The Symmetry Energy at Sub- and Supersaturation Densities in … · 2016-07-20 · The Symmetry...
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NuSYM11
Smith College, Northampton, Mass. June 17-20, 2011
The Symmetry Energyat Sub- and Supersaturation Densities in Heavy
Ion CollisionsHermann Wolter
Ludwig-Maximilians-University München
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The Symmetry Energyat Sub- and Supersaturation Densities in Heavy
Ion CollisionsHermann Wolter
Ludwig-Maximilians-University München
NuSYM11
Smith College, Northampton, Mass. June 17-20, 2011
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Points to discuss
explore the symmetry over a large range of densities with many probes
a satisfactory consistent picture (between different ob servables and betweendifferent groups) has not yet been achieved: it is bette r at subsaturation density butstill lacking at suprasaturation)
the momentum dependence of the symmetry energy (differenc e in neutron and proton effective masses) has to be considered for a reli able interpretation (and isstill controversial)
I report on work of the Catania reaction theory group and associated members:Massimo Di Toro, Maria Colonna, Vincenzo Greco, Joseph Rizzo, Carmelo Rizzo, Valentina Giordano, Lab. Naz. del Sud, CataniaVirgil Baran, University of Bucharest, RomaniaMalgorzata Zielinska-Pfabe, Smith Coll., USATheodoros Gaitanos, Univ. of GiessenVaia Prassa, Georgios Lalazissis, Aristotle Univ. The ssaloniki, GreeceTatiana Mikhailova, Dubna, Russia
Plan:• Relevance of symmetry energy to astrophysics• Overview over different probes at different energies• Analysis of important and illustrative cases
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Astrophysical Connection
Hillebrandt, et al., Scient. Americ. 2006
Composition of the matter
collapse
post-bounce
density: log 10n [g/cm 3]entr
opy:
log
10s[
kB/b
aryo
n]
not uniform, but light and heavy clusters(nuclei embedded in the medium)
Symmetry energy plays an essential role in astrophysics
ρρρρ0000
MeV100T0 ≤≤
10/10 08 ≤≤− ρρρρρρρρ
6.0Y0 p ≤≤
Ranges of density, temperature, asymmetry in SN event
Liebendörfer, et al., NIX XI, 2010
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EOS for use in Supernovae (and neutron stars): Cf. talk of Maria Voskresenskaya ( + S. Typel, G. Röp ke, et al.)
Parametrization of nuclearsymmetry energy of different stiffness (momentum dependentSkyrme-type) (B.A. Li)
Quantum Statistical model , T=1,4,8 MeV)
Single nucleusapprox. (Wigner-Seitz), RMF
Thermal Green Fct(quantumstatistical) model formedium dependence of clusters
+ gen RMF model (with explicitcluster degrees of freedom)
+ heavy nucleus in the medium (in Wigner-Seitz cell approx)
Comparison to low lowdensitiy SE determined in heavy ioncollisions(Natowitz et al., PRL 104 (2010))
The symmetry energy is finite at low density and temperat ures!
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
central
ρρ
ρρ ∇
∂∂
+∇∝− IE
IEjj symsympn
)()(
“Diffusion” “Drift”
Asy-soft
Asy-stiff
Symmetry energy slope
Proton and neutron currents
Sensitive to Sym. Energy and slope depending on observable
peripheral
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
deep-inelastic
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
N/Z of PLF residue= isospindiffusion
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
N/Z of PLF residue= isospindiffusion
N/Z of neck fragment and velocitycorrelations
Chimera 124Sn + 64N, 35 AMeV
neck fragmentswith largestasymmetry
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
N/Z of PLF residue= isospindiffusion
N/Z of neck fragment and velocitycorrelations
pre-equilibriumlight particles
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
N/Z of PLF residue= isospindiffusion
N/Z of neck fragment and velocitycorrelations
N/Z ratio of IMF‘s
Relativistic energies
Flow: directed and elliptic
p
nasystiffasysoft
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
N/Z of PLF residue= isospindiffusion
N/Z of neck fragment and velocitycorrelations
2. N/Z ratioof IMF‘s
Relativistic energies
Flow: directed and elliptic
Productionof particles, ππππ,K
pn
asystiffasysoft
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Reaction Mechanisms in Heavy Ion Collisions
Coulomb barrier to Fermi energies
Isospinmigration
Isospinfractionation,multifragm
centralperipheral
deep-inelastic
0 10 20 300.0
0.2
0.4
0.6
0.8
1.0
E /
E0
angle
18O + 181Ta, 35 MeV / A
Z = 6
Z = 5
Z = 4
Z = 7
Z = 8
pre-equil. dipole
N/Z of PLF residue= isospindiffusion
5. N/Z of neck fragment and velocitycorrelations
2. N/Z ratioof IMF‘s
Relativistic energies
Flow: directed and elliptic
Productionof particles, ππππ,K
pre-equilibriumlight particles
pn
asystiffasysoft
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one-body pase space density: f(r,p;t)
[ ]σ,fIfUfm
p
t
fcollp =∇∇−∇+
∂∂
r
Vlasov eq.; mean field 2-body hard collisions
[ ])1)(1()1)(1(
)()2(
1
432432
43213412
124322
3
ffffffff
ppppd
dvdpdpdp
−−−−−
−−+Ω
=→
∫∫∫ δσπ
loss term gain term
flucIδ+Fluctuations from higherorder corr.;
stochastic treatment:SMF (stochastic mean field)
fff δ+=
effective mass
Kinetic momentum
Field tensor
Relativistic BUU eq.
