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Transcript of PROBING THE DENSITY DEPENDENCE OF SYMMETRY ENERGY WITH HIC KITPC Workshop, Beijing, June09,...
PROBING THE DENSITY DEPENDENCEPROBING THE DENSITY DEPENDENCE
OF SYMMETRY ENERGYOF SYMMETRY ENERGY
WITH HICWITH HIC
KITPC Workshop, Beijing, June09, [email protected]
“Recent Progress and New Challenges in Isospin Physics with HIC” Bao-An Li, Lie-Wen Chen, Che Ming Ko Phys. Rep. 464 (2008) 113
“Reaction Dynamics with Exotic Nuclei” V. Baran, M. Colonna, V. Greco, M. Di Toro Phys. Rep. 410 (2005) 335 (Relat. Extension)
High density (Intermediate energies):Isospin effects on- fragment production in central collisions-“squeeze-out” nucleons and clusters- meson production
lack of data, but….SAMURAI at RIKEN CHIMERA+LAND at GSI Cooling Storage Ring at Lanzhou
Signals of Deconfinement?
Symmetry Energy Effects:124Sn+112Sn on Isospin Equilibration (132Sn?)124Sn+124Sn and 112Sn+112Sn on Isospin Distillation124Sn+64Ni on Neck Fragmentation58Fe+58Ni on Balance Energy197Au+197Au on Elliptic Flows
…..more RIB data are very welcome!
Imbalance Ratios: Isospin Equilibration at Fermi Energies
Esym(ρ) Sensitivity: asymmetry gradients
Isospin Diffusion
Asy-soft more effective
Value below ρ0
Interaction time selection→Centrality(?), Kinetic Energy Loss
Caution: Disentangle isoscalar and isovector effects!
(Overdamped Dipole Oscillation)
Rami imbalance ratio:
)()(
)()(2
BBAA
BBAAABR
ISOSPIN EFFECTS IN REACTIONS
Mass(A) ~ Mass(B) ; N/Z(A) = N/Z(B)
A dominance
mixing
B dominance
+1
0
-1
...,,,),(3
dY
dN
He
t
Z
NIsospin observables: isoscaling
vs. Centrality (fixed y)
vs. Rapidity (fixed centrality)
vs. Transverse momentum (fixed y, centrality)
b=8f
mb=
10fm
M : 124Sn + 112Sn
H: 124Sn + 124Sn
L: 112Sn + 112Sn
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
PII
III2R;
II
III2R
@ 35, 50 Mev/A
Smaller R values for: Asy-soft MI interaction Lower beam energy 50 AMeV
35 AMeV
I = (N-Z)/Aof PLF or TLF
B. Tsang et al. PRL 92 (2004) Isospin equilibration: Imbalance ratiosIsospin equilibration: Imbalance ratios
SMF simulations
J.Rizzo et al. NPA806 (2008) 79
Mom. Independent-asystiff ≈ Mom. Dependent-asysoft:Compensation of isoscalar/isovector effects
Imbalance ratios: isoscalar vs. isovector effectsImbalance ratios: isoscalar vs. isovector effects
If:
β = I = (N-Z)/A
τ symmetry energy
tcontact dissipation
Kinetic energy loss - or PLF(TLF) velocity - as a measure of dissipation (time of contact)
R dependent only on the isovector part of the interaction !
