Maria Colonna Laboratori Nazionali del Sud (Catania) Testing the behavior of n-rich systems away...
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Transcript of Maria Colonna Laboratori Nazionali del Sud (Catania) Testing the behavior of n-rich systems away...
Maria Colonna Laboratori Nazionali del Sud (Catania)
Testing the behavior of n-rich systems away from normal density
Eurorib’ 10June 6-11, 2010 --- Lamoura
Equation of State (EoS) of asymmetric nuclear matter the nuclear energy density functionals, effective interactions
ˆ H
E
EeffH
Self-consistent MF calculations (and extensions) are a powerful framework to understand the structure of medium-heavy nuclei.
Source: F.Gulminelli
In this context relativistic <=> non-relativistic …only a matter of functional
Isoscalar, spin, isospin densities, currents …
Widely employed in the astrophysical context (modelization of neutron stars and supernova explosion)
The largest uncertainties concern the isovector part of the nuclear interaction : The symmetry energy
E/A (ρ) = Es(ρ) + Esym(ρ) β² β=(N-Z)/A
asy-stiff
asy-soft
zoom at low density
asy-soft
asy-stiff
C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)
Esym(ρ) = J γ = L/(3J)
Esym = E/A (β=1) – E/A(β=0)
Often used parametrization:
asy-soft, asy-stiff
)/( 0potsymE
Focus on Esym at low density
The crust-core transition density decreases with L
Nuclear structure
Nuclear astrophysics
Correlation between n-skin and L
Properties of n-rich nuclei depend onlow-density Esym (because of surface effects !)
Nuclei- neutron starconnection !
M.Centelles et al, PRL(2009)I.Vidana et al., PRC80(2009)
Isospin effects in reaction mechanisms at Fermi energiesIsospin effects in reaction mechanisms at Fermi energies
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)
asy-soft
asy-stiff
Parametrizations used in SMF simulations
Esympot =
18 r (2 – r) SKM*(soft)18 r stiff18 (2r2 )/(1+r) stiff (superstiff)
r = ρ/ρ0
Transient states of nuclear matterin several conditions !
γ~0.6
γ~1
Reactions between systems with different N/ZIsospin diffusion (in the low density interface) is driven by the symmetry energy Information on Esym at low density
INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A
ISOSPIN TRANSPORT AT FERMI ENERGIESISOSPIN TRANSPORT AT FERMI ENERGIES
1(PLF)
2(TLF)
Reaction plane1) If x = N/Z or f(N/Z) Isospin equilibration2) Contact time measured by kinetic energy dissipation Symmetry energy
x1,2(t) – xm = (x1,2 – x m) e-t/τ xm = (x1 + x2)/2
t contact timeτ dissipation time for observable x
Path towards equilibrium of the observable x
Galichet et al.,Phys. Rev. C79, 064615 (2009)
How to access the N/Z of the PLF ? Isotopic content of light charged particle emission as a function of the dissipated energy
Exchange of energy, mass,isospin between 1 and 2
Calculations:- N/Z increases with the centrality ofcollision 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
R1,2(t) = (x1,2(t) – xm) / |x1,2 – xm| R1,2 = ±e-t/τ
Xm
X2
X1
x1,2(t) – xm = (x1,2 – x m) e-t/τ xm = (x1 + x2)/2
Path towards equilibrium of the observable x B. Tsang et al. PRL 92 (2004)
1(PLF)
2(TLF)
Isospin transport ratio R Isospin transport ratio R
N/Z of largest fragment
yred
Ni + Ni@ 15,40AMeV
P.N
apol
itan
i et
al.,
PR
C(2
010)
τ Esym
Focus on Esym below normal density
Strength of PDR
Mass formula
Neutron skin thickness
Li, Lombardo, Schulze, Zuo, PRC77, 034316 (2008)
Microscopic BHF calculations
Galichet et al.,(2009)
A.C
arb
one
et a
l., P
RC
(R)
(20
10)
an
d r
ef.s
th
erei
n
Nuclear reactions:Isospin diffusion
Tsang et al., PRL(2009)
GMR (Li et al, PRL 2007)
Pre-equilibrium dipole emission
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)
Conclusions
( , , ) ( , , ) ( , , ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdt
df
Ensemble average
Langevin: randomwalk in phase-space
Transport model: Semi-classical approach to the many-body problemTransport model: Semi-classical approach to the many-body problem
Time evolution of the one-body distribution function ( , , )f r p t
Boltzmann
),,()(),(),(),( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfh
i
i
Vlasov: mean field
Boltzmann: average collision term
( ) ( ) NNf i f i
dp p E E
d
3 3 32 1 2
2 1' 2'3 3 3( , ) (12 1 2 )
d p d p d pW r p f f f w
h h h Loss term
D(p,p’,r)
SMF model : fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance: σ2f = <δfδf>
D(p,p’,r) w
Probes of the symmetry energy (at low density)
Isospin diffusion J.Rizzo et al, NPA (2008)
Pre-equilibrium dipole oscillationV.Baran et al, PRC79, 021603 (2009).
Isospin distillation (liquid-gas)
asy-stiff - - -asy-soft
M.Colonna et alPRC78,064618(2008)
Optical potentials (isospin & momentum dependence of forces)
Li & Lombardo, PRC78,047603(2008)
• Trippa, Colò, Vigezzi PRC77(2008)061304
• P.Danielewicz J.Lee nucl-th/08073743
• A.Klimkiewicz et al PRC76(2007)051603
• B.Tsang et al PRL102(2009)122701
Pygmy dipole
mass formula
Isospin
diffusion
GDR
L=3
dE
sym/d
P0 =
L/3
BHF
Fragment N/Z,Central collisions
GDR
Constraints on Esym
• Li,Lombardo et al PRC77(2008)034316
• Galichet,Colonna et al PRC79(2009)064615
• M.Colonna et alPRC78,064618(2008)
Symmetry energy at ρ0 (normal density)
C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)
E/A (ρ) = Es(ρ) + Esym(ρ) β² β=(N-Z)/A
data
Momentum dependence
effective mass different for protons and neutrons
1
2
*
1
k
U
k
m
m
m qq
m*n < m*p
m*n > m*p
Asy-softAsy-stiff
n
p
* 10%np
m
2.0
Often used parametrization:
asy-soft, asy-stiff
)/( 0potsymE
Symmetry energy and mass splittingSymmetry energy and mass splitting
asy-stiff
asy-soft
zoom at low density
asy-soft
asy-stiff
2pn
Lane
UUU
Lane potential Symmetry potential
Ediss
1(PLF)
2(TLF)
The charge of the reconstructed PLF is in reasonnable agreement with the data
The dissipated energy is well correlated to the impact parameter
Sorting variable and PLF propertiesSorting variable and PLF properties
Galichet et al.,Phys. Rev. C79, 064615 (2009)