1. 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

2.  Clusters in nuclear reactions dynamical description  Multifragmentation reactions  Spallation reactions Content

3. < 100 fm/c Cluster omnipresence in Heavy Ion Reactions: processes P.Napolitani, Asy-EOS 2015

4. Microscopic dynamical approach Mean-fieldResidual interaction Average effect of the residual interaction one-body Fluctuations TDHF one-body density matrix two-body density matrix o Mean-field (one-body) dynamics o Two-body correlations o Fluctuations

5. 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 section Effective interaction (self consistent mean-field) Skyrme, Gogny forces Transition rate W interpreted in terms of NN cross section Semi-classical approaches … Correlations, Fluctuations k δkδk Vlasov Semi-classical approximation transport theories BUU, …+ fluct. …Molecular Dyn. Boltzmann-Langevin Collision Integral

6. From BOB to BLOB …… Fluctuations from external stochastic force (tuning of the most unstable modes) Chomaz,Colonna,Guarnera,Randrup PRL73,3512(1994) Brownian One Body (BOB) dynamics λ = 2π/k

7. 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 space by agitating the spacial density profile M.Colonna et al., NPA642(1998)449 Chomaz,Colonna,Guarnera,Randrup PRL73,3512(1994) Brownian One Body (BOB) dynamics λ = 2π/k

8. 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

9. 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

10. Wave number k = n (2π)/L L = 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)

11. SMF vs AMD: central collisions at Fermi energies Indra AMD SMF Time evolution of density variance IMF formation (spinodal mechanism) + clusters P(Z) Charge distribution IMF Abundant cluster emission in AMD Colonna, Ono, Rizzo PRC 82, 054613 (2010) light clusters Sn + Sn, 50 MeV/A

12. BLOB vs SMF: IMF in central collisions at Fermi energies Onset of multifragmentation: shifted to lower beam energy in 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 304050 E/A (MeV) Multiplicity map SMF BLOB

13. 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. data Le Fevre and Aichelin, PRL100, 042701(2008 ): QMD calculations bimodality

14. 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).

15. Trajectories in ρ – T - N/Z space Time evolution of particle emission rate and excitation energy Density contour plots Hollow configurations favour instabilities N/Z of matter bound in clusters central events onset of instabilities β stability

16. Fragment (Z>4) multiplicity Charge distribution 400 fm/c 700 fm/c cold 204060 Z Events with larger multiplicity contribute to the convex-shaped distributions IMF properties: resilience vs. fragmentation Binary events obtained by re-aggregation ! Parallel velocity distribution

17. Low-density clustering in neutron stars and neutrino-nucleon scattering  Neutrino transport is influenced by the presence of clusters Cooling processes in supernova explosion and neutron stars C ≡ nuclear free-energy curvature matrix ν-nucleon elastic scattering cross section θ W = Weinberg angle cluster properties ν scattering

18. Clusters in Neutron Stars

19. λ = 2π/q Matter composed of n,p,e nuclear matter electrons 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

20. 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

21. C. Fuchs, H.H. Wolter, EPJA 30(2006)5 E/A (ρ) = E(ρ) + E sym (ρ) β² β=(N-Z)/A Often used parametrization:  asy-soft,  asy-stiff 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 γ = L/(3S 0 ) or J asy-soft asy-stiff β=0.2