ ∂y |

0.3

1

∂v

0.2

1

∂v

0.2

1

∂v

0.2

0.1

0.1

0.1

0

0

0

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

0.7

0.7

0.7

0.6

3He

0.6

4He

0.6

6He

0.5

0.5

0.5

midr

0.4

midr

0.4

midr

0.4

/ ∂y |

0.3

/ ∂y |

0.3

/ ∂y |

0.3

1

∂v

0.2

1

∂v

0.2

1

∂v

0.2

0.1

0.1

0.1

0

0

0

150

AMeV

0.7

0.6

0.5

8-6 6-4 4-2 2-0

centrality

6Li

0.7

0.6

0.5

8-6 6-4 4-2 2-0

centrality

7Li

8-6 6-4 4-2 2-0

centrality

Xe+Sn, AP AT E/A N/Z

/ ∂y |

midr

1

∂v

0.4

0.3

0.2

0.1

0

/ ∂y |

midr

1

∂v

0.4

0.3

0.2

0.1

0

124 124 100 1.38

129 124 100 1.43

124 124 150 1.38

129 124 150 1.43

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

□ ∆ neutron rich ■ ▲

129+124 124+124

neutron poor (-5 neutrons)


v 2

100 and 150 A MeV same N/Z

0.08

0.08

0.08

0.06

p

0.06

d

0.06

t

0.04

0.04

0.04

|

midr

0.02

0

|

midr

0.02

0

|

midr

0.02

0

v 2

-0.02

v 2

-0.02

v 2

-0.02

-0.04

-0.04

-0.04

-0.06

-0.06

-0.06

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

0.08

0.08

0.08

0.06

3He

0.06

4He

0.06

6He

0.04

0.04

0.04

|

midr

0.02

0

|

midr

0.02

0

|

midr

0.02

0

v 2

-0.02

v 2

-0.02

v 2

-0.02

-0.04

-0.04

-0.04

-0.06

-0.06

-0.06

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

8-6 6-4 4-2 2-0

centrality

0.08

0.08

0.06

6Li

0.06

7Li

0.04

0.04

Xe+Sn, AP AT E/A N/Z

150

AMeV

|

v 2

midr

0.02

0

-0.02

-0.04

-0.06

|

v 2

midr

8-6 6-4 4-2 2-0

8-6 6-4 4-2 2-0

centrality

centrality

0.02

0

-0.02

-0.04

-0.06

□ ∆ neutron rich ■ ▲

129+124 124+124

124 124 100 1.38

129 124 100 1.43

124 124 150 1.38

129 124 150 1.43

neutron poor (-5 neutrons)


Isospin tracer

analysis

N/Z ?

beam

124,129

Xe + 112,124 Sn isotopic cross bombardment at 100 AMeV

Idea: use sideways N/Z ratios for calibration

use forward ratios to determine isospin transparency (diffusion)


Data sideward forward

YIELD RATIO

80 o


Transparency

full

transparency

forward data

4

He/ 3 He

t/ 6 He

full mixing

10

Be/ 7 Be

(N P +N T )

d/p

t/d

8

Li/ 6 Li

Projectile

129 Xe

124 Xe

X

X

X

X

(Z P +Z T )

t/p

Target

124 Sn

112 Sn

X

X

X

X

6

He/ 3 He


Conclusion

0.35

0.3

0.25

d

0.35

0.3

0.25

t

midr

0.2

midr

0.2

1. high accuracy of flow data

due to elaborate corrections

/ ∂y |

1

∂v

0.15

0.1

0.05

0

-0.05

8-6 6-4 4-2 2-0

centrality

/ ∂y |

1

∂v

0.15

0.1

0.05

0

-0.05

8-6 6-4 4-2 2-0

centrality

0.35

0.35

2. very small isotopic effects

visible for light isotopes

/ ∂y |

midr

1

∂v

0.3

0.25

0.2

0.15

0.1

0.05

4He

/ ∂y |

midr

1

∂v

0.3

0.25

0.2

0.15

0.1

0.05

6He

0

0

3. p t and energy dependence

as expected

/ ∂y |

midr

1

∂v

-0.05

0.35

0.3

0.25

0.2

0.15

8-6 6-4 4-2 2-0

centrality

7Li

-0.05

8-6 6-4 4-2 2-0

centrality

Xe+Sn, AP AT E/A N/Z

124 112 100 1.27

0.1

0.05

4. further constraints for

129 124 100 1.43

0

-0.05

symmetry energy from

8-6 6-4 4-2 2-0

centrality

isotopic flow and diffusion

to be expected v 1 at 100 AMeV p t /m > 0.10


Acknowledgment

for references see, e.g.,

J. Łukasik et al.,

PLB 608, 223 (2005)

A. Andronic et al.,

Eur. Phys. J. A 30, 31 (2006)

work by Jerzy Łukasik

Arnaud Le Fèvre

fruitful collaboration

with Anton Andronic

Willi Reisdorf

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