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Nuclear EOS at low density

Nuclear EOS at low density. Abdou Chbihi GANIL. Nuclear EOS at low density. EOS is the fundamental property of NM that descibes the relationships between E, P, T, r, d for nuclear system. Improved understanding of the S( r ) will provide : Masses, Fission barriers,

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Nuclear EOS at low density

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  1. Nuclear EOS at low density Abdou Chbihi GANIL A. Chbihi

  2. Nuclear EOS at low density • EOS is the fundamental property of NM that descibes the relationships between E, P, T, r, d for nuclear system • Improved understanding of the S(r) will provide : • Masses, • Fission barriers, • Energies of isovector collective vibrations, • Thickness of the neutron skins of neutron rich exotic nuclei • Impact on astrophysics A. Chbihi

  3. Nuclear EOS at low density • 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) : • Stellar radii, • Moments of inertia, • Crustal vibration frequencies, • 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) A. Chbihi

  4. Exploring the density dependence of symmetry energy with heavy-ion collisions 78Kr : 0.46 92Kr : 4.35 Intermediate energies Multifragmentation Probe subsaturationdensity High energies Suprasaturation density stiff soft Intermediate energies Peripheral and semi peripheral collisions saturation density GANIL RIKEN MSU LNS GSI GSI RIKEN Density ρ/ρ0 Eincident A. Chbihi

  5. Probes of the density dependence of symmetry energy by studying heavy-ion collisions and N/Z d.o.f. • At low densities reachable at GANIL, LNS, MSU, GSI • Isotopic distribution of complex fragments (GANIL, LNS, MSU) • Isoscaling of the nuclear multi-fragmentation (GANIL, LNS, MSU, GSI) • Isospin diffusion (MSU, Chimera at LNS, GANIL) • Pre-equilibrium neutron/proton (MSU, GSI) • Spectra of light cluster 3H/3He (MSU, GANIL) • Spectra mirror nuclei 7Li/7Be (MSU, GANIL) • Differential flow (GSI, MSU) • Correlation functions at low momentum (HBT, MSU, LNS) • At high densities reachable at RIKEN and GSI • Neutron-proton differential transverse flow • Neutron/proton mid-rapidity emission • p- and p-/p+ ration, • K-/K0 ratio A. Chbihi

  6. Accessing the symmetry energyoutline • From the isotopic distributions • SMF predictions • AMD predictions • Experiments 40,48Ca+40,48Ca @ E/A = 35 MeV (INDRA-VAMOS) • From the ratio 3H/3He • SMF predictions • Experiments 124,129Xe+112,124Sn @ E/A = 65-250 MeV (INDRA@ GSI) • Conclusions A. Chbihi

  7. Accessing the symmetry energyfrom isotopic distributionSMF predictions freeze-out T = 3 MeV, Density: ρ1 = 0.025 fm-3 , 2ρ1 , 3ρ1 • 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. ρ F’ ~ T / σ A. Chbihi

  8. Accessing the symmetry energyfrom isotopic distributionSMF predictions • The Esym increases with density and the trend is more pronounced with stiff, • In general, low density ->low symener -> large variance • we should see this feature in the isotopic distribution of the fragment as well as in the LP. stiff soft F’ follows the localequilibriumvalue ! A. Chbihi

  9. Accessing the symmetry energy From isotopic distributions… AMD simulations: 40Ca+40Ca,48Ca+48Ca,60Ca+60Ca,46Fe+46Fe E/A=35 MeV and b=0 Primary 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 A. Chbihi

  10. Accessing the symmetry energy A. Ono et al., Phys. Rev. C70, 041604(R) (2004) statistical treatment - z(Z) independent of Z (negligible surface effect) symmetry energy of INM - Probe density dependence of Csym(r) at subsaturation densities r<r0 A. Chbihi

  11. Primary Secondary a=A/8 Secondary a=A/16 z(Z) z(Z) z(Z) 5 10 15 5 10 15 5 10 15 Z Z Z Effects of secondary decays A. Ono, Acta Physica Hungarica A - Heavy Ion Physics, in press 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. Chbihi

