Probing nuclear symmetry energywith nucleon collective flow

W. TrautmannGSI Helmholtzzentrum, Darmstadt, Germany

International Workshopon Nuclear Dynamics and Thermodynamics

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

Cozma et al.Russotto et al.

=1.5

=0.5

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

Fuchs and Wolter, EPJA 30 (2006)nuclear many-body theory

the symmetry energy

Esym = Esympot+Esym

kin

L = 3ρo·dEsym/dρ at ρ=ρ0

ρ/ρ0

asymmetry parameter δ = (ρn–ρp)/ρEA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)

γ L (MeV)0.5 57 1.0 901.5 123

= 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3

linear

supersoft

the symmetry energy

asymmetry parameter δ = (ρn–ρp)/ρEA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4) parameterization

in transport theory: MDI, Chen et al.

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

Fuchs and Wolter, EPJA 30 (2006)nuclear many-body theory

differential: neutrons vs. protons t vs. 3He, 7Li vs 7Be, ...

UrQMD: significant sensitivity predicted;neutron vs. proton elliptic flows inverted

reanalysis of FOPI-LAND dataAu+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) 471Trautmann and Wolter, IJMPE 21 (2012)Russotto et al., EPJA special volume, submitted

high density: elliptic flow(elliptic flow,squeeze-out))

(directed flow)

v2 second azim. Fourier coeff.

differential: neutrons vs. protons t vs. 3He, 7Li vs 7Be, ...

UrQMD: significant sensitivity predicted;neutron vs. proton elliptic flows inverted

reanalysis of FOPI-LAND dataAu+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) 471Trautmann and Wolter, IJMPE 21 (2012)Russotto et al., EPJA special volume, submitted

high density: elliptic flow

data: Reisdorf et al., NPA (2012)

UrQMD: Qingfeng Li et al.

graphics by Y. Leifels

ard

oft

0.25 < b0 < 0.45

FOPI/LAND experiment

SB: shadow bar for background measurement

LAND 2LAND 1

SB

acceptance in pt vs. rapidity

main yield hereneutron squeeze-out: Y. Leifels et al., PRL 71, 963 (1993)

Forward Wall forcentrality andreaction-plane

orientation

Large AreaNeutron Detector

5 m

results from FOPI/LAND Experiment

=1.5

=0.5

neutron/hydrogenFP1: γ = 1.01 ± 0.21FP2: γ = 0.98 ± 0.35neutron/protonFP1: γ = 0.99 ± 0.28FP2: γ = 0.85 ± 0.47adopted: γ = 0.9 ± 0.4

linear

=1.5

=0.5

Medium modifications (FU1, …) and momentum dependence (FP1, …) of nucleon-nucleon elastic Xsections

parameterizations in UrQMD

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

v2 40% largerwith FP2

small effecton ratios

=ρ/ρ0

iso-soft

iso-stiff

bands show uncertaintydue to isoscalar field“soft to hard”

analysis with Tübingen QMD*)

conclusion:super-soft not compatible with FOPI-LAND data

difference of neutron and proton squeeze-outsAu + Au @ 400 A MeV

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

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

steps towards model invariance:tested in UrQMD:FP1 vs. FP2, i.e. momentum dep. of NNECS

tested in T-QMD:soft vs. hard compressibility Kdensity dependence of NNECSasymmetry dependence of NNECSwidth L of nucleon wave packet

can this be done more systematically?

more systematic parameter test with Tübingen QMD*)

conclusion:super-soft not compatible with FOPI-LAND data

elliptic flow ratio and differenceAu + Au @ 400 A MeV

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

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

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 MeVdensity dependence of NNECSasymmetry dependence of NNECSwave packet 2.5<L<7.0 fm2

optical potentialmomentum dep. of isovector potentialsupersoftsuperstiff

parameter test with Tübingen QMD*)

conclusion:super-soft not compatible with FOPI-LAND data

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

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

supersoftsuperstiff

elliptic flow ratio and differenceAu + Au @ 400 A MeV

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 MeVdensity dependence of NNECSasymmetry dependence of NNECSwave packet 2.5<L<7.0 fm2

optical potentialmomentum dep. of isovector potential

parameter tests with Tübingen QMD and UrQMD

averaged result: x = -1.0±1.0 L = 106±46 MeV

elliptic-flow ratio and differenceAu + Au @ 400 A MeV

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

Cozma et al.Russotto et al.

forcomparison with IBUU04seeQingfeng Li et al.,arXiv:1306.4783[nucl-th]

Asy-Eos experiment S394 in May 2011

studied reactions:197Au + 197Au @ 400 A MeV96Ru + 96Ru @ 400 A MeV 96Zr + 96Zr @ 400 A MeV

CHIMERA, ALADIN Tof-wall,μ-ball, for impact parameterorientation and modulus

ALADiN ToF-Wall

Kraków hodoscope

beam

LANDCHIMERA

CHIMERA

neutron flow at mid-rapidity ALADiN ToF-Wall

KraTTA (see NIMA)

beam

LANDCHIMERA

a first preliminary resultRussotto (INPC 2013)

γ = 0.9 ± 0.6

0.35 < y < 0.55b < 7.5 fm

beam

LANDCHIMERA

neutron flow at mid-rapidity

summary and outlook

• 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 2015heavier neutron stars and smaller radii?tidal polarizability of neutron stars via gravitational waves??FAIR operating in 2019?

present outlook on FAIR

NeuLAND

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)

high density: isotopic particle (double) ratios

static calc.for infinite nucl. matter

FOPI data

HIC

Ferini et al. (RMF) stiffer for ratio upXiao et al. (IBUU) softer “Feng & Jin (ImIQMD) stiffer “Xie et al. (ImIBL) softer “consequence: extremely stiff (soft) solutions

Au+AuPRC (2007)

Reisdorf et al., NPA 781 (2007)

K+/K0 ratio π-/ π+ ratio

40Ca+40Ca