M.Di Toro, ECT*/Eurisol Jan.06, ditoro@lns.infn.it

Isospin Dynamics in Heavy Ion Collisions at Fermi Energies: EOS-sensitive Observables

Dissipative Collisions

Isospin Distillation

Neck Fragmentation

Isospin Transport

n,p collective flows

Lane Potential, E-slope

Mean FieldEffective Masses Transport Dynamics In-medium cross sections

HIC probing: - different densities - high momenta - covariant structure

Why EOS?

EOS of Symmetric and Neutron Matter

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

Ch.Fuchs, WCI Final Report 2006

GasLiquid

Density

Big Bang T

empe

ratu

re

2020

0 M

eV Plasma

of Quarks and

Gluons Crab nebula July

5, 1054

Collisions

Heavy

Ion

1: nuclei 5?

Phases of Nuclear Matter

Neutron Stars

Philippe Chomaz artistic view

...)()()(),( 42 IOIEEIE BsymBB pn

pnI

0

2

2

2

1

I

sym I

EE

Symmetry Energy

2

0

0

0

04 183

BsymB

sym

KLaE

0

0

2

220

00

9

33

B

B

B

symsym

symB

sym

EK

PE

LEsy

m

M

eV)

1 2 30

Expansion around

Pressure & compressibilityAsy

-stiff

Asy-soft

Pressure gradient sym

sym KLd

dP

9

1

3

2

Phys.Rep.410(2005)335-466

Asy-su

persti

ff

SLOPE OF THE SYMMETRY TERM

SYMMETRY PRESSURE SHIFT of

SYMMETRICNUCLEAR MATTER

20

00 0

30

0

IK

L

ddP

PII

NM

sym

Psym

I0

d

dP

Central density of Heavy Nuclei ?

0)6()( 2 ILKIK symNM

Compressibility shift

Exotic Monopole?

124Sn “asymmetry” = 0.2

Symmetry part of the mean field

neutron

proton

Nucleon emission; Flows….

Asy-superstiffAsy-stiffAsy-soft

Lane Potentials

124Sn “asymmetry” = 0.2

neutron-proton chemical potentials

neutron

protonbulk

neck

IEsympn 4

at equilibrium…

Isospin Transport and Chemical Potentials

IE

IEjj symsympn

)()(

currents

diffusion coeffs.

Diffusion DriftAsy-superstiffAsy-soft

-Isospin Distillation-Isospin Equilibration

EFFECTIVE MASS SPLITTING: SKYRME FORCES

pnq

ggmm qq

,

2111*

**pn mm

**pn mm

112222 21214

1xtxtg

02 gn-rich matter

02 g

2.0

pn

pnI

1

2

*

1

k

U

k

m

m

m qq

n-rich matter

SKYRME LANE POTENTIAL

;, 21 EggmU qqMD ;2

1 Iq

.

;

p

n

Egm

ggmCI

UUF

pn2

02100 212

7

3

2

2

E-slope same sign of 2g

)

23( 0

4

Ca F

Phys.Rep.410(2005), nucl-th/0505013 (MSU-RIA)

low energy crossing

Spinodal instabilities are directly connected to first-order phase transitions and phase co-existence:a good candidate as fragmentationmechanism

