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The High-Density Symmetry Energy in Heavy Ion Collisions. Hermann Wolter Ludwig-Maximilians-Universität München (LMU). Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012. The High-Density Symmetry Energy in Heavy Ion Collisions. - PowerPoint PPT Presentation
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The High-Density Symmetry Energy in Heavy Ion Collisions
The High-Density Symmetry Energy in Heavy Ion Collisions
Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012
Hermann WolterLudwig-Maximilians-Universität München (LMU)
The High-Density Symmetry Energy in Heavy Ion Collisions
The High-Density Symmetry Energy in Heavy Ion Collisions
Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012
Hermann WolterLudwig-Maximilians-Universität München (LMU)
Massimo Di Toro, Maria Colonna, V. Greco, G. Ferini, (LNS Catania), Theodoros Gaitanos, (Giessen),
Vaia Prassa, (Thessaloniki)
Schematic Phase Diagram of Strongly Interacting Matter
Liquid-gas coexistence
Quark-hadron coexistence
Z/N
1
0
SIS18
neutron starsSupernovae IIa
Isospin degree of freedom
1. Density dependence of the Symmetry energy in the hadronic sector2. Investigation via heavy ion collisions3. Observables in the above-saturation density regime:
difference flows, meson ratios
SIS300
...)(O)(E)(EA/),(E 42BsymBnmB
pn
pn
Equation-of-State and Symmetry Energy
pair22
s3/4
C3/1
sv )ZN/()ZN(aA)1Z(ZaAaaA/)Z,A(E BW mass formula
density-asymmetry dep. of nucl.matt.
)(Ea 0symS
stiff
soft
saturation point
Fairly well fixed! Soft!
EOS of symmetric nuclear matter
symmetry energy
asymmetry density
Symmetry energy: neutron - symm matter, rather unknown,e.g. Skyrme-like param.,B.A.Li
asy-
stiff
asy-soft
neutron matter EOS
Esympot() often parametrized as
)/(C 0
)(E)/()(E potsym
3/20F3
1sym
2
0
0sym
0
0sym 18
K
3
LJ)(E
Parametrizations around 0 :
C. Fuchs, H.H. Wolter, EPJA 30 (2006) 5
matt.nuclmatt.neutrsym EEE
The Nuclear Symmetry Energy (SE) in „realistic“ models
The EOS of symmetric and pure neutron matter in different many-body aproaches
)UU(U
n,pq;k
U
k
m1
m
m
pn21
Lane
1
q
2
*q
SE ist also momentum dependent p/n effective mass splitting
Lane potential; mom. dep.
Why is symmetry energy so uncertain?? ->In-medium mass, and short range isovector tensor correlations (B.A. Li, PRC81 (2010));
use HIC to investigate in the laboratory and neutron star observations
Rel, BruecknerNonrel. BruecknerVariationalRel. Mean fieldChiral perturb.
SE
nuclear matter
neutron matter
Esy
m
M
eV)
1 2 30
Asy-stiff
Asy-soft
Importance of Nuclear Symmetry Energy
Bayesian analysis of mass-radius relation;A. Steiner, et al., arXiv 1205.6871
neutron starsSupernovae, very dilute matter,Cluster correlations
Constraints on the Slope of SE from Structure and low-energy HIC
MeV2560L
Nat
ow
itz
et a
l., P
RL
104
(20
10)
,fIfUfm
p
t
fcollp
2-body collisions
)1)(1()1)(1(
)()2(
1
432432
43213412
1243223
ffffffff
ppppd
dvdpdpdp
loss term gain term
11 1
12
3 4
non-relativistic: BUU
Vlasov eq.; mean field
EOSisoscalar and isovector
isospin dependent, pp,nn,pn
1) Approximation to a much more complicated non-equilibrium quantum transport equation (Kadanoff-Baym) by neglecting finite width of particles (quasi-particle approximation)
2) Relativistic equivalent available; RMF or EFT models for EOS
3) Consistency between EOS and in-medium cross sections: e.g. (Dirac) Brueckner approach
4) Isovecor effects are small relative to isoscalar quantities; differences or ratios of observables to become independent of isoscalar uncertainties
5) Collision termdissipation, NO fluctuation termBoltzmann-Langevin eq.
