The symmetry energy at high density:The symmetry energy at high density:experimental probesexperimental probes

W. TrautmannGSI Helmholtzzentrum, Darmstadt, Germany

Symposium on applied nuclear physics and innovative technologies

Kraków, June 5, 2013

binding energy of nuclei

Tsang et al.,PRC (2012)

followingBrown, PRL (2000)

B(A,Z) = aV·A - aS·A2/3 - aC·Z2/A1/3 - asym·(A-2Z)2/A + aP·δ/A1/2

nuclear matter

E/A(ρ,δ) = E/A(ρ,δ=0) + Esym(ρ)·δ2 + O(δ4)

asym = 23.2 MeV

with asymmetry parameter δ = (ρn–ρp)/ρ

isospin diffusion

figure from Lattimer and Prakash, Phys. Rep. (2007)

Tsang et al., PRL 102, 122701 (2009): 0.4≤γ≤1.0(112,124Sn+112,124Sn, 50 AMeV) 45 MeV ≤L≤ 100 MeVfrom isospin diffusion and neutron-proton double ratiosinterpreted with ImQMD calculations by Y. Zhang et al.

recently M.B. Tsang, PRC 86 (2012): L = 70 ± 15 MeVpreviously: Esym(ρ) ≈ 31.6·(ρ/ρ0)0.69 with IBUU04, Li and Chen, PRC72(2005)

remember T. Twaróg, yesterday

=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)/ρ

EA(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

slide from talk of X. Viñas, ECT*, Trento, June 2011

slide from talk of X. Viñas, ECT*, Trento, June 2011

Tsang et al., PRC (2012)

high density:needs higher energy

observables: collective flows and meson production

central density

number of baryons andaverage densityin high –densityphase

Xu et al.,arXiv:1305.0091

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) 471

Trautmann and Wolter, review in IJMPE 21 (2012)

high density:elliptic flow(elliptic flowsqueeze-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) 471

Trautmann and Wolter, review in IJMPE 21 (2012)

high density:elliptic flow asy-stiff

asy-soft

UrQMD

=1.5

=0.5

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) 471

Trautmann and Wolter, review in IJMPE 21 (2012)

high density:elliptic flow asy-stiff

asy-soft

UrQMD

v2 ratios

=1.5

=0.5

=1.5

=0.5

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

the symmetry energy

ρ/ρ0

FOPI/LAND

γ L (MeV)0.5 57 1.0 901.5 123

Esym = Esympot+Esym

kin

L = 3ρo·dEsym/dρ at ρ=ρ0

L ≈ 80 MeV

= 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3

Fuchs and Wolter, EPJA 30 (2006)

asymmetry parameter δ = (ρn–ρp)/ρ

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

GSI Helmholtzzentrum für Schwerionenforschung

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

>700 elements

Large AreaNeutron Detector

5 m

azimuthal angular distributions

near target rapiditymostly directed flow

at mid-rapiditystrong squeeze-out

near projectile rapiditymostly directed flow

fitted with:f(Δφ)=a0*(1.0+2v1*cos(Δφ)+2v2*cos(2Δφ))Δφ = φparticle – φreaction plane

and compared to UrQMD model predictionsQ. Li et al., J. Phys. G 31(2005); 32 (2006)

relative to the reaction planefor neutrons, background subtracted

0 Δφ 2π

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

ALADINToF wall

four ringsof μ-ball

four double ringsof CHIMERA

AsyEos experiment S394in May 2011

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

KRATTA

experimentin May 2011

ALADiN ToF-Wall

Kraków hodoscope

beam

LANDCHIMERA

experimentin May 2011

beam

LANDCHIMERA Kraków hodoscope

coverageβtγ vs. yflow at mid-rapidity

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+Au

PRC (2007)Reisdorf et al., NPA 781 (2007)

K+/K0 ratio π-/ π+ ratio

40Ca+40Ca

authors of proposal 2009

summary and outlook

• L ≈ 60 MeV (γ ≈ 0.6) from nuclear structure and reactions probing densities of ≈ 2/3 ρ0; big expectations on PREXII, CREX (2015)

• increasingly more precise data from neutron-star observations, typically L ≈ 40 MeV; e.g. Steiner, Lattimer and Brown, ApJ (2010)

• high-densities probed in reactions at SIS energies; γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow; super-soft ruled out; study 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

• interesting new results from effective field theory (ρ≤ρ0)

• future: tidal polarizability of neutron stars via gravitational waves

parameter test 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 et al., arXiv:1305.5417

first 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 dep. of NNECSasymmetry dep. of NNECSwidth L of nucleon wave packetmomentum dependence of isovector potentialsupersoftsuperstiff

parameter test with Tübingen QMD*)

conclusion:super-soft not compatiblewith 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 et al., arXiv:1305.5417

supersoftsuperstiff

analysis of π-/π+ ratios in Au+Au at 400 A MeV FOPI data, Reisdorf et al., NPA (2007)

π ratios + IBUU04:x=1 super soft

Xiao et al., PRL 102 (2009) Feng and Jin, PLB 683 (2010)

high density: inconsistent results from pion ratios

π ratios + IBUU04:x=1 super soft

π ratios + ImIQMD:SLy6 with =2 very stiff

Fuchs and Wolter, EPJA 30 (2006)

the symmetry energy

asymmetry parameter δ = (ρn–ρp)/ρ

EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4) parameterizationin transport theory: Bao-An Li 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

from Bao-An Li, Lie-Wen Chen, Farrukh J. Fattoyev,William G. Newton and Chang Xu, arXiv:1212.0284v1

Lecture at the International Summer School for Advanced Studies, July 2012, Predeal, Romania

21 refs 10 refs

the symmetry energy: present status (2012)near and below saturation density

neutron matter in the laboratory

neutron skins

e.g., 132Sn, 208Pb

balance ofasymmetry pressure inside andneutron-matter EoS at reduced density in skin

δr

r

ρ

neutron density ρn

proton density ρp

skin δR = <rn2>1/2 - <rp

2>1/2

Fuchs and Wolter, EPJA 30 (2006)

the nuclear equation of state

why so uncertainat high density?

related touncertainty of three-body and tensor forcesat high density

normal nuclear density

balance determines skin thickness

Esym

from nuclear many-body theory

PREX I

the Z0 couples mainly to the neutron:weak charge of the proton: 1-4sinθW

with sinθW=0.23

neutron radius of 208Pb from parity-violating electron scattering

Hall AJefferson Labpolarized e-

1.06 GeV≈ 60 μA208Pb targettwin HRSθlab ~ 5o

nearly onlyelastic events

“a landmarkfor isospin physics”

(Roca-Maza et al.)

for first results see

S. Abrahamyan et al.,PRL 108 (2012)

04/22/23 W. Trautmann, GSI Darmstadt, Istanbul 2008 30

Coulomb excitation of the pygmy dipole resonance

neutron(s)

heavyfragment

beamCrystal Ball with target

Dipole magnet Aladin

Neutron detector LAND

~20 m

high-Z target

projectile

Coulomb excitation

excitation energy reconstructed from four-momenta of all outgoing projectile-like particles and γ rays

A. Klimkiewicz et al., PRC 76 (2007) (slide from talk at CHIMERA-GSI workshop)