Maria Colonna Laboratori Nazionali del Sud (Catania)

Extracting the symmetry energy from low Extracting the symmetry energy from low and medium energy heavy ion reactionsand medium energy heavy ion reactions

LEA COLLIGA workshopOctober 13-15, LNS (Catania)

ContentsContents

Nuclear dynamics at low and Fermi energies:

trying to pin down the low-density behavior of the symmetry energy

Nuclear structure Nuclear astrophysics

Collective excitations in exotic systems (pre-equilibrium dipole)

Charge equilibration in semi-central collisions

Competition between reaction mechanisms

Neck dynamics Fazia Physics Case

Dissipative dynamics: Dissipative dynamics: testing the symmetry energy Etesting the symmetry energy Esymsymin terrestrial laboratoriesin terrestrial laboratories

I

EIEjj sym

sympn

)()(

IDDj

IDDjIppp

Innn

currents

diffusion

Diffusion Drift

Direct Access to Value and Slope of the Symmetry Energy at ρ !

E/A (ρ) = Es(ρ) + Esym(ρ)I²

Nuclear EOS

drift

coefficients

Reactions at low energies: information on the EOS below normal density

I=(N-Z)/A

asy-soft

asy-stiff

Transport theories: Stochastic Mean Field (SMF)

Simple hydro picture

212

2

1

1210 RR

Z

N

Z

N

A

ZZD

D(t) : bremss. dipole radiation CN: stat. GDRInitial Dipole

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

- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion

Symmetry energy below saturation

36Ar + 96Zr40Ar + 92Zr

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

Experimental evidence of the extra-yield LNS data

Isospin gradients: Pre-equilibrium dipole emission

SPIRALS → Collective Oscillations!

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)

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

,

,

1)(

,

1)()()(

,,

,,

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

132Sn + 58Ni 124Sn + 58Ni

Larger restoring force with asy-soft larger strength !

Rotation on the Reaction Plane of the Emitting Dinuclear System

iffix

xaPaWW

,)sin(

)cos(

4

3

4

1,)(cos1)( 2220

ΔΦ=2 → x=0 → a2=-1/4 : Statistical result, Collective Prolate on the Reaction Plane

ΔΦ=0 → Φi =Φf = Φ0

)(cos)sin1(1)( 202

PW

No rotation: Φ0=0 → sin2θγ pure dipole

Φi

Φf

Dynamical-dipole emission

Charge equilibrium

Beam Axis

θγ : photon angle vs beam axis

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

Angular distribution of the extra-yield (prompt dipole): anisotropy ! Accurate Angular Distrib. Measure:

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

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

R = ± 1 Full transparencyR = 0 Full equilibration

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 ratios Isospin equilibration: Imbalance ratios

SMF simulations

J.Rizzo et al. NPA806 (2008) 79

Phys.Rep.410(2005)335Phys. Rep. 389 (2004)

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

asy-stiff

asy-soft

E.GalichetINDRA collaboration

asy-soft

asy-stiff

More dissipative neck dynamics with asy-stiff !

Observables:-Deflection (Wilczynski plots)-Fragment Deformations

M.Colonna, V.Baran et al., Spiral2 LOI Oct.2006

Neck Dynamics in Deep-Inelastic-Collisions

Sn + Ni Elab = 10 MeV/Ab = 7 fm, 9 events at t = 500 fm/cStochastic Mean Field simulations

64132

Elab = 30 Mev/A, b = 4 fm

a) -- softb) -- stiff

Competition between reaction mechanisms: fusion vs deep-inelastic

M.Colonna et al., PRC57(1998)1410

neutron-rich

proton-rich

Asy-soft more dissipative

Asy-stiff more dissipative

faster proton emission

Opposite results with respect to simulations at lower energy !

Stochastic Mean Field simulations: 132Sn + 64Ni Elab = 10 MeV/A

Binary events at freeze-out (≈500fm/c):Largest deformation of the residues

b=6fm b=7fm b=8fm AsysoftAsystiff

quadrupole

octupole

Asystiff:-larger residue deformations (more fast fission events)

200 runs eachper impact parameter,b=6,7,8fm

NN06, Rio de JaneiroNPA 787 (2007) 585c

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm, 50 AMeV

Isospin migration in neck fragmentationIsospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region

Effect related to the derivative of the symmetryenergy with respect to density

PLF, TLFneckemittednucleons

ρ1 < ρ2

Asymmetry flux

asy-stiff

asy-soft

Larger derivative with asy-stiff larger isospin migration effects

Density gradients derivative of Esym

E.De Filippo et al., PRC71,044602 (2005)E.De Filippo et al. NUFRA 2007

Experimental evidence of n-enrichment of the neck:Correlations between N/Zand deviation from Viola systematics

LNS data – CHIMERA coll.

Vrel/VViola (IMF/PLF)

(IMF/TLF)

J.Rizzo et al. NPA806 (2008) 79

Conclusions

Dissipative dynamics at Fermi energies may allow to access new,complementary information on the low density behavior of Esym

Pre-equilibrium dipole: access low-density Esym neutron skin Cooling mechanism super-heavy formation Isospin transport: Full charge equilibration at low energies ?

