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Phase transition in Nuclei Olivier LOPEZ

Phase transition in Nuclei Olivier LOPEZ. Séminaire 1-2-3 – Décembre 2006 - LPC Caen. QGP . 200 A GeV . Hadron. 100 A MeV . Gas. 50 A MeV . Liquid. 20 A MeV . Phase diagram of NM. Big Bang. 20 200 MeV. Temperature. LG Coexistence. 1 5?. Density  .

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Phase transition in Nuclei Olivier LOPEZ

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  1. Phase transition in NucleiOlivier LOPEZ Séminaire 1-2-3 – Décembre 2006 - LPC Caen

  2. QGP 200 AGeV Hadron 100 AMeV Gas 50 AMeV Liquid 20 AMeV Phase diagram of NM Big Bang 20 200 MeV Temperature LG Coexistence 1 5? Density 

  3. Underlying Physics • DFT approach to nuclear physics: towards an universal functional • Study the energy functional for asymmetric nuclear matter • Constrain the isovector part of the energy (symmetry energy) • Produce sub- and super-saturation density matter through HI-induced reactions • Nuclear matter phase diagram and finite nuclei phase transitions • Scan the low-temperature region of the nuclear matter phase diagram • Characterize the phase transition (location, order, critical points,…) • Evidence finite size effects (anomalies in thermodynamical potentials) • Complementary to the ALICE Physics program at higher energy (QGP) • From finite nuclei to dense nuclear matter • Constrain Mean-Field models for Astrophysics • Study the structure and pahse properties of Neutron Star crusts • Understand the dynamics of supernova type II explosion (EOS)

  4. E = <y | H | y> H = <f | Heff | f > = E[r] Density Functional Theory Self-consistent mean field calculations (and extensions) are probably the only possible framework in order to understand the structure of medium-heavy nuclei.

  5. Symmetry energy (basics) • Standard Bethe-Weisäcker formula for Binding Energy : E = -avA + asA2/3 + acZ2/A1/3+asym(N-Z)2/A + d • Symmetry Energy : Esym = asym(N-Z)2/A is therefore the change in nuclear energy associated to the changing of proton-neutron asymmetry N-Z • In nuclear matter (isoscalar+isovector) : E(rn, rp) = E0(r) + E1(rn, rp) with E1(rn, rp) = S(r)(rn-rp)/r2 • Pressure : P = r2E/r

  6. Symmetry Energy (questions) • Little is known at super and sub-saturation density • Dependence on the neutron-proton asymmetry ?

  7. Multifragmentation and Phase transition Phase transition and Neutron stars (Extended) MF theories with a density functional constraint in a large density domain are a unique tool to understand the structure of neutron stars.

  8. Multifragmentationas a possible signature ofthe liquid-gas phase transition

  9. Threshold for Multifragmentation From G. Bizard et al., Phys. Lett. B 302, 162 (1993)

  10. Hot nuclei and de-excitation Evaporation Multifragmentation Vaporization E*/A (MeV) 1 3 8 r < r0 T= 5-15 MeV r ~ r0 T < 5 MeV r << r0 T>15 MeV

  11. Multifragmentation as a signal of liquid-gas phase transition? • Simultaneous emission for fragments : tff < tn • Equilibrated system in (r,T) plane : Isotropic emission • Nuclear system at sub-saturation density : r/r0 << 1

  12. tFF ~ tn Ncorr(qFF) - Nuncorr(qFF) R(qFF) = Ncorr(qFF) + Nuncorr(qFF) Multifragmentation as a simultaneous process Angular correlation functions : From D. Durand, Nucl. Phys. A 630, 52c (1998)

  13. Multifragmentation as an equilibrated process… The “rise and fall” of MF emission Universality Mass scaling From A. Schuttauf et al., Nucl. Phys. A 607, 457 (1996)

  14. Volume Multifragmentation at low density … Statistical Multifragmentation Model (SMM) Statistical weight : W = eS(V,T) V=(1+c)V0 with c>0 58Ni+197Au central collisions From N. Bellaize et al., Nucl. Phys. A 709, 367 (2002)

  15. Multifragmentation and statistical description • Reaction dynamics and Fermi motion is not taken into account → additional free parameter Erad (radial flow) for Statistical Models • Is explicitly incorporated in dynamical (semi-classical) approaches like HIPSE or QMD, (quantal) like AMD/FMD… From N. Bellaize et al., Nucl. Phys. A 709, 367 (2002)

  16. Heavy Ion Phase Space ExploratorD. Lacroix, A. Van lauwe and D. Durand, Phys. Rev. C 69, 054604 (2004)

  17. Signals of Phase transitions

  18. Free nucleons gas E*  T SMM A=100 T coexistence 10 Back-bending 5 From INDRA collaboration (1999) Fermi gas E*  T2 E*/A 10 5 From J. Pochodzalla et al., Phys. Rev. Lett. 75, 1040 (1995) Signals of phase transition • Caloric curve: T=f(E*)

  19. S Entropy T T-1 = (dS/dE)V C12 C  C1 + C2 = Temperature C1 - s12/T2 C C = dE/dT Specific heat Energy Latent Heat Signals of (1st order) Phase transition Thermodynamical relations : T-1 = (S/ E) • Abnormal energy fluctuations C = ( E/  T) = -T2(2S/  E2) If one divides the system in two independent subsystems (1)+(2) : Et = E1 + E2 And we get for the partial energy fluctuations of system (1) : s12 = T2 C1C2/(C1+C2) (true at all thermodyn. conditions)