Învestigation of the symmetry energy in heavy ion collisions
Transport theory
Heavy Ion Collisions at Relativistic Energies: “Flow“
Global Global momentum momentum spacespace
Fourier analysis of momentum tensor : „flow“
v2: elliptic flowv1: directed flow
..)2cos)b,y(vcos)b,y(v1(N)b,y,(N 210
p
nasystiffasysoft
asystiff
Proton-neutron differential flow
)neutron(protonfor)1(1w
,)wp()y(p
i
)y(N
1ii
xi)y(N
1npx
132132Sn + Sn + 132132Sn @ 1.5 AGeV b=6fmSn @ 1.5 AGeV b=6fm
asysoft
Au+Au, 400AMeV asysoft
m*n>m*p
m*n<m*p
Inversion of elliptic flows with effective mass
<p
x(y)
>
<p
xp-n(y
)>
Sensitivity to SE: asy-stiff more flow of neutrons,
V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010)
Ell
ipti
c fl
ow
v2
But also to effective mass difference (i.e. momentum dep. of SE):Inversion of n/p potential at higher momentum
First measurement of isospin flow
Each band: soft vs. stiff eos of symmetric matter, (Cozma, 1102.2728) robust probe
Au+Au @ 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11))
directed flow (v1) not very sensitive,
but elliptic flow (v2), originates in compressed zone
determines a rather stiff symmetry energy, i.e.
=0.5=1.5
neutronprotonhydrogen
ASYEOS experiment at GSIMay 2011, being analyzed
also study t/3He flow!
1
1. „direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution
2. „secondary effects“: production of particles, isospin partners -,+, K0,+
NNK
K
NN N
in-medium in-elastic
K and potential (in-medium mass)
in-medium self-energies and width
potential ,
0,K, p, n
Particle production as probe of symmetry energy
Two limits:1. isobar model
(yield determined by CG-Coeff of ->N
2. chemical equilibrium
-> -/+ should be good probe!
2
2
2
Z
N
NZZ5
NZN5/
T
)(E8exp
T
)(2exp/ sympn
box calculation
Ferini et al.,
B.A.Li et al., PRL102
Therefore consider ratios -/+; K0/K+
G.Ferini et al.,PRL 97 (2006) 202301
stiffnessasywithdecrease
)(Y
)(Y
p
n,
,0
1. Mean field effect: Usym more repulsive for neutrons, and more for asystiff pre-equilibrium emission of neutron, reduction of asymmetry of residue
2. Threshold effect, in medium effective masses:
Canonical momenta have to be conserved. To convert to kinetic momenta, the self energies enter
In inelastic collisions, like nn->p-, the self-energies may change. Simple assumption about self energies of
Yield of particles depends on
Detailed analysis gives
Particle production as probe of symmetry energy (2)
Two effects:
stiffnessasywithincrease
)'f1)(f1(ff)f1)(f1(ff
)pppp()2()(vvdvdvdI
2'12121'2'1
'2'1213
inel12'2'12coll
Competing effects!- How taken into account in different calculations? - dynamics may be too simple.
thininel ss
Au+Au@1AGeV G.Ferini et al.,PRL 97 (2006) 202301
Central density
and K: production in high density phase
Pions: low and high density phase
Sensitivity to asy-stiffness
Dynamics of particle production (Dynamics of particle production (,K) in heavy ion collisions,K) in heavy ion collisions
time [fm/c]
Dependence of ratios on asy-stiffness: n/p ratio governs particle ratios
n/p 0,-/+,++
-/+ K0/K+
K0,+ multiplicity
and multiplicity
incr
easi
ng
sti
ffn
ess
Kaons were a decisive observable to determine the symmetric EOS;
perhaps also useful for SE?Kaons are closer to threshold, come only from high density, have large mean free path, small width:
Ratio of K+ yield in (Au+Au)/(C+C)
C. Fuchs et al., PRL 86(01)1974
MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09)MDI, x=1, very softNL, stiff Ferini, Gaitanos,.. NPA 762 (05)NLlinear=2, stiff Feng,… PLB 683 (10)SIII, very softsmall dep. on SE J. Hong, P.Danielewicz
FOPI, exp
Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459)
Widely differering results of transport calculations with similar input!