  12. A. Chbihi

  13. Experiments coupling INDRA-VAMOS Symmetry energy experiments • 40Ca + 40Ca @ E/A = 35 MeV • 40Ca + 48Ca @ E/A = 35 MeV isospin diffusion • 48Ca + 40Ca @ E/A = 35 MeV isospin diffusion • 48Ca + 48Ca @ 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) • 40Ar + 64Ni @ E/A = 12.7 MeV (104Pd) • 40Ar + 60Ni @ E/A = 12.7 MeV (100Pd) • 34Ar + 58Ni @ E/A = 13.5 MeV (92Pd) • 36Ar + 58Ni @ E/A = 13.3 MeV (94Pd) • 36Ar + 60Ni @ E/A = 13.3 MeV (96Pd) A. Chbihi

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

  15. INDRA-VAMOS • INDRA : • all chargedproducts, 7°<Q<176°, MINDRA≥1 • Z, Q, F, Ek and A for Z<5 • Impact parameter and excitation energy estimation. • VAMOS Spectrometer: • 2°<Q<7°, MVAMOS= 1 • PLF : A, Z, Q, F, velocity, Q etc. • Full trajectory reconstruction. A. Chbihi

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

  17. Global view of the reaction products A. Chbihi

  18. Isotopic distributions of PLF • Broad APLF distributions • Sensitive to the n-richness of the system • N/Z up to 1.58 (11% N/Z 48Ca) A. Chbihi

  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) A. Chbihi

  20. Characteristics of LCP emitted in coincidence with the PLF ZPLF = 20 proton alpha • 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 • VCM>0 A. Chbihi

  21. 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 A. Chbihi

  22. Primary charge of the fragments ZPLF can reconstruct different Zprimary OR Zprimary can populate different ZPLF On average 2 charge units transfer A. Chbihi

  23. Toward primary mass of the fragments Zprimary= 20 Zprimary= 18 is not measured Zprimary= 16 Zprimary= 12 Can be used as an observable A. Chbihi

  24. How to obtain Aprimary 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) • ZPLF, Zprimary, (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 ZPLF, APLF, MLCP, Ek LCP • Simulations are in progress. A. Chbihi

  25. First tests of the method A. Chbihi

  26. Symmetry energy from primary fragments A. Chbihi

  27. Preliminary results on Symmetry energy Esym/T for Apr and Apr-Nn are similar; for 40Ca+40Ca As expected different for APLF 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 A. Chbihi

  28. Production cross section of exotic nuclei beyond the drip lines 40Ca+40Ca Decay modes CP, n, g… spectroscopy A. Chbihi

  29. Production cross section of exotic nuclei beyond the drip lines 48Ca+48Ca A. Chbihi

  30. INDRA@GSI experiments124,129Xe+112,124Sn @ E/A = 64-250 MeV Probe : Spectra of light cluster 3H/3He Famiano et al. PRL97.052701, 2006 A. Chbihi

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

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

  33. Etr spectra and ratio 3H/3Hefor 129,124Xe+124,112Sn @ E/A = 100 MeV 124,129Xe+112,124Sn @ E/A=100 MeV Central collisions (b<0.1 bmax) 3H 3He The interval 40<Etr (MeV/A)<60 Yield ratio independent of cluster energy -> free of spurious effects (evaporation etc.) 70°< Qcm<110° Etr (MeV/A) A. Chbihi

  34. Excitation function of 3H/3He The ratio 3H/3He 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 3H/3He ratio is only sensitive to N/Z -> Esym Coulomb correction As measured Einc/A (MeV) A. Chbihi

  35. Summary and Conclusions • Exploration of Esym(r) with HI-Collisions • Accessing the symmetry energy from • Primary experimental isotopic distributions • isospin diffusion • 3H/3He ratio A. Chbihi

  36. 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 A. Chbihi

  37. Preliminary results on Symmetry energy Esym/T for Apr and Apr-Nn are similar; for 40Ca+40Ca But different for APLF A. Chbihi

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