Overdamped dipole oscillation
Fragment ProductionStochastic mean field (SMF) calculations
b = 4 fm b = 6 fm
Sn124 + Sn124, E/A = 50 MeV/A
Central collisions
Ni + Au, E/A = 45 MeV/A
(fluctuations projected on ordinary space)
Isospin Distillation + Radial Flow Isospin Migration + Alignement
Semi-Central
Multifragmentation at the Fermi Energies
Esym(ρ) Sensitivity: expansion phase, dilute matter
Isospin Distillation + Radial Flow
Asy-soft more effective
Low Density Slope Value: Symmetry Potentials
Asy-soft: compensationN-repulsion vs Z-coulomb→Flat N/Z vs kinetic energy
Isospin Distillation Mechanism:Isospin Distillation Mechanism:““direction” of the direction” of the spinodal spinodal unstable modeunstable mode
! SYME
~
y = proton fraction =Z/A
p
n
p
n
pn
Reduced N/Z of bulkSpinodal fragments inn-rich central collisions:Asysoft more effective(Isospin Distillation)
PRL86 (2001) 4492
Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132E/A = 50 MeV, b=2 fm
1200 events for each reaction
Liquid phase: n-depletion Gas phase: n-enrichement
ISOSPIN DISTILLATION
Asy-soft
Asy-stiff
112,112 112,124 124,124With Asy-stiff in the (112,112) case:- N/Z (gas) below bisectrix- N/Z (gas) < N/Z (liquid) → large proton emission
M.Colonna et al., INPC-Tokyo , NPA 805 (2008)
Asy-soft
Asy-stiff
ASY-SOFT MORE EFFECTIVE
New Observables:
N/Z vs fragment energy
N = Σi Ni , Z = Σi Zi
1.64
Double ratio = (N/Z)2/(N/Z)1
3≤ Zi ≤ 10
Asy-stiff Asy-soft
neutron repulsion
Coulomb p-repulsion
Iso-distillation
Symmetry p-compensation
Proton/neutron repulsion:* n-rich clusters emitted at larger energy in n-rich systems (Δ’>Δ)* flat spectra with Asy-softΔ’
Δ
Isospin content of IMF in central collisions
Isospin Distillation (spinodal mechanism)+ Radial Flow+ Symmetry Potentials
Primary fragment properties
M.Colonna et al., PRC 78 (2008)
N/Z:
Neck-fragmentation at the Fermi Energies
Esym(ρ) Sensitivity: density gradient around normal density
Isospin Migration + Hierarchy
Asy-stiff more effective
Slope just below ρ0IMF Mass, N/Z vs alignement/vtransverse:→ time sequence of mechanisms:Spinodal → neck instabilities→ fast fission→ cluster evaporation
124Sn+ 124Sn 50 AMeV: average asymmetry
Asy-stiff:neutron enrichmentof neck IMFs
Asy-soft
Semi-peripheral collisions
Isospin migration
V.Baran et al., NPA703(2002)603NPA730(2004)329
gas
gas
liquid
liquid
NECK FRAGMENTS: Vz-Vx CORRELATIONS
PLFIMF
TLF
Large dispersion along transversal direction, vx → time hierarchy ?
124Sn + 64Ni 35 AMeV
<0
>0
Alignement +centroid at 0 plane
Clear Dynamical Signatures !
Deviations from Violasystematics
vs. 4 CHIMERA data
E.De Filippo et al. (Chimera Coll.) PRC 71 (2005)
Si
CsI(Tl)
Beam
1m
1°
30°
176°
•good angular resolution
•identification in mass/charge of the detected particles
•low detection threshold
The 4 CHIMERA detector
TARGET
Forward part
1°
30°
2003 - CHIMERA-ISOSPIN 1192 telescopes
p
t
d
4He6He
3He
LiH.I.
