1. and the nuclear equation of state
Flow observables
and the nuclear equation of state
W. Trautmann
GSI Helmholtzzentrum, Darmstadt, Germany
52nd International Winter Meeting on Nuclear Physics
Bormio, January , 2014

2. FOPI data: directed and elliptic flow and IQMD for Au+Au at 1.5 AGeV
SM favored by directed and elliptic flows
FOPI data: directed and elliptic flow and IQMD for Au+Au at 1.5 AGeV
protons, deuterons, tritons 0.4 – 1.5 AGeV
W. Reisdorf et al., NPA 876 (2012)
see also,
Danielewicz et al., Science 298 (2002)

3. dN/d(Φ-ΦR) = N0/2π · (1+2Σvncosn(Φ-ΦR))
v2 second azim. Fourier coeff.
collective flow
(elliptic flow,
squeeze-out))
(directed flow)
dN/d(Φ-ΦR) = N0/2π · (1+2Σvncosn(Φ-ΦR))

4. the symmetry energy =1.5 =0.5 γ L (MeV)
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
=1.5
=0.5
linear
supersoft
ρ/ρ0
Fuchs and Wolter, EPJA 30 (2006)
nuclear many-body theory
Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three-body force of Urbana type.
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

5. with explicit momentum dependence in the isovector part
the symmetry energy
EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)
parameterization
in transport theory: MDI, Chen et al.
asymmetry parameter δ = (ρn–ρp)/ρ
Fuchs and Wolter, EPJA 30 (2006)
nuclear many-body theory
Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three-body force of Urbana type.
force developed by
Das, Das Gupta, Gale, and Bao-An Li,
Phys. Rev. C 67 (2003)
with explicit momentum dependence in the isovector part 5

6. "A way forward in the study of the symmetry energy ..."
Horowitz et al., arXiv:
maximum sensitivity
of structure data near 2/3 ρ0
Zhang and Chen (arXiv: )
use isotope binding energy difference and
neutron skin thickness of Sn isotopes;
B.A. Brown (arXiv: ) uses Skyrme,
properties of doubly-magic nuclei (binding
energies, rms charge radii, and single-particle
energies) and Δrnp=0.20 fm for 208Pb.

7. high density: elliptic flow
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
400 MeV per nucleon:
γpot = 0.9 ± 0.4 from n-H ratios
L = 83 ± 26 MeV
Russotto, Wu, Zoric, Chartier, Leifels, Lemmon,
Li, Łukasik, Pagano, Pawłowski, Trautmann,
PLB 697 (2011) 471
Trautmann and Wolter, IJMPE 21, (2012)
Cozma et al., PRC 88, (2013)
Russotto et al., EPJA special volume, submitted
(directed flow)
v2 second azim. Fourier coeff.

8. high density: elliptic flow
UrQMD: Q. Li et al., arXiv_
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
400 MeV per nucleon:
γpot = 0.9 ± 0.4 from n-H ratios
L = 83 ± 26 MeV
Russotto, Wu, Zoric, Chartier, Leifels, Lemmon,
Li, Łukasik, Pagano, Pawłowski, Trautmann,
PLB 697 (2011) 471
Trautmann and Wolter, IJMPE 21, (2012)
Cozma et al., PRC 88, (2013)
Russotto et al., EPJA special volume, submitted
0.25 < b0 < 0.45
ard
oft
data: Reisdorf et al., NPA (2012)
graphics by Y. Leifels

9. FOPI/LAND experiment acceptance in pt vs. rapidity SB LAND 2 LAND 1
SB: shadow bar
for background
measurement
Forward Wall for
centrality and
reaction-plane
orientation SB
Large Area
Neutron Detector
main yield here
LAND 2
LAND 1
5 m
neutron squeeze-out:
Y. Leifels et al., PRL 71, 963 (1993)

10. results from FOPI/LAND Experiment
=1.5
linear
=0.5
=1.5
=0.5
neutron/hydrogen
FP1: γ = 1.01 ± 0.21
FP2: γ = 0.98 ± 0.35
neutron/proton
FP1: γ = 0.99 ± 0.28
FP2: γ = 0.85 ± 0.47
adopted: γ = 0.9 ± 0.4

11. Qingfeng Li et al., Phys. Rev. C 83, 044617 (2011)
parameterizations in UrQMD
Medium modifications (FU1, …) and
momentum dependence (FP1, …) of
nucleon-nucleon elastic Xsections
v2 40% larger
with FP2
small effect
on ratios
=ρ/ρ0
Qingfeng Li et al., Phys. Rev. C 83, (2011)

12. analysis with Tübingen QMD*)
M.D. Cozma, PLB 700, 139 (2011)
difference of neutron and proton squeeze-outs
Au 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 compressibility K
density dependence of NNECS
asymmetry dependence of NNECS
width L of nucleon wave packet
can this be done more systematically?
iso-soft
iso-stiff
effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better.
bands show uncertainty
due to isoscalar field
“soft to hard”
*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 12

