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M.Di Toro, ECT*/Eurisol Jan.06, [email protected] Isospin Dynamics in Heavy Ion Collisions at Fermi...
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Transcript of M.Di Toro, ECT*/Eurisol Jan.06, [email protected] Isospin Dynamics in Heavy Ion Collisions at Fermi...
M.Di Toro, ECT*/Eurisol Jan.06, [email protected]
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