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Neck fragmentation
time
Semi-peripheral reactions:Fragmentation in a smaller region, but with largercross section !
Possibility to better disantangleand/or correlate kinematical and thermodynamical features
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Impact parameter dependence
E/A = 35 AMeV; b=6 fm
free cross sections half free cross sections
P=Nternary/Ntotal
124Sn+64Ni 112Sn+58Ni
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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 !
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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 Neck-IMF is weakly correlated with both PLF and TLF
V.Baran, M.Colonna, M.Di Toro NPA 730 (2004)
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Gating the reduced plot for light IMFs:Gating the reduced plot for light IMFs:
(exp. data)
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REDUCED VELOCITY PLOTS: REDUCED VELOCITY PLOTS:
BNV
V. Baran et al. Nucl. Phys A730 (2004) 329
Note: BNV model accounts only for the “prompt” component of IMF’s
Chimera 124Sn+64Ni 35AMeV data, same E_loss selections
(exp. data)
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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.
(Chimera data)
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b = 2 fm b = 4 fm b = 6 fm
Sn124 + Sn124, E/A = 50 MeV/A
Stochastic mean field (SMF) calculations
Pre-equilibrium emission
Fragment formation
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Convalidare il meccanismo di frammentazione.Nuovi aspetti legati a transizioni di fase in sistemiasimmetrici
Dedurre informazioni sul comportamento dell’energiadi simmetria in condizioni di densita’ diverse da quellenormali (bassa densita’)
Frammentazione in sistemi ricchi di neutroni
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...)()()(),( 42 IOIEEE 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 & compressibility
Asy-st
iff
Asy-soft
Pressure gradient symsym KL
d
dP
9
1
3
2
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Mean Field & Chemical Potentials
124Sn “asymmetry” = 0.2
symmetry part of the mean field neutron-proton chemical potentials
neutron neutron
proton proton
stiff
soft
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Asy-stiff
Fragment isospin properties: the iso-distillation
Asy-soft
25 % reduction
124Sn+ 124Sn 50 AMeV: average asymmetryCentral collisions
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Stochastic BNV calculationsT.X.Liu et al., PRC69(2004)
Comparison of isotopic distributions with data
124Sn+ 124Sn 50 AMeV: central collisions
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124Sn+ 124Sn 50 AMeV: average asymmetry
Asy-stiff:neutron enrichmentof light IMFs
Asy-soft
Semi-peripheral collisions
Isospin migration
V.Baran et al., NPA703(2002)603NPA730(2004)329
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Fe + Fe @ 47 AMeV Ni + Ni, @ 47 AMeV
IMF’s propertiesvs. alignement
R.Lionti et al., PLB 625 (2005) 33
d
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asy-stiff
asy-soft
Transverse velocity dependenceof fragment asymmetry
Sn124 + Sn124, E/A = 50 MeV/A b = 6 fmn-rich / n-poor ratio
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asy-stiff asy-soft 0<A<10
0 < v_tra /c < 0.02 v_tra /c > 0.02
Asymmetry distributions in velocity bins
asy-stiffasy-soft
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P(δρn – δρp) ~ exp – [ (δρn – δρp)² / (f(ρ,T) ρ/V) ]
P(N,Z) ~ exp –{ [(N-Z)-(Nº-Zº)]² / (ρV f(ρ,T)) } =
exp –{ a(N-Z)²- bN-cZ}
b = (4(Zº/ Aº)² - 1) / σ ; c = (4(Nº/ Aº)²-1) / σ
Isoscaling analysis (Y2(N,Z)/Y1(N,Z)) : exp(α N + β Z)
α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ] / σ σ = f(ρ,T) (ρV)/Aº
f(ρ,T) ~ T / Esym(ρ) (ρV)/Aº < 1
ρ is the density of the initial low density (unstable) system
Fragment isotopic distributions
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Z=1
Z=7
primary
final
yieldionlightSn
Sn112
124
T.X.Liu et al., PRC2004
α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ]/σ²
Isoscaling: a way to analyze isotopic distributions
Central collisions
α exp = 0.35
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Isoscaling in AMD (anti-symmetrized molecular dynamics)calculations A.Ono et al.
α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ] / σ σ ~ f(ρ,T) f(ρ,T) ~ T / Csym(ρ)
Extraction of Esym from isoscaling analysis
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In conclusione ….
Segnali che indicano transizione di fase liquido-gas:•Espansione radiale (bassa densita’) + bassa temperatura •Curva calorica•Bimodalita’•Calore specifico negativo•Distillazione di isospin
Segnali che supportano il meccanismo spinodale:Tempi di frammentazione (100 fm/c)Formazione di frammenti di taglia tipica (segnale che sopravvive solo in alcuni eventi)Buona corrispondenza fra le osservabili cinematiche dei frammenti e proprieta’ legate a massa e N/Z descrizione corretta della dinamica di frammentazione
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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
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Binary vs ternary reactions (neck emission)
Reactions at low energy:Elab < 10 MeV/A (SPIRAL2)
TDHF calculations:Davies et al, PRC20(1979)1372
Dynamical emission of small clustersat mid-rapidity
Kr + La, l=100 Elab = 710 MeV 86 139
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asy-soft
asy-stiff
Sn + Ni Elab = 10 MeV/Ab = 7 fm, t = 500 fm/c
More dissipative neck dynamics with asy-stiff !
64132