[[[[ ]]]] coll*)p(
)r()r( I*)p,r(f*)m*mF*p(*p ====∂∂∂∂∂∂∂∂++++++++∂∂∂∂ µµµµ
µµµµµνµνµνµνννννµµµµ
µµµµ
µµµµµµµµµµµµ ΣΣΣΣΣΣΣΣ
−=
−=
pp
;mm*
s*
µµµµννννννννµµµµµνµνµνµν ΣΣΣΣΣΣΣΣ ∂∂∂∂−−−−∂∂∂∂====F
Quantum molecular dynamics QMD
(stochastic NN collisions)
Transport Description of Heavy Ion Collisions
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Isopin diffusion
Imbalance (or Rami, transport) ratio:
ββββ asymmetry of residue (i=PLF,TLF)(also for other isospin sens.quantities) )(
)(R LL
iHHi2
1
LLi
HHi2
1mixi
i β−ββ+β−β=
Limiting values:R=0 complete equilibrationR=+-1, complete transparency
isospin transportthrough „neck“ in peripheral collisions
124Sn(H)+112Sn(L)
J.Rizzo, et al., Nucl. Phys. A806 (2008) 79 more equlibration (lower R) for longer interaction time ~ correlation with total energy loss
Simple equil. model
Ratio det. by interact. and relax. times
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Isopin transport
isospin transportthrough „neck“ in peripheral collisions
124Sn(H)+112Sn(L)
experimental data(B. Tsang et al.
PRL 92 (2004) )
J.Rizzo, et al., Nucl. Phys. A806 (2008) 79
points toward a moderately stiff ( γγγγ~1) SE, but disagreement in detail
L.W.Chen, C.M.Ko, B.A.Li, PRL 94, 032701 (2005)
M.B. Tsang, et al., PRL 102 (2008)
Imbalance (or Rami, transport) ratio:
ββββ asymmetry of residue (i=PLF,TLF)(also for other isospin sens.quantities) )(
)(R LL
iHHi2
1
LLi
HHi2
1mixi
i β−ββ+β−β=
Limiting values:R=0 complete equilibrationR=+-1, complete transparency
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ImQMD calculations, 112Sn +112Sn, 50 AMeV
Y.Zhang et al., arXiv:1009.1928
SMF
ImQMDLess dependence on impact parameter.
Similar conclusions in comparison with Antisymmetrized Mol. Dynamics (AMD):Colonna, Ono, Rizzo, PRC (2011)
Model dependence of imbalance ratio!
Analysis of differences BNV – QMD
more `explosive´dynamics:more `transparency´
6 fm8 fm
γ = 0.5
γ = 0.5
γ = 2
SMF = dashed linesImQMD = full lines
d<Z
>/dy
(per
eve
nt)
d<N
/Z>/
dy(p
er e
vent
)
Much less isospinmigration in ImQMD, Other sources of dissipation: Fragmentemission, fluctuation?
