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The symmetry energy at high density:experimental probes

W. Trautmann

GSI Helmholtzzentrum, Darmstadt, Germany

Symposium on applied nuclear physics

and innovative technologies

Kraków, June 5, 2013

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

asym = 23.2 MeV

Tsang et al.,

PRC (2012)

following

Brown, PRL (2000)

nuclear matter

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

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

remember T. Twaróg, yesterday

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 MeV

from isospin diffusion and neutron-proton double ratios

interpreted with ImQMD calculations by Y. Zhang et al.

recently M.B. Tsang, PRC 86 (2012): L = 70 ± 15 MeV

previously: Esym(ρ) ≈ 31.6·(ρ/ρ0)0.69 with IBUU04, Li and Chen, PRC72(2005)

=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

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)

needs higher energy

observables: collective flows and meson production

central density

number of

baryons and

average density

in high –density

phase

Xu et al.,

arXiv:1305.0091

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, review in IJMPE 21 (2012)

(directed flow)

v2 second azim. Fourier coeff.

asy-stiff

=1.5

UrQMD

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, review in IJMPE 21 (2012)

asy-soft

=0.5

asy-stiff

=1.5

UrQMD

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, review in IJMPE 21 (2012)

asy-soft

=0.5

v2 ratios

=1.5

=0.5

the symmetry energy

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

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

asymmetry parameter δ = (ρn–ρp)/ρ

FOPI/LAND

ρ/ρ0

Fuchs and Wolter, EPJA 30 (2006)

Esym = Esympot+Esymkin

L = 3ρo·dEsym/dρ at ρ=ρ0

L ≈ 80 MeV

= 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3

γ L (MeV)

0.5 57

1.0 90

1.5 123

FOPI/LAND experiment

acceptance in pt vs. rapidity

SB: shadow bar

for background

measurement

Forward Wall for

centrality and

reaction-plane

orientation

>700 elements

SB

Large Area

Neutron Detector

LAND 2

LAND 1

5 m

neutron squeeze-out:

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

azimuthal angular distributions

relative to the reaction plane

for neutrons, background subtracted

near target rapidity

mostly directed flow

at mid-rapidity

strong squeeze-out

near projectile rapidity

mostly directed flow

fitted with:

f(Δφ)=a0*(1.0+2v1*cos(Δφ)+2v2*cos(2Δφ))

Δφ = φparticle – φreaction plane

and compared to UrQMD model predictions

Q. Li et al., J. Phys. G 31(2005); 32 (2006)

0 Δφ 2π

in May 2011

studied reactions:

197Au + 197Au @ 400 A MeV

96Ru + 96Ru @ 400 A MeV

96Zr + 96Zr @ 400 A MeV

KRATTA

ALADIN

ToF wall

four rings

of μ-ball

four double rings

of CHIMERA

μ-ball, CHIMERA, ALADIN Tof-wall for

impact parameter orientation and modulus

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

authors of proposal 2009

- 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*)

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

difference of neutron and proton squeeze-outs

Au + Au @ 400 A MeV

conclusion:

super-soft not compatible

with FOPI-LAND data

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 K

density dep. of NNECS

asymmetry dep. of NNECS

width L of nucleon wave packet

momentum dependence 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

difference of neutron and proton squeeze-outs

Au + Au @ 400 A MeV

conclusion:

super-soft not compatible

with FOPI-LAND data

superstiff

supersoft

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

high density: inconsistent results from pion ratios

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

π ratios + IBUU04:

x=1 super soft

π ratios + ImIQMD:

SLy6 with =2 very stiff

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

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

parameterization

in transport theory: Bao-An Li et al.

asymmetry parameter δ = (ρn–ρp)/ρ

Fuchs and Wolter, EPJA 30 (2006)

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

the symmetry energy: present status (2012)

near and below saturation density

21 refs

10 refs

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

δr

neutron matter in the laboratory

neutron skins

e.g., 132Sn, 208Pb

ρ

neutron density ρn

proton density ρp

skin δR = <rn2>1/2 - <rp2>1/2

r

balance of

asymmetry pressure inside and

neutron-matter EoS at reduced density in skin

from nuclear many-body theory

why so uncertain

at high density?

related to

uncertainty of

three-body and

tensor forces

at high density

balance determines

skin thickness

Esym

Fuchs and Wolter, EPJA 30 (2006)

normal nuclear density

PREX I

neutron radius of 208Pb from parity-violating electron scattering

Hall A

Jefferson Lab

polarized e-

1.06 GeV

≈ 60 μA

208Pb target

twin HRS

θlab ~ 5o

nearly only

elastic events

“a landmark

for isospin physics”

(Roca-Maza et al.)

for first results see

S. Abrahamyan et al.,

PRL 108 (2012)

the Z0 couples mainly to the neutron:

weak charge of the proton: 1-4sinθW with sinθW=0.23

Coulomb excitation of the pygmy dipole resonance

projectile

Coulomb excitation

high-Z target

Neutron detector LAND

heavy

fragment

neutron(s)

Dipole magnet Aladin

~20 m

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

Crystal Ball with target

beam

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

8/15/2014

W. Trautmann, GSI Darmstadt, Istanbul 2008

30

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