1. ECT*, Trento 2013A. Chbihi1 Nuclear EOS at low density Abdou Chbihi GANIL

2. Nuclear EOS at low density EOS is the fundamental property of NM that descibes the relationships between E, P, T,  for nuclear system ECT*, Trento 2013A. Chbihi2 Improved understanding of the S(  ) will provide : o Masses, o Fission barriers, o Energies of isovector collective vibrations, o Thickness of the neutron skins of neutron rich exotic nuclei o Impact on astrophysics

3. Nuclear EOS at low density ECT*, Trento 2013A. Chbihi3 Neutron stars and type II supernovae are composed of macroscopic quantities of asymmetric NM at wide range of densities. Experimental information on EOS can help improving predictions of neutron star observables (satellite observatories) : o Stellar radii, o Moments of inertia, o Crustal vibration frequencies, o neutron star cooling rates Major theoretical uncertainties are due to absence of strong constraints on Esym of the EOS Constraints derived from NS observations should be supported by laboratory measurements (effective interaction)

4. ECT*, Trento 2013A. Chbihi4 Exploring the density dependence of symmetry energy with heavy-ion collisions Intermediate energies Multifragmentation Probe subsaturation density High energies Suprasaturation density soft stiff Density ρ/ρ 0 GANIL RIKEN MSU LNS GSI RIKEN Eincident Intermediate energies Peripheral and semi peripheral collisions saturation density 78 Kr : 0.46 92 Kr : 4.35

5. ECT*, Trento 2013A. Chbihi5 At low densities reachable at GANIL, LNS, MSU, GSI o Isotopic distribution of complex fragments (GANIL, LNS, MSU) o Isoscaling of the nuclear multi-fragmentation (GANIL, LNS, MSU, GSI) o Isospin diffusion (MSU, Chimera at LNS, GANIL) o Pre-equilibrium neutron/proton (MSU, GSI) o Spectra of light cluster 3 H/ 3 He (MSU, GANIL) o Spectra mirror nuclei 7 Li/ 7 Be (MSU, GANIL) o Differential flow (GSI, MSU) o Correlation functions at low momentum (HBT, MSU, LNS) At high densities reachable at RIKEN and GSI o Neutron-proton differential transverse flow o Neutron/proton mid-rapidity emission o  - and  - /  + ration, o K - /K 0 ratio Probes of the density dependence of symmetry energy by studying heavy-ion collisions and N/Z d.o.f.

6. Accessing the symmetry energy outline From the isotopic distributions –SMF predictions –AMD predictions –Experiments 40,48 Ca+ 40,48 Ca @ E/A = 35 MeV (INDRA- VAMOS) From the ratio 3 H/ 3 He –SMF predictions –Experiments 124,129 Xe+ 112,124 Sn @ E/A = 65-250 MeV (INDRA@ GSI) Conclusions ECT*, Trento 2013A. Chbihi6

7. Accessing the symmetry energy from isotopic distribution SMF predictions Full SMF simulations in a box for unstable matter allows the fragment formation Analysis for local density at the freeze-out: –The isovector variance for cells having the same density – if the equilibrium is obtain F will corresponds to the symmetry energy. ECT*, Trento 2013A. Chbihi7 freeze-out ρ F’ ~ T / σ T = 3 MeV, Density: ρ 1 = 0.025 fm -3, 2ρ 1, 3ρ 1

8. –The Esym increases with density and the trend is more pronounced with stiff, –In general, low density ->low sym ener -> large variance –we should see this feature in the isotopic distribution of the fragment as well as in the LP. ECT*, Trento 2013A. Chbihi8 F’ follows the local equilibrium value ! stiff soft Accessing the symmetry energy from isotopic distribution SMF predictions

9. ECT*, Trento 2013A. Chbihi9 Accessing the symmetry energy From isotopic distributions… AMD simulations: 40 Ca+ 40 Ca, 48 Ca+ 48 Ca, 60 Ca+ 60 Ca, 46 Fe+ 46 Fe E/A=35 MeV and b=0Primary fragment distributions A. Ono et al., Phys. Rev. C70, 041604(R) (2004) K(N,Z) : a global isotopic distribution constructed by combining all yield of the frag. obtained in the 4 sys

10. ECT*, Trento 2013A. Chbihi10 Accessing the symmetry energy -  (Z) independent of Z (negligible surface effect)  symmetry energy of INM - Probe density dependence of C sym (  ) at subsaturation densities  0 A. Ono et al., Phys. Rev. C70, 041604(R) (2004) statistical treatment

11. ECT*, Trento 2013A. Chbihi11 Effects of secondary decays PrimarySecondary a=A/8 Secondary a=A/16  (Z) Z ZZ 51015 10 55 Secondary decays need to be taken into account for comparison to experimental data (use of Statistical calculation. Or/and : experimentally provide the primary distributions A. Ono, Acta Physica Hungarica A - Heavy Ion Physics, in press