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protons vs. neutrons124Sn + 124Sn 112Sn + 112Sn
asy-soft
asy-stiff
Early emitted neutrons and protons reflect difference in potentials in expanded source, esp. ratio Y(n)/Y(p).
more emission for asy-soft, since symm potential higher
124Sn + 124Sn112Sn + 112Sn
„Double Ratios“
SMF simulations, V.Baran 07
Data: Famiano, et al., PRL 06
asy-soft
asy-stiff
softer symmetryenergy closer to data
Y. Zhang, et al., arXiv (2011)
qualitatively as seenin ImQMD, butquantitatively weakerdependence on SymEn
Central collisions at Fermi energies: Ratios of emitte d pre-equilibrium particles
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Momentum Dependence and Effective Mass Splitting
mn*>mp*asysoft (red)asystiff (blue)
asy-softmn*>mp* (red)mn*<mp* (blue)
M. Zielinska-Pfabe, IWM08
Sn+Sn, 50 AMeV
Effect of momentumdependence of symmetrymenergyas large as effect of asy-EOS itself.
Momentumdependence hererather strong
1
2
*
1−
∂∂
+=k
U
k
m
m
m qq
h
Un
,p(k
), ρ
=ρ
0
At high momentum m* splitting effect larger thanasy-stiffness
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asy-stiff
asy-soft
Light isobar 3H/3He yields
ObservableObservable veryvery sensitive at high sensitive at high ppTT
to the mass splitting and to the mass splitting and notnot to the to the asyasy --stiffnessstiffness
197Au+197Au600 AMeVb=5 fm, y(0)≤≤≤≤0.3
• m*n>m*p
• m*n<m*p
V.Giordano, M.Colonna et al., PRC 81(2010)
asy-stiff
asy-soft
Crossing of the symmetry potentials fora matter at ρ≈≈≈≈1.7ρρρρ0
n/p ratio yields
Pre-equilibrium nucleon and light cluster emission at h igher energy
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npdt3Heαααα7Li7Be
Particle Yields 136Xe + 124Sn, 32 AMeV
asy-soft EOSm*p> m*n (sop )
asy-soft EOSm*n> m*p (son )
asy-stiff EOSm*p> m*n (stp )
asy-stiff EOSm*n> m*p (stn )
Emission of light clusters
M. Zielinska-Pfabe, IWM09
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n/p and t/ 3He ratios as functions of transverse energy
green asy-soft EOS m* p> m*n (sop ) red asy-stiff EOS m* p>m*n (stp ) blue asy-stiff EOS with m* n>m*p,(stn)yellow asy-soft EOS with m* n>m*p (son )
Transverse energy (MeV/u)
0 0100 100
1
2
3
0
1
2
3
0
32 MeV/u 65 MeV/u
sop and stp n accelerate more than p, the ratio goes up. (There is a limit for first chance emission (be am+ Fermi)).stn and son decrease only. For t/ 3He goes down about beam energy (prob. statistics ).
t/3He ratios
More sensitivity to effective mass than to symmetry energ y!
136Xe+124Sn
M. Zielinska-Pfabe, IWM09
Transverse energy (MeV/u)
0 0100 100
1
2
3
0
1
2
3
0
32 MeV/u 65 MeV/u
n/p ratios
Transverse energy (MeV/u)
0 0100 100
1
2
3
0
1
2
3
0
32 MeV/u 65 MeV/u
n/p ratiost/3He ratios, energy dependence
Asystiff, mn<mp
E= 32, 45, 65, 100, 150 AMeV
Effect larger at higher energy and high p t
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Comparison of results for symmetry energy slope
extracted from Fermi energy collisions
Slope of Symmetry Energy
M.B.Tsang, et al., PRL102,122701(09)
Catania results,qualitativeS0=30 MeV
Agreement in general but differences in detail.
Point to different dynamics in the different approach es which should bebetter understood, as e.g. in Colonna et al., PRC 81 (2011)
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Heavy Ion Collisions at Relativistic Energies: “Flow“
GlobalGlobalmomentummomentumspacespace
Fourier analysis of momentum tensor : „flow“
v2: elliptic flowv1: directed flow
..)2cos)b,y(vcos)b,y(v1(N)b,y,(N 210 +++= θθθθθθθθθθθθ
To investigate symmetry energy:
differences of flow ( more sensitive for clusters ):
or differential flow
(analogous for v 1, v2, ..)
