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Probing nuclear symmetry energy with nucleon collective flow

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Probing nuclear symmetry energy

with nucleon collective flow

W. Trautmann

GSI Helmholtzzentrum, Darmstadt, Germany

Cozma et al.

Russotto et al.

International Workshop

on Nuclear Dynamics and Thermodynamics

Texas A&M University, College Station, Texas August 19-22, 2013

=1.5

=0.5

the symmetry energy

EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)

parameterization

in transport theory: UrQMD, Q.F. Li et al.

asymmetry parameter δ = (ρn–ρp)/ρ

linear

supersoft

ρ/ρ0

Fuchs and Wolter, EPJA 30 (2006)

nuclear many-body theory

Esym = Esympot+Esymkin

L = 3ρo·dEsym/dρ at ρ=ρ0

= 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3

γ L (MeV)

0.5 57

1.0 90

1.5 123

EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)

parameterization

in transport theory: MDI, Chen et al.

asymmetry parameter δ = (ρn–ρp)/ρ

Fuchs and Wolter, EPJA 30 (2006)

nuclear many-body theory

force developed by

Das, Das Gupta, Gale, and Bao-An Li,

Phys. Rev. C 67 (2003) 034611

with explicit momentum dependence in the isovector part

squeeze-out))

high density: elliptic flow

differential:neutrons vs. protons

t vs. 3He, 7Li vs 7Be, ...

UrQMD:significant sensitivity predicted;

neutron vs. proton elliptic flows inverted

reanalysis of FOPI-LAND data

Au+Au @ 400 MeV per nucleon:

γpot = 0.9 ± 0.4 from n-H ratios

Russotto, Wu, Zoric, Chartier, Leifels, Lemmon,

Li, Łukasik, Pagano, Pawłowski, Trautmann,

PLB 697 (2011) 471

Trautmann and Wolter, IJMPE 21 (2012)

Russotto et al., EPJA special volume, submitted

(directed flow)

v2 second azim. Fourier coeff.

UrQMD: Qingfeng Li et al.

differential:neutrons vs. protons

t vs. 3He, 7Li vs 7Be, ...

UrQMD:significant sensitivity predicted;

neutron vs. proton elliptic flows inverted

reanalysis of FOPI-LAND data

Au+Au @ 400 MeV per nucleon:

γpot = 0.9 ± 0.4 from n-H ratios

Russotto, Wu, Zoric, Chartier, Leifels, Lemmon,

Li, Łukasik, Pagano, Pawłowski, Trautmann,

PLB 697 (2011) 471

Trautmann and Wolter, IJMPE 21 (2012)

Russotto et al., EPJA special volume, submitted

0.25 < b0 < 0.45

ard

oft

data: Reisdorf et al., NPA (2012)

graphics by Y. Leifels

FOPI/LAND experiment

main yield here

acceptance in pt vs. rapidity

SB: shadow bar

for background

measurement

Forward Wall for

centrality and

reaction-plane

orientation

SB

Large Area

Neutron Detector

LAND 2

LAND 1

5 m

neutron squeeze-out:

Y. Leifels et al., PRL 71, 963 (1993)

results from FOPI/LAND Experiment

=1.5

linear

=0.5

=1.5

=0.5

neutron/hydrogen

FP1: γ = 1.01 ± 0.21

FP2: γ = 0.98 ± 0.35

neutron/proton

FP1: γ = 0.99 ± 0.28

FP2: γ = 0.85 ± 0.47

adopted: γ = 0.9 ± 0.4

Medium modifications (FU1, …) and

momentum dependence (FP1, …)of

nucleon-nucleon elastic Xsections

v2 40% larger

with FP2

small effect

on ratios

=ρ/ρ0

Qingfeng Li et al., Phys. Rev. C 83, 044617 (2011)

M.D. Cozma, PLB 700, 139 (2011)

difference of neutron and proton squeeze-outs

Au + Au @ 400 A MeV

conclusion:

super-soft not compatible

with FOPI-LAND data

iso-soft

iso-stiff

steps towards

model invariance:

tested in UrQMD:

FP1 vs. FP2,

i.e. momentum dep. of NNECS

tested in T-QMD:

soft vs. hard compressibility K

density dependence of NNECS

asymmetry dependence of NNECS

width L of nucleon wave packet

can this be done more systematically?

bands show uncertainty

due to isoscalar field

“soft to hard”

*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)

more systematic parameter test with Tübingen QMD*)

M.D. Cozma et al., arXiv:1305.5417

elliptic flow ratio and difference

Au + Au @ 400 A MeV

conclusion:

super-soft not compatible

with FOPI-LAND data

steps towards

model invariance:

tested in UrQMD:

FP1 vs. FP2,

i.e. momentum dep. of NNECS

tested in T-QMD:

soft vs. hard 190<K<280 MeV

density dependence of NNECS

asymmetry dependence of NNECS

wave packet 2.5<L<7.0 fm2

optical potential

momentum dep. of isovector potential

superstiff

supersoft

*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)

parameter test with Tübingen QMD*)

M.D. Cozma et al., arXiv:1305.5417

elliptic flow ratio and difference

Au + Au @ 400 A MeV

conclusion:

super-soft not compatible

with FOPI-LAND data

steps towards

model invariance:

tested in UrQMD:

FP1 vs. FP2,

i.e. momentum dep. of NNECS

tested in T-QMD:

soft vs. hard 190<K<280 MeV

density dependence of NNECS

asymmetry dependence of NNECS

wave packet 2.5<L<7.0 fm2

optical potential

momentum dep. of isovector potential

superstiff

supersoft

*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)

parameter tests with Tübingen QMD and UrQMD

M.D. Cozma et al., arXiv:1305.5417

elliptic-flow ratio and difference

Au + Au @ 400 A MeV

averaged result:

x = -1.0±1.0

L = 106±46 MeV

Cozma et al.

Russotto et al.

for

comparison with IBUU04

see

Qingfeng Li et al.,

arXiv:1306.4783[nucl-th]

Asy-Eos experiment S394 in May 2011

studied reactions:

197Au + 197Au @ 400 A MeV

96Ru + 96Ru @ 400 A MeV

96Zr + 96Zr @ 400 A MeV

CHIMERA, ALADIN Tof-wall,

μ-ball,for impact parameter

orientation and modulus

LAND

a first preliminary result

Russotto (INPC 2013)

γ = 0.9 ± 0.6

0.35 < y < 0.55

b < 7.5 fm

beam

neutron flow at mid-rapidity

- high-densities probed in reactions at SIS energies;
- γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow (2011);
- super-soft ruled out; studies of model invariance under way;
- analysis of ASY-EOS experiment in progress!
- kaon and pion ratios interesting probes but results presently inconclusive: new activity at RIKEN (Samurai) and MSU;
- HADES kaon data for Ar+KCl and Au+Au potentially useful;
- new model studies for kaon ratios?
- future: PREX and CREX in 2015
- heavier neutron stars and smaller radii?
- tidal polarizability of neutron stars via gravitational waves??
- FAIR operating in 2019?

NeuLAND

high density: isotopic particle (double) ratios

FOPI data

π-/ π+ ratio

K+/K0 ratio

Reisdorf et al., NPA 781 (2007)

PRC (2007)

Au+Au

static calc.

for infinite

nucl. matter

HIC

40Ca+40Ca

- HIC scenario:
- - fast neutron emission (mean field)
- NN=>NΔ threshold effects
- nn=>pΔ- (no chemical equilibrium)
- see, e.g., di Toro et al., J.Phys.G (2010)

Ferini et al. (RMF) stiffer for ratio up

Xiao et al. (IBUU) softer “

Feng & Jin (ImIQMD) stiffer “

Xie et al. (ImIBL) softer “

consequence: extremely stiff (soft) solutions

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