The Symmetry Energy at Sub- and Supersaturation Densities in … · 2016-07-20 · The Symmetry...
Transcript of The Symmetry Energy at Sub- and Supersaturation Densities in … · 2016-07-20 · The Symmetry...
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
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
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
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
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!
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
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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
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
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
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)
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
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)
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
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?
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
• 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