12. ECT*, Trento 2013A. Chbihi12

13. ECT*, Trento 2013A. Chbihi13 Symmetry energy experiments 40 Ca + 40 Ca @ E/A = 35 MeV 40 Ca + 48 Ca @ E/A = 35 MeV isospin diffusion 48 Ca + 40 Ca @ E/A = 35 MeV isospin diffusion 48 Ca + 48 Ca @ E/A = 35 MeV For B  (Tm)= 2.2, 2.12, 1.957, 1.80, 1.656, 1.523, 1.401, 1.289, 1.186, 1.091, 1.004, 0.923, 0.849, 0.782, 0.719, 0.661 Isospin dependence of level density experiments (N. Le Neindre) 40 Ar + 64 Ni @ E/A = 12.7 MeV( 104 Pd) 40 Ar + 60 Ni @ E/A = 12.7 MeV( 100 Pd) 34 Ar + 58 Ni @ E/A = 13.5 MeV ( 92 Pd) 36 Ar + 58 Ni @ E/A = 13.3 MeV ( 94 Pd) 36 Ar + 60 Ni @ E/A = 13.3 MeV ( 96 Pd) Experiments coupling INDRA-VAMOS

14. ECT*, Trento 2013A. Chbihi14 INDRA Q1 Q2 Dipole beam detection VAMOS PLF (E503) or residues (E494s) High Isotopic Resolution INDRA in coincidence LCP /IMF event characterization (b, excitation energy)

15. INDRA-VAMOS ECT*, Trento 2013A. Chbihi15 INDRA : all charged products, 7°<  M INDRA ≥1 Z,  E k and A for Z<5 Impact parameter and excitation energy estimation. VAMOS Spectrometer: 2°< , M VAMOS = 1 PLF : A, Z, , velocity, Q etc. Full trajectory reconstruction.

16. ECT*, Trento 2013A. Chbihi16 40 Ca + 48 Ca @ 35 MeV/A Z=N B N F C O Ne Na Mg Al Si P S Cl Ar K Ca Be Li Result @ given B  and for a given Si detector VAMOS Spectrometer INDRA

17. Global view of the reaction products ECT*, Trento 2013A. Chbihi17

18. Isotopic distributions of PLF ECT*, Trento 2013A. Chbihi18 Broad A PLF distributions Sensitive to the n-richness of the system N/Z up to 1.58 (11% N/Z 48 Ca)

19. Reaction mechanism at fermi energy Peripheral collisions : –a few nucleons exchanges –The PLF/TLF can be moderately excited and decay by a few LP Semi-peripheral collisions : –P and/or T breackup into two or more fragments –The PLF/TLF can be moderately excited and decay by a few LP Central collisions : production of fragments (multifragmentation) ECT*, Trento 2013A. Chbihi19

20. Characteristics of LCP emitted in coincidence with the PLF ECT*, Trento 2013A. Chbihi20 Two components drawing coulomb rings: One centered on the PLF velocity (origin) Second centered on the TLF. Velocity selection to associate LCP and PLF emitted from the same PLF V CM >0 proton alpha Z PLF = 20

21. ECT*, Trento 2013A. Chbihi21 Toward the primary fragment reconstruction Combining PLF and LCP information Small multiplicities proton and alpha up to 1.5 Moderate Ex* Trend in agreement with n-richness of the system

22. Primary charge of the fragments ECT*, Trento 2013A. Chbihi22 Z PLF can reconstruct different Z primary OR Z primary can populate different Z PLF On average 2 charge units transfer

23. ECT*, Trento 2013A. Chbihi23 Toward primary mass of the fragments Z primary = 18 Z primary = 20 Z primary = 16 Z primary = 12 is not measured Can be used as an observable

24. How to obtain A primary distributions ? Impossible without measuring the neutrons Even if we measure the neutron, their efficiency is poor, we cannot reconstruct the Aprimary in event/event basis Simulation with statistical model GEMINI (R. Charity) – Z PLF, Z primary, (Aprimary-Nn), (kinetic energy of LCP) experimental quantities –For each measured Zprimary -> mapping of (Aprimary, E*) –Fit -> Weight to each Zprimary, Aprimary, E* which reproduce Z PLF, A PLF, M LCP, Ek LCP Simulations are in progress. ECT*, Trento 2013A. Chbihi24

25. ECT*, Trento 2013A. Chbihi25 First tests of the method

26. Symmetry energy from primary fragments ECT*, Trento 2013A. Chbihi26

27. ECT*, Trento 2013A. Chbihi27 Preliminary results on Symmetry energy Esym/T for Apr and Apr-Nn are similar; for 40Ca+40Ca As expected different for A PLF Esym/T = 10, Zpr = 20 is compatible with Esym=27 MeV if one assumes T=2.5 MeV, and density close to the saturation Need to estimate the temperatures for the other Zpr from Ek of LCP

28. Production cross section of exotic nuclei beyond the drip lines ECT*, Trento 2013A. Chbihi28 Decay modes CP, n,  … spectroscopy 40 Ca+ 40 Ca

