Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN -...

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Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure & Astrophysical Applications July 8-12, 2013 ECT*, TRENTO

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Page 1: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Probes of EOS in Heavy Ion Collisions :results from transport theories

Maria Colonna INFN - Laboratori Nazionali del Sud (Catania)

Nuclear Structure & Astrophysical Applications

July 8-12, 2013ECT*, TRENTO

Page 2: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Heavy Ion Collisions: a way to create Nuclear Matter in several conditions of ρ, T, N/Z… Nuclear effective interaction Equation of State (EOS)

Self-consistent Mean Field calculations (like HF) are a powerful

framework to understand the

structure of medium-heavy (exotic) nuclei.

Source: F.Gulminelli

Widely employed in the astrophysical context (modelization of neutron stars and supernova explosion)

Page 3: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

2 21 1'2|(t)]ρ[H,|12t),(1,1'ρt

i

)(1'2'|(t)]ρ[H,|12t),(12,1'2'ρt

i 322 O

)(12,1'2')(2,2')ρ(1,1'ρ)(12,1'2'ρ 112 1,20 vHH

],δK[ρ]K[ρ1'|(t)]ρ,[H|1t),(1,1'ρt

i 11101

Dynamics of many-body systems

Mean-field Residual interaction

)||,( 21 vK F

),( vK F KK

Average effect of the residual interaction

one-body

Fluctuations

TDHF

0 K

Page 4: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Dynamics of many-body systems

-- If statistical fluctuations larger than quantum ones

Main ingredients:

Residual interaction (2-body correlations and fluctuations)In-medium nucleon cross section

Effective interaction(self consistent mean-field)

)'()','(),( ttCtpKtpK

ff 1

Transition rate WInterpreted in terms ofNN cross section

see BHF

K

Page 5: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

1. Semi-classical approximation

Transport equation for the one-body distribution function f Chomaz,Colonna, Randrup Phys. Rep. 389 (2004) Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005)

collcoll IfIhft

tprf

dt

tprdf

,

,,,, Residual interaction:Correlations, Fluctuationsk δk

ff 1

(1,2) (3,4)

Two-body Collision Integral

Fluctuations in collision integral Stochastic Mean-Field (SMF) model Fluctuations are projected in

coordinate space(density profile)

(semi-classical analog of Wigner function)

Vlasov

vrel

3

1

2

4

Boltzmann-Langevin (BL) equation

Page 6: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

stochastic NN collisions

Collision integral fully stochastic, but approx. description of mean-field effects…

Molecular Dynamics approaches (AMD, ImQMD, QMD,…)2.

Zhang and Li, PRC74,014602(2006)J.Aichelin, Phys.Rep.202,233(1991)

Colonna, Ono, Rizzo, Phys. Rev..C82,054613 (2010)

A.Ono, Phys.Rev.C59,853(1999)

Page 7: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

The nuclear interaction, contained in the Hamiltonian H, is represented byeffective interactions (Skyrme, Gogny, …)

E/A (ρ) = Es(ρ) + Esym(ρ) β²

β=(ρn-ρp)/ρThe density dependence of Esym is rathercontroversial, since there exist effective interactionsleading to a variety of shapes for Esym:

<1 g Asysoft, >1 g Asystiff

)/( 0symE

Investigate the sensitivity of the reaction dynamics to this ingredient Put some constraints on the effective interactions EOS

Symmetry energy

Asysoft

Asystiff

Neutron skinIsovector modesPigmy resonances

around ρ0

Effective interactions and symmetry energy

γ = 1 γ = 0.5

γ = L/(3S0) ...3

)(0

00

LSEsym

Page 8: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Low-energy reaction mechanisms: Fusion, Deep-Inelastic, Charge equilibration

Fragmentation mechanisms at Fermi energies

Study of the PDR with transport theories

Page 9: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Low energy reaction mechanismsFusion vs Deep Inelastic

Page 10: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Competition between reaction mechanisms: fusion vs deep-inelastic

Fusion probabilities may depend on the N/Z of the reaction partners: - A mechanism to test the isovector part of the nuclear interaction Important role of fluctuations

36Ar + 96Zr , E/A = 9 MeV

Fusion or break-up ?