E-TOF E-TOF M,E E-E E-E Z,E
PSD LCP
176°
124Sn + 64Ni 35 AMeV:CHIMERA data
vs. particle multiplicity (centrality)
TLF
PLF
cosθprox>0.8 cosθprox<0.8
Alignement IMF-PLF/TLFvs PLF-TLF
Semicentral (M=7)v// selection of the 3highest Z fragments:1: PLF2: TLF3: Neck source
Neutron enrichement for the largest Viola deviationsand the highest degree of alignement : Stiff Symmetry Energy
Intermediate Energies
1. Relativistic Kinematics but not fully covariant transport equations
Multifragmentation at High Energies
Esym(ρ) Sensitivity: compression phase
Isospin Distillation + Radial Flow
Asy-stiff more effective
High Density Slope Value: Symmetry Potentials
Larger N-repulsion with Asy-stiff
Problem: large radial flow → few heavier clusters survive, with memory of the high density phase
ASYSOFT
ASYSTIFF
KINETIC (FERMI)
Low density clustering: spinodal mechanism
Asysoft: more symmetric clusters, larger neutron distillationcombined to a larger pre-eq neutron emission
High density clustering: few-body correlations and p.s. coalescence
Asystiff: more symmetric clusters, combined to a larger fast neutron emission
The Isospin “Ballet” in Multifragmentation
Esym (ρ)
ρρ0
Global fit to experimental charge distributions
E.Santini et al., NPA756(2005)468
Fragment Formation in Central Collisions at Relativistic Energies
Au+Au, Zr+Zr, Ni+Ni at 400 AMeV Central Stochastic RBUU + Phase Space Coalescence
Size dependence: the lightest is the hottest?
No but
Fast clusterization in the high density phase
Time-evolution of fragment Time-evolution of fragment formationformation
(E. Santini et al., NPA756(2005)468)Au+Au 0.4 AGeV Central
Z=3,4
Heavier fragments: “relics” of the high density phase
Isospin Content vs. Symmetry Term ?
Fast clusterization in the high density phase
Stochastic RBUU + Phase Space Coalescence
Isospin content of Fast Nucleon/Cluster emission, Isospin Flows
Esym(ρ) Sensitivity: stiffness, and….
Neutron/Proton Effective Mass Splitting
High p_t selections: - source at higher density - squeeze-out - high kinetic energies
vs. ptransverse
mid-rapidity|y0|<0.3(squeeze-out)
vs. kineticenergy(all rapidities)
Particle ratioV.Giordano, ECT* May 09
Crossing of the symmetrypotentials fora matter at ρ≈1.7ρ0
Collective flowsIn-plane Out-of-plane
yyx
yxt pp
pppy
22
22
2 ),(V
ytxt pppyV /),(1
tn
tp
tnp pVpVpV 111 )(V)(V)(V n
2p2
n-p2 ttt ppp
X
Z
y = rapiditypt = transverse momentum
= 1 full outV2 = 0 spherical = + 1 full in
Flow Difference vs.Differential flows)(1),(1
),(1
),(
pn
pyvZN
pyv
i
tiitalDifferenti
+ : isospin fractionation-- : missed neutrons, smaller
V1
vs. y V2
vs pt
Transverse flow:
A probe for mean field behaviour, i.e. for EOS
impact parameter b
y/ybeam
<px>
Transverse flow
flow
antiflow
Beam energy dependence:
balance energy
Elliptic flow
Evolution with impact parameter and energy
inversion of pattern: squeeze out
J.Lukasic et al.PLB 606 (2005)
MeV
fm
Elliptic Flow vs Y/Y0
m*n>m*p
m*n<m*p
Elliptic Flow vs Pt
Dominance of mass splittingat high pt
Elliptic proton-neutron flow difference vs pt at mid-rapidity
Au+Au 400AMeV Semicentral
+ relativistic Lorentz force…..(vector charged meson)
Neutron and Z=1 Elliptic Flows from FOPI-LAND Data at SIS-GSI: Au+Au 400 AMeVW.Trautmann ECT*, May 11 2009
pt dependence, various centralities and rapidities
Esym~ Esym(fermi) + ργ
No Mom.Dep.