- -dynamics in medium (potential, widths, etc) largely unknown- threshold and mean field effects- pion potential: U=0 in most calculations. OK?- differences in simulations of collision term
G.Ferini et al.,PRL 97 (2006) 202301
132Sn+124Sn
Au+Au, 1 AGeV, central
Inclusive multiplicities
132Sn+124Sn
Nuclear matter (box calculation)
K
K 0
single ratios more sensitive
• enhanced in larger systems
- Stiffer asy-EOSlarger ratio! Opposite to mean field effect!- Kaons somewhat more sensitive than pions. esp. at low energies, close to threshold- Sensitivity reduced in finite nuclei due to evolution of asymmetry in collision
Kaon production in HIC
Comparision to FOPI data
(Ru+Ru)/(Zr+Zr)
equilibrium (box) calculations
finite nucleus calculations
Data (Fopi) X. Lopez, et al., PRC 75 (2007)
G. Ferini, et al., NPA762(2005) 147
mo
re a
sy-s
tiff
nes
s
+/- ratioB.A. Li, et al.
+/- ratio,Feng, et al.
Fermi Energy HIC, various observables, compilation MSU
Present constraints on the symmetry energy
Moving towards a determination of the symmetry energy in HIC
but at higher densitynon-consistent results of simulations for pion observables.
Au+Au, elliptic flow, FOPI
Limits on the EOS in -equilibrium,Including constraints from neutron stars and microscopic calc.
A. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871
Combined methods move towards stronger constraints
Summary and Outlook
• EOS of symmetric NM is now fairly well determined, but density (and momentum) dependence of the Symmetry Energy rather uncertain, but important for exotic nuclei, neutron stars and supernovae.
• Constraints from HIC both at sub-saturation (Fermi energy regime) and supra-saturation densities (relativistic collisions), and increasingly from neutron star observables.
• At subsaturation densities increasingly stringent (~1, L~60 MeV), but constraints are largely lacking at supra-saturation densities.
• Observables for the supra-saturation symmetry energy
N/Z of pre-equilibrium light clusters (MSU, FOPI),difference flows, (first hints -> ASYEOS)
part. production rations -/+ , K0/K+ (FOPI,HADES)
• More work to do, esp. In theory (consistency of transport codes, dynamics)
• Symmery energy important in the partonic phase or for the phase transition to the partonic phase? What is the SE in the partonic phase.
Thank you
Backup
Two models for medium effects tested:
1.Chiral perturbation (Kaplan, Nelson, et al.) (ChPT)
2.One-boson-exch. (Schaffner-Bielich, et al.,) (OBE)
density and isospin dependent
In-Medium K energy (k=0)
Test of kaon potentials models
ChPT
Ratios to minimze influence of eff kaon potentials
robust relative to K-potential, but dep.on isospin-dep part
ChPT
OBE
Splitting for K0,+
and NLand NL
Strangeness ratio : Infinite Nuclear Matter vs. HIC
Au≈0.2Au≈0.2
Au+Au@1AGeV (HIC)Au+Au@1AGeV (HIC)Au≈1.5Au≈1.5
NL→ DDF→NLρ→NLρδ : more neutron escape and more n→p transformation(less asymmetry in the source)
Density & asymmetry of the K-sourceDensity & asymmetry of the K-source
Inf. NM
G. Ferini, et al., NPA762(2005) 147
Pre-equilibrium emission (mainly of neutrons) reduced asymmetry of source for kaon production reduces sensitivity relative to equilibrium (box) calculation
asy-stiff
asy-soft
Light isobar 3H/3He yields
Observable very sensitive at high pObservable very sensitive at high pTT
to the mass splitting and to the mass splitting and notnot to the asy-stiffness to the asy-stiffness
197Au+197Au 600 AMeV
b=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≈1.7ρ0
n/p ratio yields
Pre-equilibrium nucleon and light cluster emission at higher energy
Differential elliptic flow
asystiff asysoft
m*n>m*p
m*n<m*p
Inversion of elliptic flows because of inversion of potentials with effective mass
W. Reisdorf, ECT*, May 09
Indication of experimental effect
Au+Au, 400 AMeV
t-3He pair similar but weaker
Au+Au, 600 AMeV
Elliptic flow more sensitive, since determined by particles that are emitted perp to the beam direction
V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010)
Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459)
Many attempts to understand behaviour:
Double ratio of Sn+Sn systems
Yong, et al.,PRC73,034603(06)
Sensitivity=Y(x=1)/Y(x=0)
Zhang, et al., PRC80,034616(09)
Possible causes:
- Pion are created via ‘s. dynamics in medium (potential, width, etc) largely unknown.
