From the Phys.Dept. Jan.2002 Etna Double-Face, Aug.07

ISOSPIN DYNAMICS IN HEAVY ION COLLISIONSISOSPIN DYNAMICS IN HEAVY ION COLLISIONS

From Coulomb Barrier to DeconfinementFrom Coulomb Barrier to Deconfinement

V.Baran, M.Colonna, M.Di Toro, G.Ferini, Th. Gaitanos, V.Giordano, V. Greco, Liu Bo, F.Matera, M.Pfabe, S. Plumari, C.Rizzo, J.Rizzo, and H.H.Wolter

LNS-INFN and Phys.Astron.Dept. Catania, IFIN-HH Bucharest, IHEP Beijing, Univs. of Firenze,Giessen, Munich, Smith College …….and with the contribution of a very lively Etna mountain!

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

Oct.12, 2008

From the EtnaMelting Pot

Tentative Plan of the Talk(s)

1. “Nuclear Matter” Phase Diagram Symmetry Energy Isospin Equilibration Isospin Distillation Isospin as a Tracer of the Fragment Production Mechanism Heavy Ion Collisions at Intermediate Energies: Isospin Flows

2. Quantum-Hadro-Dynamics: EoS Effective Bosons, Self Energies, N-stars QHD: Fully Covariant Transport Linear Response, Elliptic Isospin Flows, Meson Production

3. Conclusion Looking for the Critical Point at High Baryon and Isospin density

Nuclear Matter Phase Diagram….updated

Liquid-Gas

Our Tentative “Path” with Heavy Ion Collisions: From Dilute (liquid-gas) to High Baryon and Isospin Density

(Landau school)

o o o ox x x x

N N ZZ

kF

Symmetric → Asymmetric

Fermi(T=0)

≈ εF/3 ~ ρ2/3

Interaction Two-body ~ ρ , many-body correlations?

Symmetry Energy

a4 term (~30MeV) of the Weiszäcker Mass Formula: at saturation Esym(Fermi) ≈ Esym(Interaction)

E/A (ρ) = E(ρ) + Esym(ρ)I²

I=(N-Z)/A

→ search for ~ ργ

but γ can be density dependent…→ momentum dependence? neutron/proton mass splitting

EOS of Symmetric and Neutron Matter

Dirac-BruecknerVariational+3-body(non-rel.)RMF(NL3)Density-Dependent couplingsChiral Perturbative

Ch.Fuchs, H.H.Wolter, WCI Final Report EPJA 30 (2006) 5-21

“earlier” disagreement

symmetric

AFDMCV8’+3bodyFantoni et al0807.5043

Role of n-body forces (n>3) at ρ>2ρ0?

Iso-Tracer (1): Isospin Transport and Chemical Potentials

IE

IEjj symsympn

)()(

IDDj

IDDjIppp

Innn

pnqI

D

D

T

qIq

TI

qq

,,

,

currents

diffusion

Diffusion Drift

drift

Isospin Transport (Equilibration, Distillation………..)→ Direct Access to Value and Slope of the Symmetry Energy at ρ !

Asy-soft

Asy-stiff

E/A (ρ) = E(ρ) + Esym(ρ)I²I=(N-Z)/A

Symmetry energy ρ-slope

IEsympn 4Isospin chemical potential

124Sn “asymmetry” = 0.2

Iso-Tracer (2): Symmetry Potentials and Effective Masses

neutron

proton

Nucleon emission; Flows….Asy-stiffAsy-soft

Lane Potentials

**pn mm

**pn mm

Density dependence Momentum dependence1

2

*

1

k

U

k

m

m

m qq

(Un-Up)/2I

Phys.Rep.410(2005)335-466

ρ0

Near Saturation Properties

SYMMETRY PRESSURE SHIFT of

SYMMETRICNUCLEAR MATTER

20

00 0

30

0

IK

L

ddP

PII

NM

sym

Psym

)(,0 IKI NM

d

dP

Central density of Heavy Exotic Nuclei ?

0)6()( 2 ILKIK symNM

Compressibility shift

Exotic Monopole?

2

0

0

0

04 183

BsymB

sym

KLaE

Expansion around

28-32MeV Slope Curvature

Stable nuclei:nucl-ex/0709.3132:Notre Dame-Osaka exp.GMR in 112-124Sn→ ∆K = -550±100 MeV→Very stiff : L ~ +100MeV!

L~3a4γ→γ≥1→n-skin thickness?

