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< 100 fm/c Cluster omnipresence in Heavy Ion Reactions: processes P.Napolitani, Asy-EOS 2015
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Properties of clustered nuclear matter in nuclear reactions
Maria Colonna INFN - Laboratori Nazionali del Sud (Catania)
NUFRA 2015
4-11 October 2015 Kemer (Antalya), Turkey
Clusters in nuclear reactions dynamical description
Multifragmentation reactions
Spallation reactions
Content
< 100 fm/c
Cluster omnipresence in Heavy Ion Reactions: processes
P.Napolitani , Asy-EOS 2015
)(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
Microscopic dynamical approach
Mean-field Residual interaction
)||,( 21 vK F
),( vK F KK
Average effect of the residual interaction
one-body
Fluctuations
TDHF
0 K
one-body density matrixtwo-body density matrix
o Mean-field (one-body) dynamics
o Two-body correlations
o Fluctuations
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 sectionEffective interaction
(self consistent mean-field) Skyrme, Gogny forces
)'()','(),( ttCtpKtpK
ff 1
Transition rate Winterpreted in terms ofNN cross section
K
Semi-classical approaches …
collcoll IfIhft
tprfdt
tprdf
,,,,,
Correlations, Fluctuations
k δkVlasov
Semi-classical approximation transport theories
BUU, …+ fluct.
…Molecular Dyn.Boltzmann-Langevin
Collision Integral
From BOB to BLOB ……
Fluctuations from external stochastic force (tuning of the most unstable modes)
Chomaz,Colonna,Guarnera,RandrupPRL73,3512(1994)
Brownian One Body (BOB) dynamics
λ = 2π/k
From BOB to BLOB ……
Fluctuations from external stochastic force (tuning of the most unstable modes)
Stochastic Mean-Field (SMF) model :Fluctuations are projected on the coordinate spaceby agitating the spacial density profile
M.Colonna et al., NPA642(1998)449
Chomaz,Colonna,Guarnera,RandrupPRL73,3512(1994)
Brownian One Body (BOB) dynamics
λ = 2π/k
Clouds of test particles (nucleons) are moved once a collision happens Shape modulation of the packet ensures Pauli blocking is respected
Boltzmann-Langevin One Body (BLOB) model :fluctuations implemented in full phase space
From BOB to BLOB ……
Rizzo,Chomaz,Colonna, NPA 806,40(2008)Napolitani and Colonna, PLB 726,382(2013)
W.Bauer,G.F.Bertsch,S.DasGupta,PRL58,863(1987)
test particles
BLOB calculations: Unstable nuclear matter (spinodal instabilities - negative curvature of free energy)
P.Napolitani et al., EPJ Web of Conferences 88, 00003 (2015) SKM* interaction
Wave number k = n (2π)/LL = 39 fm
Fluctuations and dispersion relation
2π/k
BLOB calculations: Unstable nuclear matter
SKM* interaction
P.Napolitani et al., EPJ Web of Conferences 88, 00003 (2015)
SMF vs AMD: central collisions at Fermi energies
IndraAMD
SMF
Time evolution of density variance
IMF formation (spinodal mechanism)
+ clusters
P(Z)
Charge distribution
IMF
Abundant cluster emission in AMD
Colonna, Ono, RizzoPRC 82, 054613 (2010)
light clustersSn + Sn, 50 MeV/A
BLOB vs SMF: IMF in central collisions at Fermi energies
Onset of multifragmentation:
shifted to lower beam energyin BLOB
(in better agreement with exp.INDRA)
Multiplicity contour plot
Rizzo,Chomaz,Colonna, NPA 806,40(2008)Napolitani and Colonna, PLB 726,382(2013)
20 30 40 50E/A (MeV)
Multiplicity map
SMFBLOB
Size distribution of potential concavities bound matter
residue
fragments
Bimodality in central collisions at Fermi energies (with BLOB)
At the onset of multifragmentation: The system oscillates between resilience to a residue and fragment production
Pichon et al., NPA779, 267 (2006) : exp. dataLe Fevre and Aichelin, PRL100, 042701(2008 ): QMD calculations
bimodality
Spallation processes studied with BLOB: a dynamical description
Two contributions in the velocity spectra:
- concave shape (Coulomb ring) - convex shape : multifragmentation ??
One BLOB event
Napolitani and Colonna, PRC 92, 034607 (2015) GSI experiment, Napolitani et al., PRC 76, 064609 (2007).
Trajectories in ρ – T - N/Z space
Time evolution of particle emission rateand excitation energy
Density contour plotsHollow configurationsfavour instabilities
N/Z of matter bound in clusters
central events onset of instabilities
β stability
Fragment (Z>4) multiplicity
Charge distribution
400 fm/c700 fm/ccold
20 40 60 ZEvents with larger multiplicitycontribute to the convex-shaped distributions
IMF properties: resilience vs. fragmentation
Binary eventsobtained by re-aggregation !
Parallel velocity distribution
Low-density clustering in neutron starsand neutrino-nucleon scattering
Neutrino transport is influencedby the presence of clusters
Cooling processes in supernova explosion and neutron stars
C ≡ nuclear free-energy curvature matrix
ν-nucleon elastic scattering cross section
θW = Weinberg angle
cluster properties ν scattering
Clusters in Neutron Stars
λ = 2π/q
Matter composed of n,p,e
nuclear matterelectrons
surface terms
Coulomb terms
ν elastic cross section
Test the sensitivity to:
o Density parametrization of the symmetry energy in Skyrme interactions(SAMI 27 vs SAMI37)
o n-n pairing correlations
Crossing of spinodal border
preliminary
Burrello, Colonna, Matera, in preparation
Collaborators: P.Napolitani (IPN-Orsay)S.Burrello (LNS), F.Matera (Univ. Firenze)
o New implementations of the BL equation (BLOB model)give an improved description of IMF production
interplay between mean-field and correlation effects needs to be further investigated (see pBUU, AMD …) light cluster production
Important implications of clustering in the astrophysical context
Conclusions
C. Fuchs, H.H. Wolter, EPJA 30(2006)5
E/A (ρ) = E(ρ) + Esym(ρ) β² β=(N-Z)/A
Often used parametrization:
g1 asy-soft, g1 asy-stiff
g )/( 0potsymE
Effective interaction and Symmetry Energy
asy-stiff
asy-soft
zoom at low density
asy-soft
asy-stiff
asy-soft
asy-stiff
n
p
Symmetry potential :
- Below normal density : larger per asy-soft
- Above normal density: larger for asy-stiff
...3
)(0
00
LSEsym
γ = L/(3S0)
or J
asy-soft
asy-stiff
β=0.2