C.Rizzo et al., PRC83, 014604 (2011)

Page 11: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

36Ar + 96Zr , E/A = 9 MeV,b = 6 fm

Starting from t = 200-300 fm/c, solve the Langevin Equation (LE) for selected degrees of freedom: Q (quadrupole), β3 (octupole), θ, and related velocities

Competition between reaction mechanisms

θ

Examples of trajectories

t = 0 t = 40 t = 100 t = 140 t = 200 fm/c

z (fm)

Break-up configurations

β2 , β3, E*~250 MeV, J ~70ћ

l (ћ)

softstiff

Shvedov, Colonna, Di Toro, PRC 81, 054605 (2010)

Break-up times of the order of 500-1000 fm/c !

Extract the fusion cross section

Page 12: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Charge equilibration in fusion and D.I. collisions

D(t) : bremss. dipole radiation CN: stat. GDRInitial Dipole

A1 A2

iDKD

pNZ

PPPtDK

xNZ

XtXtXA

NZtD

npinpnp

npinpnp

,

,

1)(

,

1)()()(

,,

,,

Relative motion of neutron and proton centers of massIf N1/Z1 ≠ N2/Z2

132Sn + 58Ni , D0 = 45 fmE/A = 10 MeV

TDHF calculations

C.Rizzo et al., PRC 83, 014604 (2011)

40Ca + 100Mo

Simenel et al, PRC 76, 024609 (2007)

SMF simulations

Page 13: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

2''2

3

2

)(3

2

DA

NZ

Ec

e

dE

dP

Bremsstrahlung: Quantitative estimation

V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87 (2001)

C.Rizzo et al., PRC83, 014604 (2011)

B.Martin et al., PLB 664 (2008) 47

36Ar + 96Zr

40Ar + 92Zr

Dynamical dipole emission

D.Pierroutsakou et al., PRC80, 024612 (2009)

Experimental evidence of the extra-yield (LNS data)

soft

stiff

stiffsoft

Asysoftlarger symmetry energy, larger effect (30 %)

see also A.Corsi et al., PLB 679, 197 (2009), LNL experiments

Page 14: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

-- Charge equilibration: from dipole oscillations to diffusion

Overdamped dipole oscillation

d-t/e D(0) D(t) τd Esym

t

D(t)

Charge equilibration in D.I. collisions at ~ 30 MeV/Alow energy

Full N/Z equilibration not reached:Degree of eq. ruled by contact time and symmetry energy

Ediss / Ecm

Observable:(N/Z)CP = N/Z of light charge particlesemitted by PLF

as a function of

Dissipated energy: (impact parameter, contact time)

INDRA data, Galichet et al., PRC (2010)

TLF) (PLFE - E E kincmdiss

1(PLF)

2(TLF)

Page 15: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

B. Tsang et al., PRL 102 (2009)

Mass(A) ~ Mass(B) ; N/Z(A) = N/Z(B)

Isospin transport ratio R :

BBAA

BBAAAB

XX

XXXR

2

A dominance

mixing

B dominance

+1

0

-1-- AA and BB refer to two symmetric reactions between n-rich and n-poor nucleiAB to the mixed reaction -- X is an observable related to the N/Z of PLF (or TLF)

A

B

“Isospin diffusion” in D.I. collisions

stiff

soft

More central collisions: larger contact time more dissipation, smaller R Good sensitivity to Asy-EoS

X = N/ZPLF

SMF calculations, 124Sn +112Sn, 50 AMeV

J. Rizzo et al., NPA(2008)

(PLF)

(TLF)

X = Y(7Li)/ Y(7Be)

Comparison betweenImQMD calculations

and MSU data

B. Tsang et al., PRL 102 (2009)

Page 16: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

“Exotic” fragments in reactionsat Fermi energies

Page 17: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

TLF

PLF

)3,1(/ VIOLAREL VV

Y.Zhang et al., PRC(2011)