Q. Li
Elliptic Flow vs Y/Y0
Increasingrelevance ofmass splitting
m*n>m*p
m*n<m*p
Large rapiditiesnot much affected
Elliptic Flow vs Pt
Cluster Elliptic Flow vs Y/Y0
Larger flows (collective energy)and lessIsospin effects
Hunting isospin with v2 : the mass 3 pair
A small gradual change inThe difference 3H-3He whenRaising the beam energy forAu+Au (N/Z = 1.5)
W.Reisdorf, ECT* May 09: FOPI 3H-3He V2 Results Au+Au with increasing beam energy
Relativistic Lorentz effect?
differential elliptic flowQ.F. Li and P. Russotto
inversion of neutronand hydrogen flows
UrQMD vs. FOPI data:Au+Au @ 400 A MeV
stiff
soft
squeeze-out moresensitive than thedirected flow
Early FOPI data (Y. Leifels) and ASY_EOS Collaboration:
5.5 – 7.5 fm
H.WolterECT* May 09
Relativistic Energies
Compressed Baryon Matter
Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF)
Covariant Mean Field Dynamics
Phys.Rep.410(2005)335-466
Mean FieldsEffective Masses In-medium cross sections
Self-Energies, Form factors: “Dressed Hadrons”
Au+Au 1AGeV central: Phase Space Evolution in a CM cellAu+Au 1AGeV central: Phase Space Evolution in a CM cell
Testing EoS→CBM
K production
scattering nuclear interaction from meson exchange: main channels (plus correlations)
Isoscalar Isovector
Attraction & Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ:
ρ̂ψψˆ:
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
2
1ˆˆ4
1ˆˆˆ2
1ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space !
Esym= kin. + (vector) – ( scalar)
a4=Esym fixes (ff)
DBHF DHF
f2.0 2.5 fm2
*
BF
Fsym E
Mff
E
kE
2
*
*
2*
2
2
1
6
1
No f 1.5 fFREE
f2.5 fm2 f 5f
FREE
Liu Bo et al., PRC65(2002)045201
RMF Symmetry Energy: the δ - mechanism
28÷36 MeV
NL
NLρ
NLρδ
Constant Coupling Expectations
2
,
,,
m
gf
N
N-STARS: Present status with observation constraints
D.Page, S.Reddy, astro-ph/0608360, Ann.Rev.Nucl.Part.Sci. 56 (2006) 327
Softer EOS→smaller R (larger ρ-central), smaller maximum Mass
“The broad range of predicted radii for nucleon EOS will be narrowed inthe near future owing toneutron-skin thickness andprobably also to heavy-ion experiments”
GeneralRelativity
cddP
2/1
AAAAAA
Proton fraction, y=Z/A, fixed by Esym(ρ) at high baryon density:
β-equilibrium
3/12, )3()21)((4 yPyE eFsympne
Charge neutrality, ρe=ρp=yρ
Fast cooling: Direct URCA process
enep
Fermi momenta matching
3/12,
,
3/12,,
])1(3[
/
)3(
yP
PckTP
yPP
nF
nF
pFeF
e
9
1)1(23 DUDUDU yyy
Neutron Star (npeμ) properties
Direct URCA threshold
Mass/Radius relation
NLρ
NLρδ
NLρδ
NLρ
DD-F
DD-F
compact stars & heavy ion dataT.Klaehn et al. PRC 74 (2006) 035802
- Transition to quark matter?- Faster Cooling for Heavier NS?
Self-Energies: kinetic momenta and (Dirac) effective masses
isi
iii
Mm
kk
,*
*
3
3
),(
)(),(
jfjfpn
ffpn sss
Upper sign: n
np jjj ),(),(),( 3
2*20iii mkM
Dirac dispersion relation: single particle energies
Chemical Potentials (zero temp.)
