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Maria Colonna Laboratori Nazionali del Sud (Catania )

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Extracting the symmetry energy from low

and medium energy heavy ion reactions

Maria Colonna

Laboratori Nazionali del Sud (Catania)

LEA COLLIGA workshop

October 13-15, LNS (Catania)

Nuclear astrophysics

Nuclear structure

Contents

Nuclear dynamics at low and Fermi energies:

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

- Collective excitations in exotic systems
(pre-equilibrium dipole)

- Charge equilibration in semi-central collisions
- Competition between reaction mechanisms
- Neck dynamics
Fazia Physics Case

I=(N-Z)/A

asy-stiff

asy-soft

Dissipative dynamics: testing the symmetry energy Esym

in terrestrial laboratories

Nuclear EOS

Transport theories: Stochastic Mean Field (SMF)

E/A (ρ) = Es(ρ) + Esym(ρ)I²

Simple hydro picture

currents

drift

diffusion

coefficients

Diffusion

Drift

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

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

Pre-equilibrium Dipole Radiation

Charge Equilibration Dynamics:

Stochastic → Diffusion

vs.

Collective → Dipole Oscillations of the Di-nuclear System Fusion Dynamics

Initial Dipole

D(t) : bremss. dipole radiationCN: stat. GDR

36Ar + 96Zr

40Ar + 92Zr

Symmetry energy

below saturation

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

Experimental evidence of the extra-yield LNS data

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

Isospin gradients: Pre-equilibrium dipole emission

SPIRALS → Collective Oscillations!

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

132Sn + 58Ni

124Sn + 58Ni

Bremsstrahlung:

Quantitative estimations

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

Larger restoring force with asy-soft larger strength !

Rotation on the Reaction Plane of the Emitting Dinuclear System

Dynamical-dipole emission

Charge equilibrium

ΔΦ=2 → x=0 → a2=-1/4 : Statistical result,

Collective Prolate on the Reaction Plane

Φf

Φi

Beam Axis

θγ: photon angle vs beam axis

ΔΦ=0 → Φi =Φf = Φ0

No rotation: Φ0=0 → sin2θγpure dipole

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=8fm

b=10fm

Isospin equilibration: Imbalance ratios

B. Tsang et al. PRL 92 (2004)

M : 124Sn + 112Sn

SMF

simulations

L: 112Sn + 112Sn

Phys. Rep. 389 (2004)

H: 124Sn + 124Sn

Phys.Rep.410(2005)335

@ 35, 50 Mev/A

I = (N-Z)/A

of PLF or TLF

R = ± 1 Full transparency

35 AMeV

R = 0 Full equilibration

- Smaller R values for:
- Asy-soft
- MI interaction
- Lower beam energy

50 AMeV

J.Rizzo et al. NPA806 (2008) 79

τsymmetry energy

tcontact dissipation

Imbalance ratios: isoscalar vs. isovector effects

Overdamped dipole oscillation

If:

β = I = (N-Z)/A

Kinetic energy loss - or PLF(TLF) velocity - as a measure

of dissipation (time of contact)

asy-stiff

asy-soft

R dependent only on the isovector part

of the interaction !

E.Galichet

INDRA collaboration

Neck Dynamics in Deep-Inelastic-Collisions

132

64

Sn + Ni Elab = 10 MeV/A

b = 7 fm, 9 events at t = 500 fm/c

Stochastic Mean Field simulations

asy-stiff

asy-soft

More dissipative neck

dynamics with asy-stiff !

- Observables:
- Deflection (Wilczynski plots)
- Fragment Deformations

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

Competition between reaction mechanisms: fusion vs deep-inelastic

a) -- soft

b) -- stiff

Asy-soft more

dissipative

neutron-rich

Elab = 30 Mev/A, b = 4 fm

proton-rich

Asy-stiff more

dissipative

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

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

Asysoft

Asystiff

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

200 runs each

per impact parameter,

b=6,7,8fm

quadrupole

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

octupole

NN06, Rio de Janeiro

NPA 787 (2007) 585c

LNS data – CHIMERA coll.