Saturation density shift

Esym ≈ (ρ/ρ0)γ

collcoll IfIhft

tprf

dt

tprdf

,

,,,,

fUm

ph

2

2fwfw )1(

gain loss

STOCHASTIC MEAN FIELD TRANSPORT EQUATION:VLASOV + NN-COLLISIONS and PAULI CORRELATIONS

Fluctuations

Self-Consistent Mean Field Equation of State

Baran, Colonna, Greco, DiToroPhys.Rep. 410 (2005) 335 (Relat. Extension)

Chomaz, Colonna, RandrupPhys.Rep. 389 (2004) 263 (Fermi Energies)

Fpp

F

F

pU

mp

pm

*

The Boltzmann-Nordheim-Vlasov equation with a non local potential

)()'(exp)2( 123

' rVrppird

pVp

The BNV equation becomes:

)()()( fIffUffUm

p

t

fcollprrp

V12(r) form factor: Yukawa……

local

npppnn CCCC

IBBBB

IAAAA

)(),(

),(

),(

0

2

0

22

2

2

1),(

),(),(),(

ppppg

ppgprfprfpdpdI

),(),(),( CCBBAAkin

GBD extensionCorrespondence to Skyrme parameters

MSU-RIA05/nucl-th/0505013, NPA 806 (2008) 79-104 (Isospin Equilibration)

I=0.2

Lane Potential (Un-Up)/2I

Momentum Dependence and Effective Masses: Fast Nucleon Emission

Skyrme-like parametrization

(Yukawa)

Coulomb Barrier

Symmetry Energy below Saturation: Fusion → Collective Charge Equilibration

212

2

1

1210 RR

Z

N

Z

N

A

ZZD

D(t) : bremss.

dipole radiation

Initial Dipole

Pre-equilibrium Dipole Radiation

Charge Equilibration Dynamics:Stochastic → Diffusion vs.Collective → Dipole Oscillations of the Di-nuclear System Fusion Dynamics

Cooling on the way to Fusion

CN: Statistical GDR

…tilting lighthouse!

32S + 100Mo (6 AMeV)

32S + 100Mo (9 AMeV)

D(t)

D(t)

Dk(

t)

D

k(t)

time(fm/c)

time(fm/c)

Pre-equilibrium dipole emission

D.Pierroutsakou et al. PRC71(2005)

SPIRALS → Collective Oscillations!

DK(t)

DK(t)

2''2

3

2

)(3

2

DA

NZ

Ec

e

dE

dP

Bremsstrahlung: Quantitative estimations

V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87(2001)

b=0, central

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

,

,

1)(

,

1)()()(

,,

,,

TDHF: C.Simenel, Ph.Chomaz, G.de France

D(t)

D(t)

D.Pierroutsakou et al., New Medea Exp. at LNS-Catania,

squares 36Ar + 96Zr

circles 40Ar + 92Zr(np)-bremsstrahlung-subtracted spectra at θγ=90o vs. Beam Axis

16AMeV Fusion events: same CN selection

Difference

36Ar + 96Zr

40Ar + 92Zr

Linearized spectra: divided by the no-GDRCN evaporation component

θγ-study of the extra-yield with MEDEA

B.Martin et al., PLB 664 (2008) 47

Dipole Angular Distribution of the Extra-Yield: Anisotropy!!

)](cos1[)( 220 PaWW

vs Beam Axis

a2 = -1→Pure Dipole oscillation along the Beam Axis→ ~ sin2θγ

a2 = -0.8

a2 = -0.5

Widening: rotation of the PromptDipole Axis vs the Beam Axis ↓Accurate Angular Distrib. Measure: Dipole Clock!

36Ar+96Zr vs. 40Ar+92Zr: 16AMeV Fusion events: same CN selection

B.Martin et al., PLB 664 (2008) 47

The “Monster” 132Sn Dynamical Dipole: Symmetry Energy10AMeV, b=4fm

Larger Yield (25%)ASYSOFT: Larger Centroid Energy Larger Width

PRC 79 (2009) 021603

Power Spectrum

Prompt Dipole Oscillations

Phase Space Correlations

Asy softAsy stiff

124

132

132

124

Present problems: Beam Intensities Low energy facilities

220

160

100

40fm/c

Density Plots on the Reaction Plane: Rotation of the Oscillation Axis vs the Beam Axis

Still emitting,..although damped

132Sn:The Monster DipoleCase

b=2fm

b=4fm

Weighted anisotropies:

Total AngularDistribution

PRC 79 (2009) 021603

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

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

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

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)

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

Non-equilibrium Effects in Fragmentation - IMF hierarchy vs. v┴ : Isospin Tracer

ISOSPIN: Tracer of a “Continuous” Series of Bifurcations →from multi- to neck-fragmentation up to PLF dynamical fission

124Sn+124Sn 50AMeV semicentral

low v ┴→ more PLF-correlated→Φ-plane ≈ 0 large N/Z Viola-violation larger masses

MULTI-MODALITY Fragmentation …….just in one shot

Histogram: no Viola-violation selection

Time Hierarchy: Early Formationvia fast Spinodal Mechanism forLight Fragments → Large vtransv

→ Low alignement → Low N/Z

Chimera data: see E.De Filippo, P.Russotto INPC-Tokyo, NPA 805 (2008)

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.

