Transcript Slide 1

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
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
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 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)
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
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
central density
number of
baryons and
average density
in high –density
phase
Xu et al.,
arXiv:1305.0091
observables: collective flows and meson production
(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, review in IJMPE 21 (2012)
v2 second azim. Fourier coeff.
high density:elliptic flow
differential: neutrons vs. protons
t vs. 3He, 7Li vs 7Be, ...
asy-stiff
=1.5
UrQMD
asy-soft
=0.5
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)
high density:elliptic flow
differential: neutrons vs. protons
t vs. 3He, 7Li vs 7Be, ...
asy-stiff
=1.5
UrQMD
asy-soft
=0.5
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
v2 ratios
Russotto, Wu, Zoric, Chartier, Leifels, Lemmon,
Li, Łukasik, Pagano, Pawłowski, Trautmann,
PLB 697 (2011) 471
Trautmann and Wolter, review in IJMPE 21 (2012)
the symmetry energy
EA(ρ,δ) = EA(ρ,0) + Esym(ρ) ∙ δ2 + O(δ4)
asymmetry parameter δ = (ρn–ρp)/ρ
param. in transport: UrQMD, Q.F. Li et al.
=1.5
FOPI/LAND
=0.5
ρ/ρ0
Fuchs and Wolter, EPJA 30 (2006)
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
L ≈ 80 MeV
GSI Helmholtzzentrum für Schwerionenforschung
FOPI/LAND experiment
acceptance in pt vs. rapidity
SB: shadow bar
for background
measurement
SB
Forward Wall for
centrality and
reaction-plane
orientation
>700 elements
Large Area
Neutron Detector
LAND 1
LAND 2
5m
neutron squeeze-out:
Y. Leifels et al., PRL 71, 963 (1993)
main yield here
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
KRATTA
AsyEos experiment S394
in May 2011
studied reactions:
197Au + 197Au @ 400 A MeV
96Ru + 96Ru @ 400 A MeV
96Zr + 96Zr @ 400 A MeV
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
CHIMERA
LAND
beam
experiment
in May 2011
Kraków hodoscope
ALADiN ToF-Wall
CHIMERA
LAND
Kraków hodoscope
beam
experiment
in May 2011
flow at mid-rapidity
coverage
βtγ vs. y
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
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*)
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
superstiff
supersoft
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
*) 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)
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)
parameterization
in 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
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
neutron matter in the laboratory
neutron skins
e.g.,
132Sn, 208Pb
ρ
neutron density ρn
δr
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
the nuclear equation of state
from nuclear many-body theory
why so uncertain
at high density?
balance determines
skin thickness
Esym
related to
uncertainty of
three-body and
tensor forces
at high density
Fuchs and Wolter, EPJA 30 (2006)
normal nuclear density
PREX I
neutron radius of
Hall A
Jefferson Lab
polarized e1.06 GeV
≈ 60 μA
208Pb target
twin HRS
θlab ~ 5o
nearly only
elastic events
208Pb
from parity-violating electron scattering
“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
Neutron
detector
LAND
projectile
heavy
fragment
Coulomb
excitation
neutron(s)
high-Z target
Dipole
magnet
Aladin
~20 m
beam
Crystal Ball
with target
excitation energy reconstructed from
four-momenta of all outgoing projectilelike particles and γ rays
A. Klimkiewicz
et al., PRC
76 (2007)
from
talk at
CHIMERA-GSI workshop)
7/7/2015
W. Trautmann,
GSI(slide
Darmstadt,
Istanbul
2008
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