Density gradients derivative of Esym

Asymmetry flux

(IMF/TLF)

Vrel/VViola (IMF/PLF)

ρ2

ρ1 <

Experimental evidence of

n-enrichment of the neck:

Correlations between N/Z

and deviation from Viola

systematics

Isospin migration in neck fragmentation

- Transfer of asymmetry from PLF and TLF to
- the low density neck region
- Effect related to the derivative of the symmetry
- energy with respect to density

b = 6 fm, 50 AMeV

PLF, TLF

neck

emitted

nucleons

asy-stiff

asy-soft

E.De Filippo et al.,

PRC71,044602 (2005)

E.De Filippo et al. NUFRA 2007

Sn112

+ Sn112

Sn124

+ Sn124

Larger derivative with asy-stiff

larger isospin migration effects

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)

- Sn112 + Sn112
- Sn124 + Sn124
- Sn132 + Sn132
E/A = 50 MeV, b=2 fm

N/Z vs fragment energy (1)

N = Σi Ni ,Z = Σi Zi

3≤ Zi ≤ 10

asy-stiff - - -asy-soft

1.64

1200 events for each reaction

N/Z vs charge

“gas” phase

(pre-equilibrium)

“liquid”

- Proton/neutron repulsion:
- larger negative slope in the stiff case
(lower symmetry energy)

- n-rich clusters emitted at larger
- energy in n-rich systems

asy-stiff asy-soft

n

p

Isospin distillation in presence of radial flow

Central collisions

- Sn112 + Sn112
- Sn124 + Sn124
- Sn132 + Sn132
E/A = 50 MeV, b=2 fm

Different radial flows for neutrons and protons

Fragmenting source with isospin gradient

N/Z of fragments vs. Ekin !

r

N = Σi Ni ,Z = Σi Zi

3≤ Zi ≤ 10

asy-stiff - - -asy-soft

Double ratios (DR)

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

- Proton/neutron repulsion:
- larger negative slope in the stiff case
(lower symmetry energy)

- n-rich clusters emitted at larger
- energy 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-EoS

is observed in the double N/Zs ratio

If N/Zfin = a(N/Z +b), N/Zs not affected by secondary decay !

arXiv:0707.3416

129Xe+124Sn, 100AMeV

124Xe+112Sn, 100AMeV

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

Larger 3He flow (triangles)

Coulomb effects

Larger difference

for m*n>m*p

m*n>m*p

m*n<m*p

Triton/Helium transverse flow ratio:

smaller for m*n>m*p

Good sensitivity to the mass splitting

The variance of the distribution function

Best volume: p = 190 MeV/c, θ = 20°

p = 190 MeV/c

Δθ = 30°

Set of coordinates

Clouds position

t = 100 fm/c

t = 0 fm/c

p = 260 MeV/c, Δp = 10 MeV/c,

- spherical coordinates
- fit the Fermi sphere
- allow large volumes

DEVIATIONSFROMVIOLASYSTEMATICS

r - ratio of the observed PLF-IMFrelative velocityto

the corresponding Coulombvelocity;

r1- the same ratio for the pair TLF-IMF

TheIMF is weakly correlated with both PLF and TLF

124Sn + 64Ni

35 AMeV

Wilczynski-2 plot !

CM Vz-Vx CORRELATIONS

v_par

Sn124 + Sn124,

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

v_x (c)

Distribution after secondary

decay (SIMON)

v_z (c)

58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV:

Freeze-out Asymmetry distributions

Fe

Ni

Ni

Fe

White circles: asy-stiff

Black circles: asy-soft

Fe: fast neutron emission

Ni: fast proton emission

Asy-soft: small isospin migration

Details of SMF model

- Correlations are introduced in the time evolution of the one-body density: ρρ +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 ?

T

gas

liquid

ρ

Extract random A nucleons among test particle

distribution Coalescence procedure

Check energy and momentum conservation

A.Bonasera et al, PLB244, 169 (1990)

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

Fragment

Recognition

Fragment excitation energy evaluated by subtracting

Fermi motion (local density approx) from Kinetic energy

- 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)

Angular distributions: alignment characteristics

Out-of-plane angular distributions for the “dynamical” (gate 2) and “statistical” (gate 1) components: these last are more concentrated in the reaction plane.

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

Dynamical Isoscaling

Z=1

Z=7

Asy-stiff

Asy-soft

A

primary

50 AMeV

(central coll.)

final

not very sensitive to Esym ?

124Sn Carbon isotopes (primary)

T.X.Liu et al.

PRC 2004

50 MeV/A

35 MeV/A

Imbalance ratios

If:

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

then:

RP = 1 – c ; RT = c - 1

- Larger isospin equilibration with MI
- (larger tcontact ? )
- Larger isospin equilibration with asy-soft
- (larger Esym)
- More dissipative dynamics at 35 MeV/A

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

vtra

124Sn + 64Ni 35 AMeV ternary events

φ

Transp. Simulations (124/64)

Experiment

Histogram: no selection

Asystiff

Asysoft

Asystiff: more isospin migration to the neck fragments

Chimera data: see E.De Filippo, P.Russotto

NN2006 Contr., Rio

V.Baran, Aug.06

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

Au+Au 250 AMeV, b=7 fm

Mass splitting: Transverse Flow Difference

Difference of n/p flows

Larger effects at high momenta

Z=1 data

M3 centrality

6<b<7.5fm

Triton vs. 3He Flows?

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