PROBING THE DENSITY DEPENDENCEPROBING THE DENSITY DEPENDENCE

OF SYMMETRY ENERGYOF SYMMETRY ENERGY

WITH HICWITH HIC

KITPC Workshop, Beijing, June09, ditoro@lns.infn.it

“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?