FP2 γ=0.98(35)
Russotto, et al., PLB 697, 471 (2011)
Au+Au @ 400 AMeV, FOPI-LAND
stiff
soft
Recent study by Cozma, arxiv 1102.2728
band: soft vs. stiff eos of symmetric matter, robust probe
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Differential elliptic flow
asystiff asysoft
m*n>m*p
m*n<m*p
Inversion of elliptic flowsbecause of inversion of potentials with effective mass
W. Reisdorf, ECT*, May 09
Indication of experimental effect
Au+Au, 400 AMeV
t-3He pair similar butweaker
Au+Au, 600 AMeV
Elliptic flow more sensitive, since determined by particl es that are emitted perp to the beam direction
V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010)
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Difference in neutron and proton potentials
1. „direct effects“: difference in proton and neutron (o rlight cluster) emission and momentum distribution
2. „secondary effects“: production of particles, isospin partners ππππ-,+, K0,+
NππππNΛΛΛΛK
ΛΛΛΛK
NN N∆∆∆∆
in-mediumin-elastic σσσσ,,,,
K and ΛΛΛΛpotential (in-medium mass)
∆∆∆∆ in-mediumself-energiesand width
ππππpotential,
G.Ferini et al.,PRL 97 (2006) 202301
asyEOSstifferwithdecrease)(Y)(Y
pn
,
,0
↓↓⇒⇒↓ +
−
+++
−
ππππππππ
∆∆∆∆∆∆∆∆1. Mean field effect: U sym more repulsive
for neutrons, and more for asystiff pre-equilibrium emission of neutron, reduction of asymmetry of residue
2. Threshold effect, in medium effectivemasses: m*
N,, m*∆∆∆∆, , , , contribution of symmetry
energy; m *K, models for K-potentials
( )thin ss −= σσσσσσσσ
stiffnessasywithincrease −↑+
−
ππππππππ
0,K, +±ππππp, n
Particle production as probe of symmetry energy
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MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09)MDI, x=1, very softNLδδδδ, stiff Ferini, Gaitanos,.. NPA 762 (05)NL, , , , soft, no Esymγγγγ=2, stiff Feng,… PLB 683 (10)SIII, very soft
FOPI, exp
Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459)
Contradictory results of different calculations;
Reason: Treatment of ∆∆∆∆ dynamics?
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FromFrom soft to soft to stiffstiff fromfrom lowerlower to to upperupper curvescurves ::Stiffer asy-EOS larger ratio!Threshold dominates mean field effect; largerat lower energies
Kaon ratio still a bit more sensitive probe:~15% difference betw. very soft and stiffsmall but perhaps measurable!double ratio data by FOPI (Lopez, et al.,
PRC75 (07)
Effect reduced in finite nuclei (pre-equilemission reduces asymmetry)
Kaons a good probe for the EOS – also for the Symmetry Ene rgy?
Kaons are a more sensitive and clean probe of the high density EOS. Demonstrated by Fuchs, et al., PRL 86 (01), C.M. Ko & J . Aichelin, PRL55(85) for symmetric matter in comparison with KAOS data.
Kaons are closer to threshold , come only from high density , havelarge mean free path , small width :
Also a probe for the symmetry energy for ratio of differ entcharge states, K 0/K+?
G.Ferini et al.,PRL 97 (2006) 202301, V. Prassa, et al ., NPA 832 (2010)
132Sn+124
Sn
Au+Au, 1 AGeV, central
Inclusive multiplicities
132Sn+124
SnNuclear matter (box calculation)
+
−
ππππππππ
+KK 0
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• Investigated different probes for the SymmetryEnergy in heavy ion collisions with transport theoryat different energy (density) ranges
• Explore the sensitivity to the ingredients (asy-EOS, momentum dependence of SymEn, medium, esp. isospin dependence of cross sections)
• Still considerable differences between different codes. Continue code comparison initiative (?)
• Consistent description of many observablesmandatory, also from structure and astrophysics
• Many knotty problems!
• Investigated different probes for the SymmetryEnergy in heavy ion collisions with transport theoryat different energy (density) ranges
• Explore the sensitivity to the ingredients (asy-EOS, momentum dependence of SymEn, medium, esp. isospin dependence of cross sections)
• Still considerable differences between different codes. Continue code comparison initiative (?)
• Consistent description of many observablesmandatory, also from structure and astrophysics
• Many knotty problems!
Summary and Outlook:Summary and Outlook:
Thank you!
Trento, Duomo