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

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!

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:

ρψψˆ:

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

DIRAC OPTICAL POTENTIAL

Dispersion relation 2220 smpE

22 mkm

mm

V ssopt02

02

0 2

1

sD

sDS

mm

mm

m

mm

*

0*

00

* )(1

Schrödinger mass

3

300

Sss

B

f

f

)()(),(*

*

30**

fE

mfmpnm

F

DBsymsDsymS

richnBnBpB ,03 upper signs: neutronAsymmetric Matter

),,,(

RMF

)()(

)()(**

**

pmnm

pmnm

SS

DD

Phys.Rep.410(2005)335-466, MSU-RIA05 nucl-th/0505013 AIP Conf. 791(2005)70-82

~50 MeV

1

2

*

1

k

U

k

m

m

m qq

Dirac mass

BEYOND RMF: k-dependence of the Self-Energies

'00

'0

** )()()( mmmm sssDS

Schroedinger mass

Asymmetric Matter

),(),,,( kff Bi

)(,)(

)()(

**

**

pmnm

but

pmnm

SS

DD

DBHF

0

0

'

0'0

d

dd

d

ss

High momentum saturation of the optical potential

High momentum increase of the Dirac Mass

Phys.Rep.410(2005)335-466, MSU-RIA05 nucl-th/0505013 AIP Conf. 791(2005)70-82

Problem still open……..sensitive observables

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

Local Mean Free Path Montecarlo Collision Procedure

- i,j collision candidates if TP

NNij N

d

- Collisional time:ijNNij

coll vvijt

1

)(

- Collision Probability)(

)(

ijt

timestept

collij

- Random choice of x in (0,1) → if accepted Then check Pauli Blocking

ijx

A.Bonasera et al. Phys.Rep. 243 (1994)

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

Au+Au 800 A MeV elliptic flows, semicentral

Rapidity selections

v2(n)

|y°| < 0.5

v2(n), v2(p) vs. p_tv2(p)

All rapidities

v2(n) v2(p)

Low p_t spectator contributions

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

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 /4exp/)(2exp

~ 5 (NLρ) to 10 (NLρδ)

asysoft

asystiff

-/+ increase around threshold for large asymmetries: FOPI data vs. transport models

vs. IBUU (B.A.Li)

vs. IQMD

W.Reisdorf et al. NPA781 (2007) 459

……not fully covariant approaches

The Threshold Puzzle

Au+Au 400 A MeV, semicentral: Pion production:Threshold effect

π-/π+ ratios vs. p_t, all rapidities

π-/π+ ratios vs. beam energy, inclusive

Sharp increase at low energy

Too large values:- Semicentral (less - abs.)?- Exp.filters?

Very softSymmetry Term!!Z.Xiao et alPRL 102 (2009)

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

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 BY

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

finite nucleus calculations

• sensitivity reduced in collisions of finite nuclei

• single ratios more sensitive

• enhanced in larger systems

• larger asymmetries

• more inclusive data H.Wolter, ECT* May 09

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.?

“Exotic Matter” in collisions of n-rich systems at few AGeV

Gibbs Conditions and Symmetry Repulsion at high density

132Sn and 238U “paths”

Signals from a Mixed Phase?

Isospin in Partonic Effective Lagrangians

ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS: - Earlier Deconfinement at High Baryon Density - Is the Critical Point affected?

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

Lower Boundary of the Binodal Surface vs. NM Asymmetry

NLHadron :

NLGM 3

vs. Bag-constant choice

Proton-fraction

symmetric

NPA775(2006)102-126

α = 1-2 Z/A

AGeVUU 1,238238 fmb 7,

Exotic matter over 10 fm/c ?

In a C.M. cell

NPA775(2006)102-126

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?

