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LNSLNS--CataniaCatania, NIPNE, NIPNE--HH HH BucharestBucharest, INFN and , INFN and PhysPhys. . DeptDept. Catania, . Catania, INFN and INFN and Phys.Dept.Phys.Dept. Napoli, INFN and Napoli, INFN and Phys.Dept.Phys.Dept. Padova, INFN and Padova, INFN and Phys.Dept.Phys.Dept. Milano Milano
…… and and withwith the the contributioncontribution of a of a veryvery livelylively Etna mountain!Etna mountain!
From the Phys.Dept. Jan.2002 Etna Double-Face, Aug. 2007
PROMPT DIPOLE RADIATIONPROMPT DIPOLE RADIATION
PEOPLE: PEOPLE: TheoryTheory: : V.BaranV.Baran, M.Colonna, M.Di Toro, , M.Colonna, M.Di Toro, C.RizzoC.RizzoExperimentExperiment: : D.PierroutsakouD.Pierroutsakou, , B.MartinB.Martin……F.CameraF.Camera, , A.BraccoA.Bracco, , A.CorsiA.Corsi, ,
G.BenzoniG.Benzoni……C.SignoriniC.Signorini, , M.MazzoccoM.Mazzocco……DD. . SantonocitoSantonocito and MEDEA and MEDEA CollabCollab..
1. Charge Equilibration in Fusion Collisions: The Dynamical Dipole
- Entrance Channel effect;- Collective Emission of the Dinuclear System;- Dynamical Features: Energy Range, Damping, Angular
Distribution.
The The DynamicalDynamical DipoleDipole RadiationRadiation in Dissipative in Dissipative HeavyHeavy IonIonCollisionsCollisions
PI32 workshop Padova 07.03.08, [email protected]
2. Probing the Symmetry Energy at Sub-Saturation Density
- The “Monster” Prompt Dipole with 132Sn Exotic Beams.
ReactionsReactions havehave beenbeen simulatedsimulated byby consideringconsidering a a stochasticstochastic extensionextension of of microscopicmicroscopic trasporttrasport equationequation BNV, BNV, followingfollowing a a testtest--particleparticle evolutionevolution: : ••VLASOV + NNVLASOV + NN--COLLISIONS and PAULI CORRELATIONS :COLLISIONS and PAULI CORRELATIONS :
( )0 0
U A Bσ
ρ ρρρ ρ
⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
••SOFT: A = SOFT: A = --358,1MeV; B = 304,8MeV; 358,1MeV; B = 304,8MeV; σσ = 7/6 = 7/6 →→ K=K=201MeV201MeV••STIFF: A = STIFF: A = --123,6MeV; B = 70,4MeV; 123,6MeV; B = 70,4MeV; σσ = 2 = 2 →→ K=K=377MeV377MeV
EQUATION OF STATE:EQUATION OF STATE:
( ) ( ) ( ) 2, ,0 symEE EI IA A A
ρ ρ ρ= +
( ) ( ) ( ) ( ) ( )3 2
KIN POTsym sym sym FE E E C F uA A A
ε ρρ ρ ρ= + = +
( ) ( ) { } [ ] collcoll IfIhft
tprfdt
tprdf δ+=+∂
∂= ,,,,,
[ ]fUm
ph +=2
2 fwfw −+ −− )1(gain loss
Fluctuations
••SELFSELF--CONSISTEN MEAN FIELD:CONSISTEN MEAN FIELD: SkyrmeSkyrme standard standard parameterizationparameterization
Phys.Rep. 410 (2005) 335-466
Bpn
pnIρρ
ρρρρ 3≡
+
−=
APPROACH PHASEAPPROACH PHASE DINUCLEAR PHASEDINUCLEAR PHASE CN: CN: stat.GDRstat.GDR
DYNAMICAL DIPOLE: DYNAMICAL DIPOLE: PrePre--equilibriumequilibrium dipoledipole mode in mode in phasephase dinucleardinuclear givegiverise rise toto a a promptprompt γγ--rayray emissionemission whichwhich dependsdepends::•• on on initialinitial dipoledipole moment, ;moment, ;
•• on the on the symmetrysymmetry termterm (< (< ρρ00)), , IsovectorIsovector RestoringRestoring Force Force →→ CentroidCentroid, , YieldYieldNeutronNeutron emissionemission →→ DampingDamping
•• on the on the fusionfusion dynamicsdynamics,, NeckNeck DynamicsDynamics (Mass (Mass AsymmetryAsymmetry))AnisotropyAnisotropyCoolingCooling on the way on the way toto FusionFusion
40fm
40fm
CHARGE EQUILIBRATION DYNAMICS:CHARGE EQUILIBRATION DYNAMICS:••STOCHASTIC STOCHASTIC →→ DiffusionDiffusion..