Fragmentation mechanisms at Fermi energies

IMF

124Sn + 64Ni 35 AMeV:4π CHIMERA detector

Fragment emission at mid-rapidity (neck emission) neutron-enrichment of the neck region

dynamical emission

E. De Filippo et al., PRC(2012)

Charge Z

Page 18: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Isospin migration in neck fragmentation

Transfer of asymmetry from PLF and TLF to the low density neck region: neutron enrichment

of the neck region Effect related to the derivative of the symmetry

energy with respect to density

PLF, TLF

neckemitted

nucleons

ρIMF < ρPLF(TLF)

Asymmetry flux

Sn112 + Sn112

Sn124 + Sn124

b = 6 fm, 50 AMeV

Density gradients derivative of Esym

The asymmetry of the neck is larger than the asymmetry of PLF (TLF) in the stiff case

J.Rizzo et al. NPA806 (2008) 79

asy-soft

asy-stiff

Larger derivative with asy-stiff larger isospin migration effects

stiff - full

Page 19: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Comparison with Chimera data

124Sn + 64Ni 35 AMeVDESE

Properties of ‘dynamically emitted’ (DE) fragments

Charge distributionParallel velocity distribution

E. De Filippo et al., PRC(2012)

Good reproduction of overall dynamics The N/Z content of IMF’s in better reproducedby asystiff (L =75 MeV)

Page 20: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

“Exotic” collective excitations in Nuclei

Page 21: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

X neutrons – protons

Xc core neutrons-protons

Y excess neutrons - core

Neutron center of mass

Proton center of mass

Isovector dipole response

PDR

GDR

The Isovector Dipole Response (DR) in neutron-rich nuclei

X.Roca-Maza et al., PRC 85(2012)

Pygmy dipole strength

Giant DR

Pygmy DR

Klimkiewicz et al.

Page 22: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

• Pygmy-like initial conditions (Y)

X

Y

X c

Neutron skin and core are coupled

The low- energy response is not sensitive tothe asy-stiffness

-- soft-- stiff-- superstiff

Baran et al.

25.0

see M.Urban, PRC85, 034322 (2012)

132Sn

Page 23: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

• GDR-like initial conditions (X)

Fourier transform of D Strength of the Dipole Response

PDR is isoscalar-like frequency not dependent on Esym

GDR is isovector-like dependent on Esym

The strength in the PDR region depends on the asy-stiffness(increases with L)Larger L larger strength , but also

Larger L larger neutron skin

2.7 % soft4.4 % stiff4.5 % superstiff

see A.Carbone et al., PRC 81 (2010)

E (MeV)

Page 24: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

The energy centroid of the PDR as a function of the mass for Sn isotopes, 48Ca, 68Ni, 86Kr, 208Pb ~ 41 A-1/3

PDR energy and strength (a systematic study)

Neutron skin extension with soft, stiff and superstiff

Correlation between the EWSR exhausted by the PDR

and the neutron skin extension

V.Baran et al., arXiv:1306.4969

soft

superstiff

stiff

soft

stiffsuperstiff

Page 25: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

A.Carbone et al., PRC 81 (2010)

“Summary” of Esym constraints

V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo, (LNS, Catania)

M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich)E.Galichet, P.Napolitani (IPN, Orsay)

Galichet 2010De Filippo 2012

Reduce experimental error bars

Perform more complete analyses

Improve theoretical description (overcome problems related to

model dependence)

Asysoft

Asystiff

Isospin diffusion

Page 26: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Heavy Ion Collisions (HIC) allow one to explore the behavior of nuclear matter under several conditions of density, temperature, spin, isospin, …

HIC from low to Fermi energies (~10-60 MeV/A) are a way to probe the density domain just around and below normal density.The reaction dynamics is largely affected by surface effects, at theborderline with nuclear structure. Increasing the beam energy, high density regions become accessible.

Varying the N/Z of the colliding nuclei (up to exotic systems) , it becomes possible to test the isovector part of the nuclear interaction(symmetry energy) around and below normal density.