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

NJL Effective Lagrangian (two flavors): non perturbative ground state with q-qbar condensation

M.Buballa, Phys.Rep. 407 (2005)

0)]2([

;)]2([ 2

qGmi

LagrangeEuler

qqGqGmiqLNJL

1

1

03

3

]1/)[exp(),(

]1/)[exp(),(

)],(),(1[)2(

4

TETn

TETn

TnTnE

MpdNNmM

pp

pp

ppp

cf

p

Gap Equation

→ 1

→ 0

→ 1/2

→ 1/2

Large μ Large T 0or

Chiral restoration

M.Buballa, Phys.Rep. 407 (2005)

Parameters: Λp, G, m vs.Mπ, fπ, <qqbar> (estimation)

ρB=0 T=0

mu,d=5.5MeV

mu,d=0.0

NJL Phase Diagram

S.Plumari, Thesis 2009

Standard Parameters

● Coexistence◊ Spinodal

Isospin Extension of the NJL Effective Lagrangian (two flavors)

Mass (Gap) – Equation with two condensates

dduu

dujiGGmM

du

jiii

,

),(,44 21

02

01 )1(

GG

GG

α : flavor mixing parameter → α = ½ , NJL, Mu=Md α → 0 , small mixing, favored → physical η mass α → 1 , large mixing

M.Buballa, Phys.Rep. 407 (2005)

Quark Dynamics at High Baryon Density

)()1(44

)(44

00

00

duud

duuu

GGmM

GGmM

Neutron-rich matter at high baryon density:|Фd| decreases more rapidly due to the larger ρd

→ (Фu – Фd) < 0

**

**

1

0

npdu

npdu

MMMM

MMMM

α in the range 0.15 to 0.25……

Very n-rich matter: I=(N-Z)/A=0.4

Masses in the Chiral Phase

α =0.2

α =1

Solutions of the Iso-Gap Equation S.Plumari, Thesis 2009

Iso-NJL

m = 6MeVΛ = 590MeVG0Λ2=2.435→Mvac=400MeV<qbarq>=(-241.5MeV)3

mπ=140.2MeVfπ=92.6MeV

Symmetry Energy in the Chiral Phase: something is missing

….only kinetic contribution

Nuclear Matter Phase Diagram….

Every Complex Problem has a Simple Solution

…my journey is around here

….most of the time Wrong (Umberto Eco)

Conclusion:

Back-up Slides

Isospin Equilibration: Dynamical Dipole in Fusion Reactions

Esym(ρ) Sensitivity

Value (<ρ0)

Restoring Force → Centroid, Yield

Neutron Emission Reaction MechanismNN cross sections

Damping

Anisotropy

Linear Response

Dirac Eq. inWigner

formalism

Fermi-Dirac

distribution

npsnspdecomppx ,,,),(G . System of eq.s

4 4

Expansion at I° orderExpansion at I° orderCollective modesCollective modesperturbation

“zero sound” (VS >VF)

Asymmetric NM pn ≠ ρp/ρn

Longitudinal Wave

0),(ˆ)()()()(2

),(ˆ),(ˆ),(ˆ2

33

**

pxFxfxfxjfxjfi

pxFMpxFppxFi

iSS

iiiii

Two kinds of collective modesTwo kinds of collective modes:

I) Isoscalar : in phase pn)

II) Isovector : out of phase pn

K Esym

a

F

Fsym

S

F

F

FE

kE

FE

kK

0*

2

0*

2

16

13

Pomeranchuck stability conditionPomeranchuck stability condition

0),(

F

BSF EM

MkA

pnF NN ,2 = Density of states at kF

''

'0

0000 ,

qqqq

qqq

pnnpppnn

NF

FFFF

),(1

1

),(1

1

*2*

2*

000

*2*

2*

000

MkAfE

MffNFFF

MkAfE

MffNFFF

FFF

npnna

FSFSVF

npnnS

Landau Fermi liquid response

Relativistic Dispersion Relation in SNM

Isovector

F

S

v

vs

Lindhard function

K Esym

Isoscalar

0)(193

1 2*

*2

*2

*

s

E

Mf

E

kfK

k

E

FS

F

FB

potNM

F

F

0)(12

161 2*

*2

*42

*

s

E

Mf

E

kfa

k

E

FS

F

FB

pot

F

F

0

0*

AEMfEF

smaller M* larger f

same monopole if larger KNM

larger flarger f

same a4 but reduced dipole frequency

1

1ln

2

11)(

s

ss

NLρδ

NLρ

Liquid-gas Phase TransitionIn Asymmetric Matter:Isospin Distillation

Instability region(T=0)

“Dilute” response not muchaffected by the δ-meson

but effects at high densities….