VS.VS.••COLLETTIVE COLLETTIVE →→ DipoleDipole OscillationsOscillations of the of the DiDi--NuclearNuclear System in System in FusionFusion DynamicsDynamics
betweenbetween collidingcolliding ionsions withwith differentdifferent N/Z N/Z ratiosratios.
( )212
2
1
1210 )( RR
ZN
ZN
AZZtD +⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
( ) ( )max
0
ti tD D t e dtωω −′′ ′′= ∫
( ) ( ) ( )1 1
p nZ Ni ip n
i ii i
X XNZD t t tA n n= =
⎛ ⎞= −⎜ ⎟
⎝ ⎠∑ ∑
npinpnp p
NZPPPtDK ,
, ,1)( Σ≡→−≡
[ ] hitDKtD =)(),(
DK(t)-D(t) SPIRALS→ denotes the collectivenature of the Oscillations!
FromFrom the time the time evolutionevolution of the of the dipoledipole moment in rmoment in r--space space wewe can can applyapply aaBremsstrahlung approach for a Quantitative estimationsof the Dynamical Dipole
V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87(2001)
2''2
3
2
)(3
2 ωπ γγ
DA
NZEc
edEdP
⎟⎠⎞
⎜⎝⎛=
h
Statistical emission GDRStatistical emission GDR
36Ar(N/Z=1)+96Zr(N/Z=1,4)The STARTING TIME of the collettive preequilibrim GDR mode in the entrance
channel dynamics:• t≈60fm/c, to≈40fm/c at 6AMeV beam energy, • t≈52fm/c, to≈35fm/c at 9AMeV,• t≈25fm/c, to≈20-25fm/c at 16-20AMeV,
dipends :Neck Dynamics
ASYMMETRY MASSBEAM ENERGY
D(t0dinucl)≠D(t0)
D(t) [fm]
DK
(t) [
fm-1
]
Increasing BEAM ENERGY we aspect a faster dinucleus formation.
9MeV
16MeV
20MeV
CHARGE ASYMMETRY
36Ar(N/Z=1)+96Zr(N/Z=1,4)16O(N/Z=1)+116Sn(N/Z=1,3)
9MeV
16MeV
20MeV
8MeV
15MeV
20MeV
D(t) [fm]
DK
(t) [f
m-1
]
D(t) [fm]
b=4b=2b=0
b=2fmb=0fm
DK
(t) [
fm-1
]
D(t) [fm]
dP/d
E[M
eV-1
]3232S+S+100100Mo Mo SystemsSystems at 9AMeV at 9AMeV beambeam energyenergy: CENTRALITY DEPENDENCE of the : CENTRALITY DEPENDENCE of the SpectraSpectra
b=0fm
b=2fm
b=4fm
IncreasingIncreasing impact impact parameterparameter::•• LowerLower centroidcentroid energyenergy→→ largerlarger deformationdeformation;;
• LowerLower total total yieldyield→→ smallersmaller interaction interaction
regionregion;;
- SmallerSmaller widthwidth→→ lowerlower nucleonnucleon emissionemission.
3636Ar(N/Z=1)+Ar(N/Z=1)+9696Zr(N/Z=1,4)Zr(N/Z=1,4), , D(t=0)=20,63fmD(t=0)=20,63fmE/A=6MeV E/A=9MeV E/A=16MeV E/A=20MeVb=0fm b=0fm b=0fmb=0fm
dP/d
E[M
eV-1
]
DominantDominant DampingDamping MechanismMechanism: : at higher beam energies we aspect a Quenching of the Prompt Dipole Radiation for two main reasons both due to the increasing importance of hard NN collisions:
ENERGY ENERGY DEPENDENCE of the DEPENDENCE of the SpectraSpectra::IncreasingIncreasing aboveabove the Coulomb the Coulomb BarrierBarrier →→ fasterfaster dinucleusdinucleus formationformation, , butbut ……
RISE AND FALL
• a a largerlarger fast fast nucleonnucleon emissionemission thatthat willwill equilibrate the equilibrate the isospinisospin beforebefore the the collettive collettive dipoledipole startsstarts up;up;• a a largerlarger dampingdamping of the collettive mode due of the collettive mode due toto npnp collisionscollisions..
