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