the symmetry energy at high density: experimental probes
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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. binding energy of nuclei. - PowerPoint PPT PresentationTRANSCRIPT
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)