Neck dynamics: investigate the properties of the low-density interface

Sensitivity to detail of nuclear interaction: information on the nuclear force

V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo (LNS-Catania)M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich)

N/Z vs charge

1200 events for each reaction

Proton/neutron repulsion:larger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

N/Z vs fragment energy (1) Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132E/A = 50 MeV, b=2 fm

“gas” phase(pre-equilibrium)

asy-stiff asy-soft

“liquid”

N = Σi Ni , Z = Σi Zi

1.64

3≤ Zi ≤ 10

asy-stiff - - -asy-soft

Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132E/A = 50 MeV, b=2 fm

N = Σi Ni , Z = Σi Zi 3≤ Zi ≤ 10 asy-stiff - - -asy-soft

Proton/neutron repulsion:larger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems

To access the variation of N/Z vs. E: “shifted” N/Z: N/Zs = N/Z – N/Z(E=0) Larger sensitivity to the asy-EoSis observed in the double N/Zs ratio If N/Zfin = a(N/Z +b), N/Zs not affected by secondary decay !

Different radial flows for neutrons and protonsFragmenting source with isospin gradient N/Z of fragments vs. Ekin !

Dou

ble

ratio

s (

DR

)

Central collisions

pn

r

arXiv:0707.3416

DR = (N/Z)2 / (N/Z)1

Transverse flow of light clusters: 3H vs. 3He

m*n>m*p m*n<m*p

129Xe+124Sn, 100AMeV

124Xe+112Sn, 100AMeV

Larger 3He flow (triangles) Coulomb effects

Larger differencefor m*n>m*p

Triton/Helium transverse flow ratio:smaller for m*n>m*p

Good sensitivity to the mass splitting

dppddp )sin(,,Set of coordinates

)sin( p = 260 MeV/c, Δp = 10 MeV/c,

t = 0 fm/c t = 100 fm/c

)cos(3

23

p

V

The variance of the distribution function

p = 190 MeV/c Δθ = 30°

spherical coordinates fit the Fermi sphere allow large volumes

Clouds position

Best volume: p = 190 MeV/c, θ = 20°

12.0)(2 Ff E

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 !

124Sn + 64Ni 35 AMeV

v_z (c)

v_x

(c)

Distribution after secondary decay (SIMON)

Sn124 + Sn124, E/A = 50 MeV/A, b = 6 fm

CM Vz-Vx CORRELATIONS

v_par

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: small isospin migration

Fe: fast neutron emission

Ni: fast proton emission

Liquid phase: ρ > 1/5 ρ0 Neighbouring cells are connected (coalescence procedure)

Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationA.Bonasera et al, PLB244, 169 (1990)

Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy

• Correlations are introduced in the time evolution of the one-body density: ρ ρ +δρ as corrections of the mean-field trajectory• Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density

Fragmentation Mechanism: spinodal decomposition

Is it possible to reconstruct fragments and calculate their properties only from f ?

Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model

Statistical analysis of the fragmentation path

Comparison with AMD results

Chomaz,Colonna, Randrup Phys. Rep. 389 (2004)Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005)Tabacaru et al., NPA764, 371 (2006)

A.H. Raduta, Colonna, Baran, Di Toro, ., PRC 74,034604(2006) iPRC76, 024602 (2007) Rizzo, Colonna, Ono, PRC 76, 024611 (2007)

Details of SMF model

T

ρ

liquid gas

Fragment Recognition

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 2) and “statistical” (gate 1) components: these last are more concentrated in the reaction plane.

Dynamical Isoscaling

Z=1

Z=7

primary

final

yieldionlightSn

Sn112

124

A

ZNR

AfZNY

12221

2

2

2ln

)(exp)(),(

not very sensitive to Esym ?

124Sn Carbon isotopes (primary)

AAsy-soft

Asy-stiffT.X.Liu et al.

PRC 2004

50 AMeV

(central coll.)

I = Iin + c(Esym, tcontact) (Iav – Iin), Iav = (I124 + I112)/2

RP = 1 – c ; RT = c - 1

112112T

124124T

112112T

124124T

MT

T112112P

124124P

112112P

124124P

MP

PII

III2R;

II

III2R

Imbalance ratios

If:

then:

50 MeV/A 35 MeV/A

• Larger isospin equilibration with MI

(larger tcontact ? ) • Larger isospin equilibration with asy-soft

(larger Esym)• More dissipative dynamics at 35 MeV/A

124Sn + 64Ni 35 AMeV ternary events

N/Z vs. Alignement Correlation in semi-peripheral collisions

Experiment Transp. Simulations (124/64)

Chimera data: see E.De Filippo, P.Russotto NN2006 Contr., Rio

Asystiff

Asysoft

V.Baran, Aug.06

Asystiff: more isospin migration to the neck fragments

Histogram: no selection

E.De Filippo et al. , PRC71(2005)

φ

vtra

Au+Au 250 AMeV, b=7 fm

Z=1 dataM3 centrality6<b<7.5fm

Difference of n/p flows

Larger effects at high momenta

Triton vs. 3He Flows?

**pn mm

Mass splitting: Transverse Flow Difference

MSU/RIA05, nucl-th/0505013 , AIP Conf.Proc.791 (2005) 70