Page 27: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

A.Carbone et al., PRC 81 (2010)

M.B.Tsang et al., PRC (2012)

“Summary” of Esym constraints

V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo, (LNS, Catania)

M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich)E.Galichet, P.Napolitani (IPN, Orsay)

Page 28: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Calculations:- N/Z increases with the centrality of

collision for the two systems and energies(For Ni + Ni pre-equilibrium effects)- In Ni + Au systems more isospin

diffusion for asy-soft (as expected)- (N/Z)CP linearly correlated to (N/Z)QP

PLF

PLF

CP

CP

PLF

PLF

CP

CP

N/ZCP

-- stiff (γ=1) + SIMON-- soft(γ=0.6) + SIMON

SMF transport calculations:N/Z of the PLF (Quasi-Projectile)

Squares: soft Stars: stiff

After statistical decay :

N = Σi Ni , Z = Σi Zi

Charged particles: Z=1-4

forward n-n c.m.

forward PLF

Comparison with data

Data: open points higher than full points

(n-rich mid-rapidity particles) Isospin equilibration reached for

Ediss/Ecm = 0.7-0.8 ? (open and full dots converge)

Data fall between the two calculations

Page 29: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Interpretation in terms of isovector-like and isoscalar-like modes in asymmetric systems

22 2 nnnpnnpppp

)3

(8)2tan(

0

LEI

c

ba

c

sym

Isoscalar-like

Isovector-like

soft

stiff

Energy-density variation

Curvature matrix Normal modes

n

p

)tan(

α increases with L strength in the PDR region (isoscalar-like mode) increases with L

α =450 for symmetric matter

Zero temperature

Page 30: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

stiff

soft

Fragment isotopic distribution and symmetry energy

Fragmentation can be associated with mean-field instabilities(growth of unstable collective modes)

Oscillations of the total (isoscalar-like density) fragment formation and average Z/A (see δρn /δρp )

Oscillations of the isovector density (ρn - ρp ) isotopic variance and distributions (Y2 / Y1 , isoscaling)

Study of isovector fluctuations, link with symmetry energy in fragmentation

Isovector density ρv = ρn –ρp

λ = 2π/k

nuclear matter in a box

At equilibrium, according to the fluctuation-dissipation theorem

What does really happen in fragmentation ?

Fv coincides with the free symmetry energy at the considered density

Page 31: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Full SMF simulations

T = 3 MeV, Density: ρ1 = 0.025 fm-3 , 2ρ1 , 3ρ1 I = 0.14

T

ρ

F’ follows the local equilibrium value !

The isospin distillation effect goes together with the isovector variance

Ihigh density low density

ρ

Nuclear matter in a box

freeze-out

F’ ~ T / σ

stiffsoft

stiff

soft

M.Colonna, PRL,110(2013) Average Z/A and isovector fluctuations as a function of local density ρ

Page 32: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Dissipation and fragmentation in “MD” models

ImQMD calculations, 112Sn +112Sn, 50 AMeV

More ‘explosive’ dynamics:more fragments and light clusters emittedmore ‘transparency’

What happens to charge equilibration ?

Rather flat behavior with impact parameter b:- Weak dependence on b of reaction dynamics ?- Other dissipation sources (not nucleon exchange) ? fluctuations, cluster emission weak nucleon exchange

z vy

Isospin transport ratio R

Y.Zhang et al., PRC(2011)

124Sn +112Sn, 50 AMeV

Page 33: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

Comparison SMF-ImQMD

6 fm8 fm

γ = 0.5

SMF = dashed linesImQMD = full lines

For semi-central impact parameters:

Larger transparency in ImQMD (but not so a drastic effect)

Other sources of dissipation (in addition to nucleon exchange)More cluster emission

SMF

ImQMD

γ = 0.5

Different trends in ImQMD and SMF!

What about fragment N/Z ?

γ = 2 Isospin transport R around PLF rapidity:

Good agreement in peripheral reactions

Elsewhere the different dynamics(nucleon exchange less important in ImQMD) leads to less iso-equilibration

Page 34: Probes of EOS in Heavy Ion Collisions : results from transport theories Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Nuclear Structure &

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