Nuclear EOS at low density
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Transcript of Nuclear EOS at low density
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ECT*, Trento 2013 A. Chbihi 1
Nuclear EOS at low density
Abdou ChbihiGANIL
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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
ECT*, Trento 2013 A. Chbihi 2
• Improved understanding of the S(r) will provide :o Masses,o Fission barriers, o Energies of isovector collective vibrations,o Thickness of the neutron skins of neutron rich exotic nucleio Impact on astrophysics
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Nuclear EOS at low density
ECT*, Trento 2013 A. Chbihi 3
• 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)
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ECT*, Trento 2013 A. Chbihi 4
Exploring the density dependence of symmetry energy with heavy-ion collisions
Intermediate energiesMultifragmentationProbe subsaturation density
High energiesSuprasaturation density
soft
stiff
Density ρ/ρ0GANILRIKENMSULNSGSI
GSIRIKEN Eincident
Intermediate energiesPeripheral and semi peripheral collisionssaturation density
78Kr : 0.4692Kr : 4.35
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• At low densities reachable at GANIL, LNS, MSU, GSIoIsotopic distribution of complex fragments (GANIL, LNS, MSU)oIsoscaling of the nuclear multi-fragmentation (GANIL, LNS, MSU, GSI)oIsospin diffusion (MSU, Chimera at LNS, GANIL)oPre-equilibrium neutron/proton (MSU, GSI)oSpectra of light cluster 3H/3He (MSU, GANIL)oSpectra mirror nuclei 7Li/7Be (MSU, GANIL)oDifferential flow (GSI, MSU)oCorrelation functions at low momentum (HBT, MSU, LNS)
• At high densities reachable at RIKEN and GSIoNeutron-proton differential transverse flowoNeutron/proton mid-rapidity emissionop- and p-/p+ ration,oK-/K0 ratio
Probes of the density dependence of symmetry energyby studying heavy-ion collisions and N/Z d.o.f.
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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
ECT*, Trento 2013
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Accessing the symmetry energyfrom 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 2013
freeze-out
ρ
F’ ~ T / σ
T = 3 MeV, Density: ρ1 = 0.025 fm-3 , 2ρ1 , 3ρ1
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– 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 2013
F’ follows the local equilibrium value !
stiff
soft
Accessing the symmetry energyfrom isotopic distribution
SMF predictions
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Accessing the symmetry energyFrom 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
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ECT*, Trento 2013 A. Chbihi 10
Accessing the symmetry energy
- z(Z) independent of Z (negligible surface effect) symmetry energy of INM- Probe density dependence of Csym(r) at subsaturation densities r<r0
A. Ono et al., Phys. Rev. C70, 041604(R) (2004)
statistical treatment
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A. Chbihi 11ECT*, Trento 2013
Effects of secondary decaysPrimary Secondary a=A/8 Secondary a=A/16
z(Z)
z(Z) z(
Z)
Z Z Z5 10 15 15 1510 105 5
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
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ECT*, Trento 2013 A. Chbihi 12
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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 MeVFor Br (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 , 0.661Isospin 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)
Experiments coupling INDRA-VAMOS
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INDRA
Q1Q2
Dipole
beam
detection
VAMOS PLF (E503) or residues (E494s)High Isotopic Resolution
INDRA in coincidence LCP /IMF event characterization (b, excitation energy)
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A. Chbihi 15
INDRA-VAMOS
ECT*, Trento 2013
INDRA : • all charged
products, 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.
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40Ca + 48Ca @ 35 MeV/AZ=N
BNF C
ONeNa MgAlSiP SClArKCa
BeLi
Result @ given Br and for a given Si detector
VAMOS Spectrometer
INDRA
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A. Chbihi 17
Global view of the reaction products
ECT*, Trento 2013
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Isotopic distributions of PLF
ECT*, Trento 2013
• Broad APLF distributions• Sensitive to the n-richness of the system• N/Z up to 1.58 (11% N/Z 48Ca)
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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 2013
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Characteristics of LCP emitted in coincidence with the PLF
ECT*, Trento 2013
• 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
proton alphaZPLF = 20
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A. Chbihi 21ECT*, Trento 2013
Toward the primary fragment reconstructionCombining PLF and LCP information
• Small multiplicitiesproton and alpha up to 1.5
• Moderate Ex*
• Trend in agreementwith n-richness of the system