Nuclear matter phase diagram: Liquid-Gas Transition

V A way to test thelow-density behaviourof the symmetry energy

0N

F

N

F

N

F1

N

F1np

n

pn0

p

np02

nn

nn02

pp

pp0

F = Free energy density

Instability ConditionInstability Condition

0,,

PT

p

yT y

P

Mechanical Chemical

X u2+Y v2 < 0X<0 isoscalar-likeY<0 isovector-like

u= cos p+sen n

v= cos p-sen n

)F(1N)F(1N

FNFN2tg pp

0nnn0p

np0p

pn0n

n = p

X Y= 0)1( ,,

2

22

PT

p

yT

np

y

P

y

NN

F 03 rd

p

n

p

n

Chemicaleffect

0N

F

N

F

N

F1

N

F1np

n

pn0

p

np02

nn

nn02

pp

pp0

F = Free energy density

Instability ConditionInstability Condition

0,,

PT

p

yT y

P

Mechanical Chemical

X u2+Y v2 < 0X<0 isoscalar-likeY<0 isovector-like

u= cos p+sen n

v= cos p-sen n

)F(1N)F(1N

FNFN2tg pp

0nnn0p

np0p

pn0n

n = p

X Y= 0)1( ,,

2

22

PT

p

yT

np

y

P

y

NN

F 03 rd

p

n

p

n

Chemicaleffect

PRL86 (2001) 4492

Multifragmentation: Instabilities of binary systems

y: proton fraction

X<0

Y>0

X=

1+

Fs ,

Y

=1+

Fa

attractive int.0Fnp0

0

0

,

,

PT

p

yT

y

P

X<0

In Symmetric NM

PT

p

yT

yY

PX

,

,

0P chem

ical

UNIQUE INSTABILITY: isoscalar-like

PRL86 (2001) 4492

Instability Region: just from 40 a !!

Isospin Distillation Mechanism:Isospin Distillation Mechanism:““direction” of the spinodal unstable modedirection” of the spinodal unstable mode

! SYME

~

y = proton fraction =Z/A

p

n

p

n

pn

STOCHASTIC MEAN-FIELD TRANSPORT APPROACH

VLASOV + COLLISION and PAULI CORRELATIONS

collcoll IfIhft

tprf

dt

tprdf

,

,,,,

fUm

ph

2

2

,ff

fwfw )1(

22 )( f

)(2)(

2 22

tDtdt

d

wwt

1)(

wfwftD )1()(2

)1()()( eqeqeqeq fftDt

,0I )'()(2)'()( tttDtItI

ff 122 22

)(

2

tdt

d

FLUCTUATIONS

2Equilibrium in aphase space cell

OK iftot. number of collisions

Initial: 02 any time ff 12

FLUCT.-DISS. THEOREM

gain loss

Markov

2

NPA 642 (1998)

Fusion - Deep Inelastic Competition

E= 30 AMeV , b=0.45 bmax

46Ar + 64Ni (1.55) (1.29)

n-rich

46V + 64Ge

n-poor

M. Colonna et al., PRC57 (1998)

Asy-soft

Asy-stiff

Asy-soft

Asy-stiff

More fast proton emission

Asy-soft more attractive

Asy-stiff more attractive

Isospin Effect on Dissipation at lower energies

Asy-soft Asy-stiff

tfm/c

Neutron-rich system:124Sn+64Ni semicentral

E=10AMeV

Asy-soft more repulsive

Interaction region below normal density:Sensitive to E_sym(ρ) atρ<ρ_0 and not to cross sections

Opposite with respect to the Fermi Energies

M.Colonna for Spiral2 proposals 2005

b = 2 fm b = 4 fm b = 6 fm

124Sn+ 124Sn, E/A = 50 MeV/A

Stochastic mean field (SMF) “fragmentation events”

Freeze-outconfigurations

Time-scale matching:Instability growth vs Interaction time

t fm/c

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

VELOCITY CORRELATIONS: DEVIATIONS FROM VIOLA SYSTEMATICS

r - ratio of the observed PLF-IMF relative velocity to the

corresponding Coulomb velocity;

r1- the same ratio for the pair TLF-IMF

The IMF is weakly correlated with both PLF and TLF

Wilczynski-2 plot !

V.Baran et al. NPA 730 (2004)

Fragment clock

REDUCED VELOCITY PLOTS: REDUCED VELOCITY PLOTS:

BNV

V. Baran et al. Nucl. Phys A730 (2004) 329

Note: stochastic BNV model accounts only for the “prompt” component of IMF’s

E.De Filippo et al. (Chimera Coll.) PRC71(2005)044602 and 064604

Chimera 124Sn+64Ni 35AMeV data, same E_loss selections

Gating the reduced plot for light IMFs:Gating the reduced plot for light IMFs:

E.De Filippo et al. (Chimera Coll.) PRC71(2005)044602 and 064604

Alignement

Angular distributions: alignment characteristicsAngular distributions: alignment characteristics

plane is the angle, projected into the reaction plane, between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Out-of-plane angular distributions for the “dynamical” (gate II) and “statistical” (gate I) components

E.De Filippo et al. (Chimera Coll.) PRC71(2005)044602 and 064604

Relatively large alignement even for the “statistical” cut

N

= 0.95 Z=1Z=3Z=2

Z=5 Z=7Z=6

Z=8

Z=4

Z=9lnR

21NECK ISOSCALING

NiSn

NiSn58112

64124

at 35 MeV/n

(b=6,7,8fm)

asysoft asystiff superasystiff 0.69 0.95 1.10

V. Baran, M. Colonna, M. Di Toro : NPA 370 (2004) 329

Increasing slope with Z?