- Threshold and mean field effects
- Pion potential: U=0 in most calculations. OK?
- differences in simulations, esp. collision term
- Urgent problem to solve!!!
Transverse Pion Flows
FOPI: W.Reisdorf et al. NPA781 (2007) 459
Antiflow: decoupling of the pion/nucleon flowsOK general trend. but:- smaller flow for both - and +-not much dependent on Iso-EoS
IQMD softMD FOPI IQMD stiffMD
Au+Au
General behaviour (centrality dep.)
+
-
-
+
--
+
+
Simulations: V.Prassa, PhD Sept.07
Rapidity dependence
stiff
soft
asy-stiff
asy-soft
C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)
matt.nuclmatt.neutrsym EEE
Rel, BruecknerNonrel. BruecknerVariationalRel. Mean fieldChiral perturb.
The Nuclear Symmetry Energy in different „realistic“ models
The EOS of symmetric and pure neutron matter in different many-body aproaches
SE
asy-soft at0
(asystiff very similar)
n,pq
;k
U
k
m1
m
m1
q
2
*q
Isovector (Lane) potential: momentum dependence
)UU()k(U pn21
Lane
SE ist also momentum dependent p/n effective mass splitting
Why is symmetry energy so uncertain?? ->In-medium mass, and short range tensor correlations (B.A. Li, PRC81 (2010));
Neutron stars: a laboratory for the high-density symmetry energy
A normal NS (n,p,e)
… or exotic NS ??
Typical neutron stars
Neutron star mass dep. on Symmetry Energy
pro
ton
fra
ctio
n x
Onset of direct URCA (x>1/9)
Fast cooling of NS: direct URCA process
enep
Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802
Neutron star cooling: a test of the symmetry energy
A given symmetry energy behavior leads to a distribution of NS masses:
Comparison to mass distribution from population synthesis models (Popov et al., A&A 448 (2006)
plus other neutron star observables;consistency far from obvious
e.g. for DBHF EOS)
D. Blaschke, Compstar workshop, Caen, 10
Limits on the EoS from a Bayesian analysis of NS mass-Radius observationsA. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871
Comparison to models
many Skyrme models eliminated
Limits on the EOS in -equilibrium Limits on SE powerlaw
Lattimer, Lim, arxiv 1203.4286
Synthesis of constraints
..but measurement in very different density ranges!
Astrophysics: Supernovae and neutron stars
A normal NS (n,p,e)
or exotic NS?PSR J1614-2730
typical neutron stars
heaviest neutron star
Onset of direct URCA: Yp>.11;Too fast cooling
central density
Comparison to models
many Skyrme models eliminated
Limits on the EoS from a Bayesian analysis of NS mass-Radius observationsA. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871
Deconfinement Transition with Large Asymmetry
EOS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings
DiToro,et al.,, NPA775(2006)102-126
Quark:Fermi only
symmetricneutron
NLρ
NLρδGM3
1 AGeV
300 AMeV
132Sn+124Sn, semicentral
B1/4 =150 MeVHadronSymmetry energy