32*2
BBiFi ffmk
richnBnBpB ,03
n-rich:- Neutrons see a more repulsive vector field, increasing with fρ and isospin density- m*(n)<m*(p)
fkinE Bsympn 2)(4
asymmetry parameter
RBUU transport equation
Collision term:
collprr IfUfm
p
t
f
Wigner transform ∩ Dirac + Fields Equation Relativistic Vlasov Equation + Collision Term…
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean field
isi
iii
Mm
kk
,*
*
F
“Lorentz Force”→ Vector Fields pure relativistic term
testAN
iii ppgxxgdpxf
1
))(())((),(
Relativistic Landau Vlasov Propagation
Discretization of f(x,p*)Discretization of f(x,p*) Test particles represented by covariant Test particles represented by covariant Gaussians in xp-space Gaussians in xp-spaceDiscretization of f(x,p*)Discretization of f(x,p*) Test particles represented by covariant Test particles represented by covariant Gaussians in xp-space Gaussians in xp-space
→ → RelativisticRelativistic Equations of motion for x Equations of motion for x and p* and p* for centroids of for centroids of GaussiansGaussians→ → RelativisticRelativistic Equations of motion for x Equations of motion for x and p* and p* for centroids of for centroids of GaussiansGaussians
Test-particle 4-velocity → Relativity: - momentum dependence always included due to the Lorentz term - E*/M* boosting of the vector contributions
u
Fu
Collision Term: local Montecarlo Algorithm imposing an average Mean Free Path plus Pauli Blocking → in medium reduced Cross Sections
C. Fuchs, H.H. Wolter, Nucl. Phys. A589 (1995) 732
Isospin Flows at Relativistic Energies
Esym(ρ): Sensitivity to the Covariant Structure
Enhancement of the Isovector-vector contribution via the Lorentz Force
High p_t selections: source at higher density → Symmetry Energy at 3-4ρ0
Elliptic flow Elliptic flow DifferenceDifference
Difference at high pt first stage
approximations
potsym
F
EE
Mff
Bρ
42
0.3<Y/Yproj<0.8
132Sn+132Sn, 1.5AGeV, b=6fm: NL- NL-( +
High pt neutrons are emitted “earlier”
Dynamical boosting of thevector contribution
V.Greco et al., PLB562(2003)215
Equilibrium (ρ,δ) dynamically broken:Importance of the covariant structure
Meson Production at Relativistic Energies: -/ +, K 0/K +
Esym(ρ): Sensitivity to the Covariant Structure
Self-energy rearrangement in the inelastic vertices withdifferent isospin structure → large effects around the thresholds
High p_t selections: source at higher density → Symmetry Energy at 3-4ρ0
PION PRODUCTION
Main mechanism NNNN
.1
NLNLNLdecreaseY
Y
p
n
:)(
)(,
,0
2. Fast neutron emission: “mean field effect”
1. C.M. energy available: “threshold effect”
Vector self energy more repulsive for neutrons and more attractive for protons
Some compensationin “open” systems, HIC,but “threshold effect” more effective, in particular at lowenergies
n→p “transformation”
nn
n0
n- p-
p+n++
n+ p+
pp
p-
3*,, BBpnpn ffE
NLsNLsNLs
NLsNLsNLs
pppppp
nnnnnn
π(-) enhanced
π(+) reduced
G.Ferini et al., NPA 762 (2005) 147, NM Box PRL 97 (2006) 202301, HIC
No evidence of Chemical Equilibrium!!
