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 ). L EA C OLLIGA workshop October 13-15, LNS (Catania). Nuclear astrophysics. Nuclear structure. Contents. Nuclear dynamics at low and Fermi energies: - PowerPoint PPT PresentationTRANSCRIPT
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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)
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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
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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
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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
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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 !
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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
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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)
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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
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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
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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 !
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.)
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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
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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
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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