Download Probing nuclear symmetry energy with nucleon collective flow

Probing nuclear symmetry energy
with nucleon collective flow
W. Trautmann
GSI Helmholtzzentrum, Darmstadt, Germany
Cozma et al.
Russotto et al.
International Workshop
on Nuclear Dynamics and Thermodynamics
Texas A&M University, College Station, Texas
August 19-22, 2013
the symmetry energy
EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)
asymmetry parameter δ = (ρn–ρp)/ρ
parameterization
in transport theory: UrQMD, Q.F. Li et al.
=1.5
linear
=0.5
supersoft
ρ/ρ0
Fuchs and Wolter, EPJA 30 (2006)
nuclear many-body theory
γ
0.5
1.0
1.5
L (MeV)
57
90
123
Esym = Esympot+Esymkin
= 22 MeV·(ρ/ρ0)γ+12 MeV·(ρ/ρ0)2/3
L = 3ρo·dEsym/dρ at ρ=ρ0
the symmetry energy
EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)
asymmetry parameter δ = (ρn–ρp)/ρ
Fuchs and Wolter, EPJA 30 (2006)
nuclear many-body theory
parameterization
in transport theory: MDI, Chen 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
(elliptic flow,
squeeze-out))
high density: elliptic flow
differential: neutrons vs. protons
t vs. 3He, 7Li vs 7Be, ...
(directed flow)
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, IJMPE 21 (2012)
Russotto et al., EPJA special volume, submitted
v2 second azim. Fourier coeff.
high density: elliptic flow
differential: neutrons vs. protons
t vs. 3He, 7Li vs 7Be, ...
UrQMD: Qingfeng Li et al.
0.25 < b0 < 0.45
UrQMD: significant sensitivity predicted;
neutron vs. proton elliptic flows inverted
ard
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, IJMPE 21 (2012)
Russotto et al., EPJA special volume, submitted
oft
data: Reisdorf et al., NPA (2012)
graphics by Y. Leifels
FOPI/LAND experiment
acceptance in pt vs. rapidity
SB: shadow bar
for background
measurement
Forward Wall for
centrality and
reaction-plane
orientation
SB
Large Area
Neutron Detector
LAND 1
LAND 2
5m
neutron squeeze-out:
Y. Leifels et al., PRL 71, 963 (1993)
main yield here
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
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, 044617 (2011)
analysis with Tübingen QMD*)
M.D. Cozma, PLB 700, 139 (2011)
difference of neutron and proton squeeze-outs
Au + Au @ 400 A MeV
iso-soft
conclusion:
super-soft not compatible
with FOPI-LAND data
steps towards
model invariance:
iso-stiff
bands show uncertainty
due to isoscalar field
“soft to hard”
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?
*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)
more systematic parameter test with Tübingen QMD*)
M.D. Cozma et al., arXiv:1305.5417
elliptic flow ratio and difference
Au + Au @ 400 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
superstiff
supersoft
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
*) 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
elliptic flow ratio and difference
Au + Au @ 400 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
superstiff
supersoft
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
*) V.S. Uma Maheswari, C. Fuchs, Amand Faessler, L. Sehn, D.S. Kosov, Z. Wang, NPA 628 (1998)
parameter tests with Tübingen QMD and UrQMD
M.D. Cozma et al., arXiv:1305.5417
elliptic-flow ratio and difference
Au + Au @ 400 A MeV
averaged result:
x = -1.0±1.0
Cozma et al.
Russotto et al.
L = 106±46 MeV
for
comparison with IBUU04
see
Qingfeng Li et al.,
arXiv:1306.4783[nucl-th]
Asy-Eos experiment S394 in May 2011
studied reactions:
197Au + 197Au @ 400 A MeV
96Ru + 96Ru @ 400 A MeV
96Zr + 96Zr @ 400 A MeV
CHIMERA, ALADIN Tof-wall,
μ-ball, for impact parameter
orientation and modulus
CHIMERA
LAND
beam
Kraków hodoscope
CHIMERA
ALADiN ToF-Wall
CHIMERA
LAND
beam
KraTTA (see NIMA)
neutron flow at mid-rapidity
ALADiN ToF-Wall
CHIMERA
LAND
beam
a first preliminary result
Russotto (INPC 2013)
γ = 0.9 ± 0.6
0.35 < y < 0.55
b < 7.5 fm
neutron flow at mid-rapidity
summary and outlook
•
high-densities probed in reactions at SIS energies;
γpot = 0.9 ± 0.4 from FOPI/LAND elliptic flow (2011);
super-soft ruled out; studies 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;
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?
present outlook on FAIR
NeuLAND
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