The symmetry energy at high density: experimental probes

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The symmetry energy at high densityexperimental
probes
W. Trautmann GSI Helmholtzzentrum, Darmstadt,
Germany
Symposium on applied nuclear physics and
innovative technologies Kraków, June 5, 2013
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binding energy of nuclei
B(A,Z) aVA - aSA2/3 - aCZ2/A1/3 -
asym(A-2Z)2/A aPd/A1/2
asym 23.2 MeV
Tsang et al., PRC (2012) following Brown, PRL
(2000)
nuclear matter
E/A(?,d) E/A(?,d0) Esym(?)d2 O(d4)
with asymmetry parameter d (?n?p)/?
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isospin diffusion
remember T. Twaróg, yesterday
figure from Lattimer and Prakash, Phys. Rep.
(2007)
Tsang et al., PRL 102, 122701 (2009)
0.4?1.0 (112,124Sn112,124Sn, 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(?) 31.6(?/?0)0.69 with
IBUU04, Li and Chen, PRC72(2005)
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the symmetry energy
parameterization in transport theory UrQMD, Q.F.
Li et al.
EA(?,d) EA(?,0) Esym(?) d2 O(d4)
asymmetry parameter d (?n?p)/?
linear
supersoft
?/?0
Fuchs and Wolter, EPJA 30 (2006) nuclear
many-body theory
Esym EsympotEsymkin L 3?odEsym/d?
at ??0
22 MeV(?/?0)?12 MeV(?/?0)2/3
? L (MeV) 0.5 57 1.0 90 1.5 123
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slide from talk of X. Viñas, ECT, Trento, June
2011
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slide from talk of X. Viñas, ECT, Trento, June
2011
Tsang et al., PRC (2012)
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high density needs higher energy obse
rvables collective flows and meson production
central density number of baryons
and average density in high density phase Xu
et al., arXiv1305.0091
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(elliptic flow squeeze-out))
high densityelliptic 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 AuAu _at_ 400 MeV per nucleon ?pot
0.9 0.4 from n-H ratios Russotto, Wu,
Zoric, Chartier, Leifels, Lemmon, Li, Lukasik,
Pagano, Pawlowski, Trautmann, PLB 697 (2011)
471 Trautmann and Wolter, review in IJMPE 21
(2012)
(directed flow)
v2 second azim. Fourier coeff.
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high densityelliptic flow
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 AuAu _at_ 400 MeV per nucleon ?pot
0.9 0.4 from n-H ratios Russotto, Wu,
Zoric, Chartier, Leifels, Lemmon, Li, Lukasik,
Pagano, Pawlowski, Trautmann, PLB 697 (2011)
471 Trautmann and Wolter, review in IJMPE 21
(2012)
asy-soft
?0.5
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high densityelliptic flow
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 AuAu _at_ 400 MeV per nucleon ?pot
0.9 0.4 from n-H ratios Russotto, Wu,
Zoric, Chartier, Leifels, Lemmon, Li, Lukasik,
Pagano, Pawlowski, Trautmann, PLB 697 (2011)
471 Trautmann and Wolter, review in IJMPE 21
(2012)
asy-soft
?0.5
v2 ratios
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the symmetry energy
EA(?,d) EA(?,0) Esym(?) d2 O(d4)
param. in transport UrQMD, Q.F. Li et al.
asymmetry parameter d (?n?p)/?
FOPI/LAND
?/?0
Fuchs and Wolter, EPJA 30 (2006)
Esym EsympotEsymkin L 3?odEsym/d?
at ??0 L 80 MeV
22 MeV(?/?0)?12 MeV(?/?0)2/3
? L (MeV) 0.5 57 1.0 90 1.5 123
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GSI Helmholtzzentrum für Schwerionenforschung
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FOPI/LAND experiment
acceptance in pt vs. rapidity
SB shadow bar for background measurement

• Forward Wall for
• centrality and
• reaction-plane
• orientation
• gt700 elements

SB
Large Area Neutron Detector
LAND 2
LAND 1
5 m
neutron squeeze-out Y. Leifels et al., PRL 71,
963 (1993)
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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(?f)a0(1.02v1cos(?f)2v2cos(2?f
)) ?f fparticle freaction plane and compared
to UrQMD model predictions Q. Li et al., J. Phys.
G 31(2005) 32 (2006)
0 ?f 2p
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AsyEos experiment S394 in May 2011 studied
reactions 197Au 197Au _at_ 400 A MeV 96Ru 96Ru
_at_ 400 A MeV 96Zr 96Zr _at_ 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
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LAND
CHIMERA
beam
Kraków hodoscope
experiment in May 2011
ALADiN ToF-Wall
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LAND
CHIMERA
Kraków hodoscope
beam
experiment in May 2011
coverage ßt? vs. y
flow at mid-rapidity
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high density isotopic particle (double) ratios
FOPI data
p-/ p ratio
K/K0 ratio
Reisdorf et al., NPA 781 (2007)
PRC (2007)
static calc. for infinite nucl. matter
AuAu
HIC
40Ca40Ca

• HIC scenario
• - fast neutron emission (mean field)
• NNgtN? threshold effects
• nngtp?- (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
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The Asy-Eos Collaboration
authors of proposal 2009
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summary and outlook

• L 60 MeV (? 0.6) from nuclear structure and
  reactions probing densities of 2/3 ?0 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
• ?pot 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 ArKCl and AuAu
  potentially useful
• interesting new results from effective field
  theory (??0)
• future tidal polarizability of neutron stars via
  gravitational waves

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parameter test with Tübingen QMD)
M.D. Cozma et al., arXiv1305.5417
difference of neutron and proton squeeze-outs Au
Au _at_ 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
supersoft
superstiff
) V.S. Uma Maheswari, C. Fuchs, Amand Faessler,
L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)
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parameter test with Tübingen QMD)
M.D. Cozma et al., arXiv1305.5417
difference of neutron and proton squeeze-outs Au
Au _at_ 400 A MeV
conclusion super-soft not compatible with
FOPI-LAND data
supersoft
superstiff
) V.S. Uma Maheswari, C. Fuchs, Amand Faessler,
L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)
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high density inconsistent results from pion
ratios
analysis of p-/p ratios in AuAu at 400 A MeV
FOPI data, Reisdorf et al., NPA (2007)
p ratios IBUU04 x1 super soft
p ratios IBUU04 x1 super soft
p ratios ImIQMD SLy6 with ?2 very stiff
Xiao et al., PRL 102 (2009)
Feng and Jin, PLB 683 (2010)
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the symmetry energy
EA(?,d) EA(?,0) Esym(?) d2 O(d4)
parameterization in transport theory Bao-An Li
et al.
asymmetry parameter d (?n?p)/?
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
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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,
arXiv1212.0284v1 Lecture at the International
Summer School for Advanced Studies, July 2012,
Predeal, Romania
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neutron matter in the laboratory
neutron skins
e.g., 132Sn, 208Pb
?
neutron density ?n
proton density ?p
skin dR ltrn2gt1/2 - ltrp2gt1/2
r
balance of asymmetry pressure inside
and neutron-matter EoS at reduced density in skin
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the nuclear equation of state
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
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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 ?lab 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 1-4sin?W
with
sin?W0.23
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Coulomb excitation of the pygmy dipole resonance
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 ?
rays
Crystal Ball with target
beam
7/27/2015
W. Trautmann, GSI Darmstadt, Istanbul 2008
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A. Klimkiewicz et al., PRC 76 (2007) (slide from
talk at CHIMERA-GSI workshop)