The Threshold Effect: nn→pΔ- vs pp→nΔ++ The Threshold Effect: nn→pΔ- vs pp→nΔ++
pp→nΔ++
nn→pΔ-
20*4 nnin Es
200 )()()()( sspth mppms
200 )()()()( ssnth mnnms
20*4 ppin Es Compensation of Isospin Effects
Almost same thresholds → the sin(NN) rules the relative yields → very important at low energies
increasenear threshold
Pion/Kaon production in “open” system: Au+Au 1AGeV, central
Pions: large freeze-out, compensation
Kaons:- early production: high density phase- isovector channel effects → but mostly coming from second step collisions… → reduced asymmetry of the sourceG.Ferini et al.,PRL 97 (2006) 202301
Au+Au central: Pi and K yield ratios vs. beam energy
Pions: less sensitivity ~10%, but larger yields
K-potentials:similar effectson K0, K+
Kaons:~15% difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
G.Ferini et al.,PRL 97 (2006) 202301
132Sn+124Sn
Soft ESoft Esymsym
stiff Estiff Esymsym
Equilibrium Pion Production : Nuclear Matter Box Results → Chemical Equilibrium
Density and temperature like in Au+Au 1AGeV at max.compression (ρ~2ρ0, T~50MeV)
vs.asymmetry
Larger isospin effects: - no neutron escape
- Δ’s in chemical equilibrium, less n-p “transformation”
NPA762(2005) 147
TfT Bpn /2exp/)(exp
~ 5 (NLρ) to 10 (NLρδ)
Kaon production in “open” system: Au+Au 1AGeV, central Main Channels
K0 vs K+:opposite contribution of the δ-coupling….but second steps
NN BYK
---------
N BYK
BYK
N YK
YK
Au+Au 1AGeV: density and isospin of the Kaon source
n,p at High density
n/p at High density
Drop:Contribution of fast neutron emission andInelastic channels: n→p transformation
Time interval of Kaon production
“central”density
Nuclear Matter Box Results
Density and temperature like in Au+Au 1AGeV at max.compression
vs.asymmetry
Larger isospin effects: - no neutron escape - Δ’s in chemical equilibrium→less n-p “transformation”
NPA762(2005) 147
Kaon ratios: comparison with experimentKaon ratios: comparison with experiment
G. Ferini, et al., NPA 762 (2005) and PRL 97 (2006)
Data (Fopi)
X. Lopez, et al. (FOPI), PRC 75 (2007)
Comparision to FOPI data
(Ru+Ru)/(Zr+Zr)
equilibrium (box) calculations
• sensitivity reduced in collisions of finite nuclei
• single ratios more sensitive
• enhanced in larger systems
• larger asymmetries
• more inclusive data
Open system(reaction) calculations
GasLiquid
Density
Big Bang T
empe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
Heavy
Ion
1: nuclei 5?
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin ?
Mixed PhaseIn terrestrialLabs.?
ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS: - Earlier Deconfinement at High Baryon Density - Is the Critical Point affected?
AGeVUU 1,238238 fmb 7,
Exotic matter over 10 fm/c ?
In a C.M. cell
NPA775(2006)102-126
EoS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings
Symmetry energies
hadron
Quark:Fermi only
symmetric
neutron
Testing deconfinement with RIB’s?
(T,) binodal surface
Hadron-RMF
Quark-Bag model
(two flavors)
trans onset of the mixed phase → decreases with asymmetry
Signatures?
DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126
),,(),,(
(....)(....)
),,(),,(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
QH
QB
HBB
333 )1(
)1(
Mixed Phase →
NLρ
NLρδGM3
1 AGeV
300 AMeV
132Sn+124Sn, semicentral
B1/4 =150 MeV
Liu Bo, M.D.T., V.Greco May 09
Mixed Phase: Boundary Shiftsat Low Temperature
Lower Boundary muchaffected by the Symmetry Energy
Liu Bo, M.D.T., V.Greco May 09
mu=md=5.5MeV
Χ=0.0Χ=1.0
Critical Point for Symmetric Matter?
π-production is softening the hadron phase ?
LowerΧ=0.0
UpperΧ=1.0
Symmetric to Asymmetric (not Exotic) Matter
lower
upper
upper
lower
NLρδ :more repulsive high densitySymmetry EnergyIn the hadron phase
Dependence on theHigh Density Hadron EoS
Long way to reach 20% quark matter, but…
Isospin Asymmetry in the Quark Phase: large Isospin Distillation near the Lower Border?
20%
0.2
lower upper
Signatures? Neutron migration to the quark clusters (instead of a fast emission)
→ Symmetry Energy in the Quark Phase?
χ
Nuclear Matter Phase Diagram….
Every Complex Problem has a Simple Solution
…my journey is around here
….most of the time Wrong (Umberto Eco)
Conclusion:
Points for this week, June 15-19, discussions
Status of Esym(ρ); new suggestions?
Isoscalar vs. Isovector effects on the Reaction Dynamics
Esym(ρ) at high density: N-Stars, Deconfinement….
Microscopic DFT inputs?