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, rizzoc@lns.infn.it

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