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Testing the behavior of n-rich systems away from normal density. Maria Colonna Laboratori Nazionali del Sud (Catania ). Eurorib’ 10 June 6-11, 2010 --- Lamoura. Equation of State (EoS) of asymmetric nuclear matter the nuclear energy density functionals,

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slide1

Testing the behavior of n-rich systems

away from normal density

Maria Colonna

Laboratori Nazionali del Sud (Catania)

Eurorib’ 10

June 6-11, 2010 --- Lamoura

slide2

Equation of State (EoS) of asymmetric nuclear matter

the nuclear energy density functionals,

effective interactions

  • Self-consistent MF calculations (and extensions) are a powerful framework to understand the structure of medium-heavy nuclei.

Isoscalar, spin, isospin densities, currents …

Source: F.Gulminelli

In this context relativistic <=> non-relativistic …only a matter of functional

  • Widely employed in the astrophysical context (modelization of neutron stars
  • and supernova explosion)
slide3

Often used parametrization:

g<1 asy-soft, g>1 asy-stiff

asy-stiff

asy-soft

asy-stiff

asy-soft

zoom at low density

The largest uncertainties concern the isovector part of the nuclear interaction :

The symmetry energy

Esym = E/A (β=1) – E/A(β=0)

E/A (ρ) = Es(ρ) + Esym(ρ) β²

β=(N-Z)/A

C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)

Esym(ρ) = J

γ = L/(3J)

slide4

Nuclear astrophysics

Nuclear structure

Nuclei- neutron star

connection !

Focus on Esym at low density

M.Centelles et al, PRL(2009)

I.Vidana et al., PRC80(2009)

Correlation between n-skin and L

Properties of n-rich nuclei depend on

low-density Esym (because of surface effects !)

The crust-core transition density

decreases with L

slide5

asy-soft

18 r (2 – r) SKM*(soft)

18 r stiff

18 (2r2 )/(1+r) stiff (superstiff)

Esympot =

asy-stiff

r = ρ/ρ0

Isospin effects in reaction mechanisms at Fermi energies

Transient states of nuclear matter

in several conditions !

  • Symmetry energy parameterizations are implemented into

transport codes (Stochastic Mean Field - SMF) and confronted

to experimental data for specific reaction mechanisms and related observables Chomaz,Colonna, Randrup Phys. Rep. 389 (2004)

  • Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005)

Parametrizations used in SMF simulations

γ~0.6

γ~1

slide6

ISOSPIN TRANSPORT AT FERMI ENERGIES

  • Reactions between systems with different N/Z
  • Isospin diffusion (in the low density interface) is driven by the symmetry energy
  • Information on Esym at low density

1(PLF)

Exchange of energy, mass,

isospin between 1 and 2

2(TLF)

Reaction plane

  • If x = N/Z or f(N/Z)
  • Isospin equilibration
  • 2) Contact time measured by
  • kinetic energy dissipation
  • Symmetry energy

Path towards equilibrium of the observable x

x1,2(t) – xm = (x1,2 – x m) e-t/τ

xm = (x1 + x2)/2

t contact time

τ dissipation time

for observable x

  • How to access the N/Z of the PLF ?
  • Isotopic content of light charged particle emission
  • as a function of the dissipated energy

Galichet et al.,

Phys. Rev. C79, 064615 (2009)

INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A

slide7

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

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

Comparison with data

-- stiff (γ=1) + SIMON

forward PLF

-- soft(γ=0.6) + SIMON

forward n-n c.m.

PLF

PLF

CP

CP

N/ZCP

PLF

PLF

CP

CP

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
slide8

Path towards equilibrium of the observable x

x1,2(t) – xm = (x1,2 – x m) e-t/τ

xm = (x1 + x2)/2

Isospin transport ratio R

1(PLF)

X1

2(TLF)

B. Tsang et al. PRL 92 (2004)

Xm

X2

R1,2(t) = (x1,2(t)– xm) / |x1,2 – xm|

R1,2 = ±e-t/τ

τ Esym

N/Z of largest fragment

Ni + Ni

@ 15,40

AMeV

P.Napolitani et al., PRC(2010)

yred

slide9

Microscopic BHF calculations

Nuclear reactions:

Isospin diffusion

Li, Lombardo, Schulze, Zuo,

PRC77, 034316 (2008)

Tsang et al., PRL(2009)

Focus on Esym below normal density

Strength of PDR

Galichet et al.,(2009)

Mass formula

Neutron skin thickness

A.Carbone et al., PRC(R) (2010) and ref.s therein

GMR (Li et al, PRL 2007)

Pre-equilibrium dipole emission

slide10

Conclusions

  • Need to enlarge the systematics of data (and calculations) to
  • validate the current interpretation and the extraction of Esym
  • (consensus on Esym~(ρ/ρ0)γ with γ~0.6-1 at low density)
  • Still large uncertainties at high density (FAIR, NICA,
  • RIKEN, …)

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)

slide11

Time evolution of the one-body distribution function

Vlasov

Boltzmann

Langevin

Loss term

Transport model: Semi-classical approach to the many-body problem

Vlasov

Boltzmann

Langevin

Vlasov: mean field

Boltzmann: average collision term

Langevin: randomwalk in phase-space

D(p,p’,r)

D(p,p’,r)

w

Ensemble average

Fluctuation variance:

σ2f =<δfδf>

SMF model : fluctuations projected onto ordinary spacedensity fluctuations δρ

slide12

J.Rizzo et al, NPA (2008)

Isospin diffusion

Pre-equilibrium dipole oscillation

V.Baran et al, PRC79, 021603 (2009).

M.Colonna et alPRC78,064618(2008)

Isospin distillation (liquid-gas)

asy-stiff - - -asy-soft

Optical potentials

(isospin & momentum dependence of forces)

Li & Lombardo, PRC78,047603(2008)

Probes of the symmetry energy (at low density)

slide13

Constraints on Esym

GDR

Fragment N/Z,

Central collisions

mass formula

L=3r0dEsym/dr|r0

GDR

P0=r0L/3

Isospin

diffusion

BHF

Pygmy dipole

  • M.Colonna et alPRC78,064618(2008)
  • Galichet,Colonna et al
  • PRC79(2009)064615
  • B.Tsang et al
  • PRL102(2009)122701
  • Trippa, Colò, Vigezzi
  • PRC77(2008)061304
  • P.Danielewicz J.Lee
  • nucl-th/08073743
  • A.Klimkiewicz et al
  • PRC76(2007)051603
  • Li,Lombardo et al
  • PRC77(2008)034316

Symmetry energy at ρ0 (normal density)

slide14

Lane potential

n

effective mass different for protons and neutrons

data

p

Symmetry energy and mass splitting

E/A (ρ) = Es(ρ) + Esym(ρ) β²

β=(N-Z)/A

asy-stiff

Often used parametrization:

g<1 asy-soft, g>1 asy-stiff

asy-soft

asy-stiff

asy-soft

C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)

Momentum dependence

zoom at low density

Symmetry potential

m*n < m*p

Asy-soft

Asy-stiff

m*n > m*p

slide15

1(PLF)

2(TLF)

Ediss

Sorting variable and PLF properties

The dissipated energy is well correlated to

the impact parameter

The charge of the reconstructed PLF is

in reasonnable agreement with the data

Galichet et al.,

Phys. Rev. C79, 064615 (2009)

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