Reaction mechanisms in transport theories:a test of the nuclear effective interaction

Maria Colonna INFN - Laboratori Nazionali del Sud (Catania)

NN201211TH INTERNATIONAL CONFERENCE ON

NUCLEUS-NUCLEUS COLLISIONSMay 27-June 1, 2012San Antonio, Texas

Collective excitations in neutron-rich systems

Dissipation and fragmentation mechanisms at Fermi energies

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)

Mean-field effects well described, but fluctuations underestimated…

collcoll IfIhft

tprf

dt

tprdf

,

,,,, Residual interaction:Correlations, Fluctuationsk δk

)(KC F

ff 1(1,2) (3,4)

ˆ H

E

EeffH

Effective interactions

EDF theories: The exact density functional is approximated with powers and gradients of one-body nucleon densities and currents.

Stochastic Mean-Field (SMF) model

Two-body Collision Integral

Fluctuations in collision integral

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

)/( 0potsymE

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

Symmetry energy

Asysoft

Asystiff

Neutron skinIsovector modesPigmy resonances

around ρ0

Effective interactions and symmetry energy

γ = 2

γ = 0.5

“Exotic” collective excitations in Nuclei

Isovector dipole response

PDR

GDR

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

The DR in 132Sn: a study within semi-classical transport theories

The neutron skin is sensitive to asy-stiffness: larger in the stiff cases

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

Pygmy dipole strength

Giant DR

Pygmy DR

Klimkiewicz et al.

Isovector dipole moment (L = 1)

X neutrons – protons

Xc core neutrons-protons

Y excess neutrons - core

Neutron center of mass

Proton center of mass

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

19.5%: too much !

Analysis of collective motion with transport theory (Vlasov)

• Pygmy-like initial conditions (Y)

X

Y

Fourier transform of D Strength of the Dipole Response

X c

Neutron skin and core are coupled

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

-- soft-- stiff-- superstiff

Baran et al.

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

D

Pygmy-like

GDR (isovector-like)

PDR (isoscalar-like)

θ

PDR is isoscalar-like 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 θ , but also Larger L larger neutron skin

2.7 % soft4.4 % stiff4.5 % superstiff

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

Fermi energy mechanisms: Dissipation and fragmentation

in Heavy Ion Collisions

Diffusion: mass exchange, charge equilibration, energy dissipation

Dissipation and fragmentation in “MF” models

d-t/AB e (t)R ex-t/τ

kin ABkin e 0)(t E (t)E exd /ττ

kinkin ABAB 0)](tE/ [E R

R

SMF calculations, 124Sn +112Sn, 50 AMeV

Isovector modes faster than isoscalar modes: τd/τex < 1

Larger symmetry energy at low density:

Faster equilibration with soft

(PLF)

(neck)

Neck instabilities: important role of fluctuations….but still ‘mean-field’ dominated mechanism: isospin migration

soft

stiff

Relative weight of Is and Iv dissipation:

J. Rizzo et al., NPA(2008)

Isospin transport ratio

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

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

Look at the correlation betweencharge and velocity of PLF residues

and IMF’s (2<Z<9) multiplicity

N/Z of neck fragments can help to check the reaction dynamics Isospin as a tracer

• Mid-peripheral impact parameters: Results are model-dependentImportant to study the reaction dynamics (dissipation and nature of dissipation)

Summary

Mechanisms at Fermi energies

PLF

IMF’s V.Baran, B.Frecus (Bucharest),M. Di Toro (LNS)Y.Zhang (CIAE, Beijing)

In collaboration with

Collective excitation in n-rich nuclei:

transport theories predict a good sensitivity to asy-EoS (GDR energy) PDR is isoscalar-like, its relative strength depends on asy-EoS

Isospin transport and fragmentation mechanisms in semi-central collisions

Simple hydro picture

IDDj

IDDjIppp

Innn

I

EIEjj sym

sympn

)()(

Diffusion Driftdrift diffusion

-- Drift: Isospin migration

ρneck < ρPLF(TLF)

Asymmetry flux

-- Diffusion: charge equilibrationOverdamped dipole oscillation

d-t/e D(0) D(t) τd Esym

t

D(t)

neck instabilitiessoft

stiff

β=(ρn-ρp)/ρ

Sn112 Sn124

b = 6 fm, 50 AMeV

Neck fragments are neutron-richer than PLF-TLF

neck

PLF-TLF

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

R(t) = 2(xAB(t) – xm) / (xA – xB) RAB = e-t/τd τd Esym

-- X is an observable related to the N/Z of the projectile-like fragments (PLF)

A

B

Tools to study charge equilibration between A and B

xm = (xA + xB)/2

stiff

soft

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

SMF calculations

124Sn +112Sn,50 AMeV

X = N/ZPLF

t = contact time

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

1) GDR-like initial conditions (X)D

GDR (isovector-like)

PDR (isoscalar-like)

Pygmy-like

GDR (isovector-like)

PDR (isoscalar-like)

θ

2.7 % soft4.4 % stiff4.5 % superstiff

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' ),|(| 2 vKK F' )||,( 21 vF'

Average effect of the residual interaction

one-body

Fluctuations

TDHF

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