1616O+O+116116Sn,Sn,6464Ni+Ni+6868ZnZn→→ LNL(LNL(GarfieldGarfield) Milano Group, 2007) Milano Group, 2007
36,4036,40Ar+Ar+96,9296,92Zr Zr →→ LNS(Medea) 2007: LNS(Medea) 2007: AngularAngular DistributionDistribution!!
TP
TP
RRRR
+
−=
DynamicalDynamical DipoleDipole SystematicsSystematics
CN: CN: 132132CeCemass mass regionregion
CN
Mass Mass asymasym
D.Pierroutsakou et al., New Medea Exp. at LNS-Catania, July 07
■ 36Ar + 96Zr○ 40Ar + 92Zr
•Bremsstrahlung-subtracted γ-rayspectra at θγ=90o (vs. Beam Axis) in coincidence whit the evaporation residues.
3636Ar+Ar+9696Zr Zr vs.vs. 4040Ar+Ar+9292Zr Zr atat 16AMeV 16AMeV beambeam energyenergy. . FusionFusion eventsevents: : samesame CN CN selectionselection
••DifferenceDifference..
AnAn increaseincrease of the GDR of the GDR γγ--rayrayintensityintensity isis foundfound byby goinggoing towardtoward the the more more chargecharge asymmeticasymmetic system.system.θθγγ-- studystudy of the of the extraextra--yieldyield withwithMEDEAMEDEA
■ 36Ar + 96Zr○ 40Ar + 92Zr
The data are The data are linearizedlinearized byby theoreticalγγ--rayray spectrum of the charge symmetricreaction calculated with the statisticaldecay code CASCADE results withouta CN GDR
DipoleDipole AngularAngular DistributionDistribution of the of the ExtraExtra--YieldYield, (10<E, (10<Eγγ<15 <15 MeVMeV))
B.Martin, D.Pierroutsakou et al., Medea Exp. at LNS-Catania, arXiv:0710.1512[nucl-ex]
)](cos1[)( 220 γγ ϑϑ PaWW +=
vs Beam Axis
A strong A strong dipoledipole--likelike photonphoton angularangulardistributiondistribution hashas beenbeen observedobserved, , withwith the the parameterparameter aa2 2 = = --1, 1, W(W(ƟƟγγ,CM,CM))�� sinsin22ƟƟγγ,CM,CM
a2 = -0.8
a2 = -0.5
Widening: rotation of the PromptDipole Axis vs the Beam Axis
3636Ar+Ar+9696Zr Zr vs.vs. 4040Ar+Ar+9292Zr Zr atat 16AMeV 16AMeV beambeam energyenergy. . FusionFusion eventsevents: : samesame CN CN selectionselection
a2 = -1
Accurate Angular Distrib. Measure:Dipole Clock!
W(W(ƟƟ γγ,CM,CM) ) isis anisotropicanisotropic withwith a a maximummaximum aroundaround 9090°° and and itit isisconsistentconsistent withwith emissionemission fromfrom a a
dipoledipole oscillatingoscillating alongalong the the beambeamaxisaxis. .
■ 36Ar + 96Zr○ 40Ar + 92Zr
Gamma Gamma AngularAngular DistributionDistribution, 10<E, 10<Eγγ<15 <15 MeVMeV
“Symmetric” reaction:CN Deformations?
Density Plots on the Reaction Plane: Rotation of the Oscillation Axis vs the Beam Axis
time(fm/c)
time(fm/c)
40fm/c
220fm/c
The Monster Dipole Case 132132Sn+Sn+5858Ni Ni atat 10AMeV 10AMeV beambeam energyenergy. . FusionFusion eventsevents: b=4fm: b=4fm
StillStill emittingemitting,.,..although.although dampeddamped
60fm/c 80fm/c 100fm/c
120fm/c 140fm/c 160fm/c 180fm/c 200fm/c
Rotation on the Reaction Plane of the Emitting Dinuclear System
•All probed Rotating angles: ΔΦ = 2π →→ x = 0 →→ a2 = -1/4Statistical result, Collective Prolate on the Reaction Plane
•Fixed Rotating angle: ΔΦ = 0 →→Φi = Φf = Φ0
•No rotation: Φ0=0 →→ sin2θγPure Dipole
Dominant since the prompt dipole is rapidlydamped? Angular Distribution→→ Dynamic Dipole Lifetime
[ ])(cos)sin1(1)( 202
γγ ϑϑ PW Φ−−∝
θγ : photon angle vs. beam axis
[ ]
iffix
xaPaWW
Φ−Φ=ΔΦΔΦΔΦ
Φ+Φ=
⎟⎠⎞
⎜⎝⎛ +−=+=
,)sin()cos(
43
41,)(cos1)( 2220 γγ ϑϑ
reaction plane
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
beam axis
cos Φ
The “Monster” 132Sn Dynamical Dipole: Angular Distributionsb=2fm b=4fm
Expected Angular Distributions
Slowing down of the rotation:Coupling to other modes?