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Primary charge of the fragments
ECT*, Trento 2013
ZPLF can reconstruct different Zprimary
ORZprimary can populate different ZPLF
On average 2 charge units transfer
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A. Chbihi 23ECT*, Trento 2013
Toward primary mass of the fragments
Zprimary = 18Zprimary = 20
Zprimary = 16Zprimary = 12
is not measured
Can be used as an observable
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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. ECT*, Trento 2013
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A. Chbihi 25ECT*, Trento 2013
First tests of the method
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Symmetry energy from primary fragments
ECT*, Trento 2013
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A. Chbihi 27ECT*, Trento 2013
Preliminary results on Symmetry energy
Esym/T for Apr and Apr-Nnare similar; for 40Ca+40Ca
As expected different for APLF
Esym/T = 10, Zpr = 20is compatible with Esym=27 MeVif one assumes T=2.5 MeV, and density close to the saturation
Need to estimate the temperatures for the other Zprfrom Ek of LCP
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Production cross section of exotic nuclei beyond the drip lines
ECT*, Trento 2013
Decay modesCP, n, g… spectroscopy
40Ca+40Ca
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A. Chbihi 29ECT*, Trento 2013
Production cross section of exotic nuclei beyond the drip lines
48Ca+48Ca
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ECT*, Trento 2013 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
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A. Chbihi 31
Study of Light Fragment Emission: 136,124Xe+124,112Sn, E = 32,.,150 AMeV , Single yield ratios
son: asysoft, mn*>mp* stn: asystiff, mn*>mp* sop: asysoft, mn*<mp* stp: asystiff, mn*<mp*
Single ratio n/pneutron rich
Single ratio t/3Heneutron rich
Single ratio n/pneutron poor
Effects smaller For light clusterst/He
Smaller neutron excess: effects smaller
E=32 AMeV E=65 AMeVAsyEOS – eff mass dominates
Possibility to separate density and momentum dependence of symmetry energy
E=150 AMeV
Etransverse/A
E=150 AMeV
ECT*, Trento 2013
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A. Chbihi 32
Study of Light Fragment Emission: 136,124Xe+124,112Sn, E = 32,.,150 AMeV , Double yield ratios
Single ratio n/pneutron poor
Double ratio n/pneutron richneutron poor
Effects smaller For neutron poor system
Double ratio also shows effect but less sensitive to symmetry energy
E=32 AMeV E=65 AMeVAsyEOS – eff mass dominates
Possibility to separate density and momentum dependence of symmetry energy
E=150 AMeV
Etransverse/A
E=150 AMeV
son: asysoft, mn*>mp* stn: asystiff, mn*>mp* sop: asysoft, mn*<mp* stp: asystiff, mn*<mp*
Single ratio n/pneutron rich
ECT*, Trento 2013
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A. Chbihi 33
Etr spectra and ratio 3H/3Hefor 129,124Xe+124,112Sn @ E/A = 100 MeV
124,129Xe+112,124Sn @ E/A=100 MeVCentral collisions (b<0.1 bmax)
70°< Qcm<110°
3H
3He
Etr (MeV/A)
The interval 40<Etr (MeV/A)<60Yield ratio independent of cluster energy-> free of spurious effects (evaporation etc.)
ECT*, Trento 2013
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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
As measured
Coulomb correction
Einc/A (MeV)
ECT*, Trento 2013
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• Exploration of Esym(r) with HI-Collisions• Accessing the symmetry energy from
– Primary experimental isotopic distributions– isospin diffusion– 3H/3He ratio
ECT*, Trento 2013 A. Chbihi 35
Summary and Conclusions
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ECT*, Trento 2013 A. Chbihi 36
A. Chbihi, G. Verde, J.D. Frankland, J. Moisan, B. Sorgunlu, F. Rejmund, M. Rejmund, J.P. Wieleczko, Sarmishtha Bhattacharya, P. NapolitaniGANIL, CEA, IN2P3‑CNRS, FRANCE
INFN, Catania, ITALYE. 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, FRANCED. Guinet, P. Lautesse
Institut de Physique Nucléaire, IN2P3‑CNRS et Université, Caen Cedex, FRANCER. Bougault, O. Lopez, B. Tamain, E. Vient
LPC. IN2P3‑CNRS. ENSICAEN et Université, Caen Cedex, FRANCEA. Ono
Department of Physics, Tohoku University, Sendai, JAPANR. Roy
Université de Laval, Quebec, CANADAW. Trautmann, J. Lukasik
GSI, D-64291 Darmstadt, GERMANYE. Rosato, M. Vigilante
Dipartimento di Scienze Fisiche, Un. Federico II, Napoli, ITALYM. Bruno, M. D’Agostino, E. Geraci, G. Vannini
INFN and Dipartimento di Fisica, Bologna ITALYL. Bardelli, G. Casini, A. Olmi, S. Piantelli, G. Poggi
INFN and Dipartimento di Fisica, Firenze,ITALYF. Gramegna, G. Montagnoli
INFN, Laboratori Nazionali di Legnaro, ITALYU. Abbondanno
INFN, Trieste, ITALYM. Parlog, G. Tabacaru
National Institute for Physics and Nuclear Engineering, Bucarest‑Maguerele, ROMANIASaila. Bhattacharya, G. Mukherjee
Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata, INDIA
Paola Marini, Mark Boisjoli
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A. Chbihi 37ECT*, Trento 2013
Preliminary results on Symmetry energy
Esym/T for Apr and Apr-Nnare similar; for 40Ca+40CaBut different for APLF