29. ECT*, Trento 2013A. Chbihi29 Production cross section of exotic nuclei beyond the drip lines 48 Ca+ 48 Ca

30. ECT*, Trento 2013A. Chbihi30 INDRA@GSI experiments 124,129 Xe+ 112,124 Sn @ E/A = 64-250 MeV Probe : Spectra of light cluster 3 H/ 3 He Famiano et al. PRL97.052701, 2006

31. Study of Light Fragment Emission: 136,124 Xe+ 124,112 Sn, E = 32,.,150 AMeV, Single yield ratios son: asysoft, m n *>m p * stn: asystiff, m n *>m p * sop: asysoft, m n *<m p * stp: asystiff, m n *<m p * Single ratio n/p neutron rich Single ratio t/3He neutron rich Single ratio n/p neutron poor Effects smaller For light clusters t/He Smaller neutron excess: effects smaller E=32 AMeVE=65 AMeV AsyEOS – eff mass dominates Possibility to separate density and momentum dependence of symmetry energy E=150 AMeV E transverse /A E=150 AMeV ECT*, Trento 2013A. Chbihi31

32. Study of Light Fragment Emission: 136,124 Xe+ 124,112 Sn, E = 32,.,150 AMeV, Double yield ratios Single ratio n/p neutron poor Double ratio n/p neutron rich neutron poor Effects smaller For neutron poor system Double ratio also shows effect but less sensitive to symmetry energy E=32 AMeVE=65 AMeV AsyEOS – eff mass dominates Possibility to separate density and momentum dependence of symmetry energy E=150 AMeV E transverse /A E=150 AMeV son: asysoft, m n *>m p * stn: asystiff, m n *>m p * sop: asysoft, m n *<m p * stp: asystiff, m n *<m p * Single ratio n/p neutron rich ECT*, Trento 2013A. Chbihi32

33. E tr spectra and ratio 3H/3He for 129,124 Xe+ 124,112 Sn @ E/A = 100 MeV 124,129 Xe+ 112,124 Sn @ E/A=100 MeV Central collisions (b<0.1 bmax)  cm <110° 3H3H 3 He E tr (MeV/A) The interval 40<E tr (MeV/A)<60 Yield ratio independent of cluster energy -> free of spurious effects (evaporation etc.) ECT*, Trento 2013A. Chbihi33

34. Excitation function of 3 H/ 3 He The ratio 3 H/ 3 He is taken in the interval [40,60] MeV/A of Etrans spectra Yield ratio at mid- rapidity in central collisions is nearly constant. If corrections for Coulomb effects are included, the 3 H/ 3 He ratio is only sensitive to N/Z -> Esym As measured Coulomb correction Einc/A (MeV) ECT*, Trento 2013A. Chbihi34

35. Exploration of E sym (  ) with HI-Collisions Accessing the symmetry energy from –Primary experimental isotopic distributions –isospin diffusion –3H/3He ratio ECT*, Trento 2013A. Chbihi35 Summary and Conclusions

36. ECT*, Trento 2013A. Chbihi36 A. Chbihi, G. Verde, J.D. Frankland, J. Moisan, B. Sorgunlu, F. Rejmund, M. Rejmund, J.P. Wieleczko, Sarmishtha Bhattacharya, P. Napolitani GANIL, CEA, IN2P3 ‑ CNRS, FRANCE INFN, Catania, ITALY E. Bonnet, B. Borderie, E. Galichet, N. Le Neindre, M.F. Rivet IPN Orsay, IN2P3 ‑ CNRS, FRANCE R. Dayras, L. Nalpas, C. Volant DAPNIA/SPhN, CEA Saclay, FRANCE D. Guinet, P. Lautesse Institut de Physique Nucléaire, IN2P3 ‑ CNRS et Université, Caen Cedex, FRANCE R. Bougault, O. Lopez, B. Tamain, E. Vient LPC. IN2P3 ‑ CNRS. ENSICAEN et Université, Caen Cedex, FRANCE A. Ono Department of Physics, Tohoku University, Sendai, JAPAN R. Roy Université de Laval, Quebec, CANADA W. Trautmann, J. Lukasik GSI, D-64291 Darmstadt, GERMANY E. Rosato, M. Vigilante Dipartimento di Scienze Fisiche, Un. Federico II, Napoli, ITALY M. Bruno, M. D’Agostino, E. Geraci, G. Vannini INFN and Dipartimento di Fisica, Bologna ITALY L. Bardelli, G. Casini, A. Olmi, S. Piantelli, G. Poggi INFN and Dipartimento di Fisica, Firenze,ITALY F. Gramegna, G. Montagnoli INFN, Laboratori Nazionali di Legnaro, ITALY U. Abbondanno INFN, Trieste, ITALY M. Parlog, G. Tabacaru National Institute for Physics and Nuclear Engineering, Bucarest ‑ Maguerele, ROMANIA Saila. Bhattacharya, G. Mukherjee Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata, INDIA Paola Marini, Mark Boisjoli

37. ECT*, Trento 2013A. Chbihi37 Preliminary results on Symmetry energy Esym/T for Apr and Apr-Nn are similar; for 40Ca+40Ca But different for A PLF