Pure Pure DipoleDipole
a2 = -1/4 (prolate, statistical)
coscosΦΦ: b=2fm: b=2fm
coscosΦΦ: b=4fm (: b=4fm (notnot dampingdamping))
cos Φ
b=2fm
b=4fm
( ) ( ) ( ) 2, ,0 symEE EI IA A A
ρ ρ ρ= +
( ) ( ) ( )KIN POT
sym sym symE E EA A A
ρ ρ ρ= +
The Prompt Dipole Radiation as a Probe of the Symmetry EnergyDynamical Dipole vs Symmetry Energy
The Prompt Dipole Radiation as a Probe of the Symmetry EnergyDynamical Dipole vs Symmetry Energy
Bpn
pnIρρ
ρρρρ 3≡
+
−=
2
0
0
0
04 183 ⎟⎟
⎠
⎞⎜⎜⎝
⎛ −+⎟⎟⎠
⎞⎜⎜⎝
⎛ −+=
ρρρ
ρρρ BsymB
sym
KLaE
ExpansionExpansion aroundaround ρρ00
2828--32MeV 32MeV SlopeSlope CurvatureCurvature
ISOSPIN DYNAMICS IN DISSIPATIVE HEAVY ION ISOSPIN DYNAMICS IN DISSIPATIVE HEAVY ION COLLISIONS AT COLLISIONS AT SUB-SATURATION DENSITY
Neutron SkinPigmy Resonances
Neutron Stars- mass/radius-”hybrid structure”
Asy-superstiff
Asy-stiff
Asy-soft
132Sn(N/Z=1,64)+58Ni(N/Z=1,07)10AMeV b=4fm
132Sn(N/Z=1,64)+58Ni(N/Z=1,07)10AMeV b=4fm
Asy-Soft: neutrons see a more repulsiveSymmetry Potential below ρ0
Dis
t pro
-ber
[fm
]
Dis
t pro
-ber
[fm
] 124Sn(N/Z=1,48)+58Ni(N/Z=1,07)10AMeV b=4fm
124Sn(N/Z=1,48)+58Ni(N/Z=1,07)10AMeV b=4fm
Asy-superstiff
Asy-soft
Asy-superstiff
Asy-soft
neutrons
protons
Fast emitted nucleons
Asy-superstiff
Asy-soft
Distance between n-p center of mass
Distance between 132Sn and 58Ni center of mass
V.Baran and C.Rizzo (Master Thesis) LNS August 07
ASY SOFT:→→ Earlier start;→→ Larger amplitude;→→ Higher frequency.
The Monster Dipole Case 132132Sn+Sn+5858Ni, D(t=0)>50fm,atNi, D(t=0)>50fm,at 10AMeV 10AMeV beambeam energyenergy..FusionFusion eventsevents: b=4fm: b=4fm
Dynamical Dipole: Exotic Spiralling vs Symmetry EnergyDynamical Dipole: Exotic Spiralling vs Symmetry Energy
132Sn+58Ni 10AMeV b=4fm
132Sn+58Ni 10AMeV b=4fm
124Sn+58Ni 10AMeV b=4fm
124Sn+58Ni 10AMeV b=4fm
V.Baran and C.Rizzo (Master Thesis) LNS August 07
Asy-soft
Asy-superstiff
b(fm)
AsyAsy--SoftSoft vsvs AsyAsy--SuperStiffSuperStiff
Larger Damping +15%fast neutron emission
••LargerLarger restoringrestoring force:force:→→ larger symmetry energybelow ρ0
→→ larger Centroid Energy
--LargerLarger WidthWidth centroidcentroid +20%+20%
••LargerLarger yieldyield +20%+20%AsyAsy--SoftSoft ::
ISOSPIN DYNAMICS IN DISSIPATIVE HIC: ISOSPIN DYNAMICS IN DISSIPATIVE HIC:
ISOISO--EOS EOS –– SENSITIVE OBSERVABLESSENSITIVE OBSERVABLES
“Violent“ Collisions of Radioactive Beams
AroundAround normalnormal density: Low density: Low toto Fermi Fermi energiesenergies
-- The The PromptPrompt DipoleDipole RadiationRadiation in in FusionFusion ReactionsReactions::YieldYield, , SpectrumSpectrum, , DampingDamping (Energy (Energy DependenceDependence), ), AngularAngular DistributionDistribution