Neck-frag. Iso-migration:heavier fragments moreneutron rich!

Fine structure of mid-rapidity fragments

Fe + Fe, Ni + Ni @ 47 AMeV IMF’s propertiesvs. alignement

~ N/Z

Mass-alignementcorrelation:reaction mechanism,not Iso-EOS dependent

N/Z-alignementcorrelation:iso-migration, Iso-EOS dependent

even for Ni+Ni !

R.Lionti et al., PLB625 (2005) 33

Cou

nts

asy-stiff

asy-soft

0<A<10

IMF hierarchy effects in v_tra : asymmetry

small Imiddle Ilarge I

v_tra (x 100)0 2 4

0 2 4 6

Larger v_tra: smaller alignement

Smaller masses and asymmetries

Continous transition from multi- to neck-fragmentation up to PLF dynamical fission

Isospin migration

Isospin distillation

Natura non facit saltus

124Sn+124Sn 50AMeV semicentral

b=8f

mb=

10fm

ISOSPIN TRANSPORT AT FERMI ENERGIES

124Sn + 112Sn at 50 AMeV

a) the neck region – low density interface

b) pre-equilibrium particle emission

BNV - transport modelb=8fmb=9 fmb=10fm

120fm/c100fm/c80fm/c

contact time

Concentration(diffusion) andDensity (drift)Gradients

V.Baran et al., nucl-th/0506078, PRC in press

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

Nisoscaling

vs. Centrality (fixed y)

vs. Rapidity (fixed centrality)

vs. Transverse momentum (fixed y, centrality) ?

ISOSPIN IMBALANCE RATIO

asysoft eos superasystiff eos

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

PII

III2R;

II

III2R

ASYSOFT EOS – FASTER EQUILIBRATION

experimental data(B. Tsang et al. PRL 92 (2004) )

Asysoft: more efficient for concentration gradients + larger fast neutron emission Asystiff: more efficient for density gradients + larger n-enrichement of the neck IMFs

-Momentum Dependence: faster dynamics and smaller isodiffusion-In medium cross-sections: just scaling with the effective masses?

Collective flowsIn-plane Out-of-plane

22

22

2 )(Vyx

yxt pp

ppp

i

xix ypyN

yp )()(

1)(

iixi

np ypyN

yF )()(

1)( )(V)(V)(V n

2p2

n-p2 ttt ppp

1 < V2 < +1

X

Z

y = rapiditypt = transverse momentum

= 1 full outV2 = 0 spherical = + 1 full in

ASY-STIFF ASY-SOFT

Isospin effects on Transverse Flows:Fermi Energies

Fe-Fe (1.24)vsNi-Ni (1.07)

p-Fen-Fe

p-Ni

Light isobar flow

3H

3Hebelow balance : opposite to

Coulomb

• pT selection

• ninformatioM,M *p

*nScalone et al.,

PLB (1999)

npppnn CCCC

BBBB

AAAA

)(),(

),(

),(

0

2

0

22

2

2

1),(

),(),(),(

ppppg

ppgprfprfpdpdI

),(),(),( CCBBAAkin

GBD extensionCorrespondence to Skyrme parameters

NPA732(2004)202, nucl-th/0505013, nucl-th/0508008 PRC in press

I=0.2

Lane Potential

Momentum Dependence and Effective Masses: Fast Nucleon Emission

Skyrme-like parametrization

132Sn+124Sn, 50 AMeV, b=2 fm, y(0)0.3

m*n>m*

p

m*n<m*

p

No mass splitting !

