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