13. more systematic parameter test with Tübingen QMD*)
M.D. Cozma et al., PRC 88, (2013)
elliptic flow ratio and difference
Au A MeV
conclusion:
super-soft not compatible
with FOPI-LAND data
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 MeV
density dependence of NNECS
asymmetry dependence of NNECS
wave packet 2.5<L<7.0 fm2
optical potential
momentum dep. of isovector potential
effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better.
superstiff
supersoft
*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 13

14. more systematic parameter test with Tübingen QMD*)
elliptic flow difference
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 MeV
density dependence of NNECS
asymmetry dependence of NNECS
wave packet 2.5<L<7.0 fm2
optical potential
momentum dep. of isovector potential
effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better.
superstiff
supersoft
*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 14

15. more systematic parameter test with Tübingen QMD*)
elliptic flow ratio
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 MeV
density dependence of NNECS
asymmetry dependence of NNECS
wave packet 2.5<L<7.0 fm2
optical potential
momentum dep of isovector potential
effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better.
superstiff
supersoft
*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998) 15

16. parameter tests with Tübingen QMD and UrQMD
M.D. Cozma et al., PRC 88, (2013)
elliptic-flow ratio
and difference
Cozma et al.
Russotto et al.
averaged result:
x = -1.0±1.0
L = 106±46 MeV
conclusion:
super-soft not
compatible
with FOPI-LAND
data
effective mass scaling model for the in-medium NN cross-sections and explicit momentum dependence of the symmetry energy part. Requires experimental data for the elliptic flow of both charged and neutral particles of high quality, of an accuracy of 1% or better.
for comparison
with IBUU04 see
Qingfeng Li et al.,
arXiv: [nucl-th] 16

17. Asy-Eos experiment S394 in May 2011

18. Asy-Eos experiment S394 in May 2011
CHIMERA, ALADIN Tof-wall,
μ-ball, for impact parameter
orientation and modulus
studied reactions:
197Au A MeV
96Ru A MeV
96Zr A MeV

19. 19

20. CHIMERA
LAND
beam
Kraków hodoscope
ALADiN ToF-Wall
CHIMERA

21. CHIMERA
LAND
beam
KraTTA (see NIMA)
ALADiN ToF-Wall
neutron flow at mid-rapidity

22. a first preliminary result
CHIMERA
LAND
a first preliminary result
Russotto (INPC 2013)
γ = 0.9 ± 0.6
0.35 < y < 0.55
b < 7.5 fm
beam
neutron flow at mid-rapidity

23. latest news from Catania:
1991 data, Russotto et al., PLB 697, 471
2011 data, Russotto et al., 2014, preliminary
γ = 0.84 ± 0.11
L= 79 ± 8 MeV
γ = 1.01±0.21
preliminary result from S394:
obviously less fluctuations and smaller errors,
previous result confirmed within uncertainties

24. summary and outlook
high-densities probed in reactions at SIS energies;
γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow (2011);
super-soft and super-stiff ruled out; studies of model invariance under way: L = 80 – 110 MeV;
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 2015
heavier neutron stars and smaller radii?
tidal polarizability of neutron stars via gravitational waves??
FAIR operating in 2019!

25. present outlook on FAIR

26. present outlook on FAIR
NeuLAND

27. K+/K0 double ratio 2014: Horowitz et al., arXiv:1401.5839 96Zr+96Zr
cite Ferini et al. PRL 97 (2006)
96Zr+96Zr
96Ru+96Ru
X. Lopez et al.
PRC (2007)
static calc.
for infinite
nucl. matter
Au+Au 1AGeV
different assumptions
on symmetry energy
FOPI data
HIC
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)
pion ratios presently inconclusive

28. high density: isotopic particle (double) ratios
FOPI data
K+/K0 ratio
π-/ π+ ratio
Reisdorf et al., NPA 781 (2007)
PRC (2007)
static calc.
for infinite
nucl. matter
Au+Au
HIC
40Ca+40Ca
the HIC scenario exhibits two important dynamical effects:
fast neutron emission (mean field effect) and transformation
of neutron into proton in inelastic channels (no-chemical
equilibrium
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

29. Danielewicz et al., Science 298 (2002)
symmetric matter
KAOS data
K+ ratios
Au+Au vs. C+C
normalized to <Apart> ...
... favor soft EoS
1 A GeV Au+Au
pressure contours
density contours
flow data rule out repulsive and super-soft EoS
Danielewicz et al., Science 298 (2002)
Sturm et al., Fuchs et al., PRL 86 (2001)

30. γ = 0.84 ± 0.11
L= 79 ± 8 MeV

32. 2013: Li and Han, arXiv:
analyses of terrestrial experiments
average: S0 = 31.5 MeV
astrophysical
observations
astrophysical
observations
analyses of terrestrial experiments
average: L = 58.9 MeV