High p_t “gas” asymmetry: Observable very sensitive to the mass splitting and not to the asy-stiffness

Pre-equilibrium emission: 132Sn projectile

Gas asymmetry vs. p_tdifferent times: end of pre-eq., freeze out

8/0

Light isobar (3H vs. 3He) measurements ?: equil.asymmetry

132Sn+124Sn, 100 AMeV, b=2 fm, y(0)0.3

m*n>m*

p

m*n<m*

p

Pre-equilibrium emission (2)

Enhanced effects

at higher energy

J.Rizzo et al., nucl-th/0508008, PRC in press

Gas asymmetry vs. p_t

t=50 fm/c

t=80 fm/c

132Sn+124Sn, b=2 fm, y(0)0.3

50 AMeV

100 AMeV

t=60 fm/c

t=100 fm/c

m*n>m*

p

m*n<m*

p

Pre-equilibrium emission (3)

Asy-soft Asy-stiff

Asy-soft Asy-stiff

Gas asymmetry vs. rapidity

7.05.0 )0( y

9.07.0 )0( y

1.19.0 )0( y

Au+Au 250 AMeV, b=7 fm

3.0)0( y 7.03.0 )0( y

9.06.0 )0( y

Z=1 dataM3 centrality6<b<7.5fm

Difference of n/p flows

Larger effects at high momenta

Triton vs. 3He Flows?

**pn mm

Differential Transverse Flows

nucl-th/0505013

Au+Au 250 AMeV, b=7 fm

7.03.0 )0( y

9.06.0 )0( y

3.0)0( y

protonsneutrons

3.0)0( y

15.0)0( y

m*n<m*p : larger neutron squeeze out at mid-rapidity

Z=1 data, M3 centrality, 6<b<7.5fm

**pn mm

Differential Elliptic Flows

Global fit to experimental charge distributions

E.Santini et al., NPA756(2005)468

Fragment Formation in Central Collisions at Intermediate Energies

Au+Au, Zr+Zr, Ni+Ni at 400 AMeV Central Stochastic RBUU + Phase Space Coalescence

Size dependence: the lightest is the hotter?

No but

Fast clusterization in the high density phase

In-medium effects of In-medium effects of NNNN on stopping on stopping

(E. Santini et al., NPA756(2005)468)

C.Fuchs at al.,PRC64(2001)024003Fragmentz- and x- rapidity distributions

Transparency properties of protons & Transparency properties of protons & clustersclusters

(E. Santini et al., NPA756(2005)468)

Opposite trend for protons vs clusters: correlation between fragment multiplicity and stopping

Deuteron coalescence problem: protons overestimated (but not Z=1-6)

System size behaviour of System size behaviour of clustersclusters

(E. Santini et al., NPA756(2005)468)

Li-stopping correlation

Z=1-10 cluster directed flow

Size (Z_sys^2)-dependence of heavycluster multiplicity

Seeds: two-body correlations

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 ?

1. N/Z of fast particle emission , hard photons

2. Fusion-Deep Inelastic Competition

3. E-slope Lane Potential

4. Isospin distillation (from Fermi to Intermediate En.)

5. Isospin transport *

6. Neck fragments: N/Z, alignement, size… *

7. n – p collective flows light isobar flows *

* Asy-stiff indications (around saturation) but low asymmetries so far

?)( *qm

Isospin in Reactions at Fermi Energies: Iso-EOS Sensitive Observables

People: V.Baran, M.Colonna, M.Di Toro, R.Lionti, M.Pfabe, J.Rizzo, E.Santini, and H.H.Wolter

RIB up to 100AMeV & 4πDetectors, low threshold and high mass resolution

NECK FRAGMENTATION: CM Vz-Vx CORRELATIONS

PLFIMF

TLF

Large dispersion also along transversal, x, direction

124Sn + 64Ni 35 AMeV<0

>0Alignement +Centroid at 0 plane

Clear Dynamical Signatures !

58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV:Freeze-out Asymmetry distributions

Fe

Ni

Fe Ni

White circles: asy-stiffBlack circles: asy-soft

Asy-soft: smaller isospin migration

Fe: fast neutron emission

Ni: fast proton emission

R.Lionti et al., PLB625 (2005) 33