Probing nuclear symmetry energy with nucleon collective flow
description
Transcript of Probing nuclear symmetry energy with nucleon collective flow
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