  20. Signals of (1st order) Phase transition Peripheral Au+Au reactions Central Xe+Sn reactions M. D’Agostino et al., Physics Letters B 473, 219 (2000) N. Le Neindre, PHD Thesis Caen (1999)

  21. Liquid-gas phase transition • Critical phenomena : power laws, scalings, exponents • Caloric curves : back-bending • Universal scaling : D-scaling (order-disorder) • Disappearance of collective properties : Hot GDR, Shape transition (Jacobi) • Abnormal fluctuations : negative capacities/susceptibilities • Charge correlations : spinodal decomposition • Bimodality : order parameter for phase transition

  22. The case of Bimodality

  23. Bimodality : theoretical aspects • Related to a convex intruder of the S(X) • Appearance of a double-humped distri-bution for the proba-bility distribution P of the order parameter X • Examples : X=E X=V From Ph. Chomaz, M. Colonna and J. Randrup, Phys. Rep. 389, 263 (2004)

  24. Bimodality : experimental results • Peripheral Au+Au reactions at E/A=80 MeV • Transverse energy sorting (→ T) • Bimodality of Zmax, Zasym is observed in the third panel From M. Pichon, B. Tamain et al., Nucl. Phys. A 779, 267 (2006)

  25. Bimodality : interpretation Normal density (J) vs dilute (E*) system ? Same T From O. Lopez, D. Lacroix and E. Vient, Phys. Rev. Lett. 95, 242701 (2005)

  26. Futures

  27. SPIRAL/SPIRAL2 • Isospin dependence of the level-density parameter for medium-sized nuclei • Limiting temperature for nuclei • Cluster emission threshold for p-rich nuclei around A=115 for moderate E*/A (~1-2 MeV) • Isospin dependence of the liquid-gas phase transition • Mass splitting of p-n in asymmetric nuclear matter • Link to astrophysics and compact nuclear matter (NS)

  28. INDRA-SPIRAL experiments : status • E494S : Isospin dependence of the level-density parameter • 33,36,40Ar + 58,60,64Ni at E/A=11.1-11.7 MeV => Pd isotopes, E*/A=2-3 MeV • Coupling with VAMOS • Scheduled in March-April 2007 (moving D5-G1 is planned 01/07) • E475S : Emission threshold for complex fragments from compound nuclei of A=115 and N~Z (p-rich) • 75,78,82Kr + 40Ca at E/A=5.5 MeV • Done in March 2006 (calibration under progress)

  29. Isospin dependence of the level-density parameter a • E* dependence : a = a A with : a = 1/(K+kE*/A) K =7 , k =1.3 • N-Z dependence is assumed • (A) a = a Ae-b(N-Z)2 • (B) a = a Ae-g(Z-Z0)2 From S. I. Al-Quraishi et al., Phys. Rev. C 63 (2005), 065803

  30. Long-term range

  31. MINIBALL/MSU EOS ALADIN ISIS INDRA CHIMERA NIMROD LHASSA Need for new detectors 4p array (exclusive measurements) Low Energy thresholds (E/A<1 MeV/u) Mass and charge identification (1<A<100) Very High angular resolution (Dq<0.5°) Modularity / Flexibility (coupling/transportation) FAZIA Four pi A and ZIdentification Array

  32. FAZIA : next generation 4p array • Compactness of the device • Ebeam from barrier up to 100 A.MeV • Telescopes: Si-ntd/Si-ntd/CsI • Possibility of coupling with other detectors • Complete Z (~70) and A (~50) id. • Low-energy & identification threshold • Digital electronics for energy, timing and pulse-shape id.

  33. FAZIA project • Visit us at http://fazia.in2p3.fr Courtesy of JM Gautier (LPC Caen)

  34. FAZIA : next-gen 4p array E/A= 6.2 MeV • Digital electronics • Pulse Shape Analysis E/A= 7.8 MeV 36Ar 40Ar Tandem Orsay (2003) CIME / GANIL Sept. 06

  35. Long-term range is: EURISOL • (I) Density dependence of the nuclear symmetry energy (DDSE) 56Ni - 74Ni, 106Sn -132Sn, E/A = 15 – 50 MeV • (II) Neutron-Proton effective mass splitting (NPMS) 56Ni - 74Ni, 106Sn - 132Sn , E/A=50-100 MeV • (III) Isospin-dependent phase transition (IDPT) 56Ni - 74Ni, 106Sn -132Sn, 200Rn - 228Rn, E/A = 30 – 100 MeV • (IV) Isospin fractionation, Isoscaling (IFI) 56Ni - 74Ni, 106Sn -132Sn, 200Rn - 228Rn, E/A = 30 – 100 MeV Key Points are : • large panoply of beams (light, medium, large A) over the maximal N/Z extension • Beam energy range around and above the Fermi domain (15-100AMeV) • Beam intensity around 106-108pps, small emittance, good timing (<1ns)

  36. Phase transition in Nuclei To be continued…

  37. Nature of Phase transitions Phase transitions reflect the self-organization of a system and are ruled by common properties such as predicted by universality classes and Renormalization Group theory. • Solid, liquid and gas phases • Plasma (electrons, QGP, ...) • Magnetic properties in solid state matter (para/ferromagnets) • Bose-Einstein condensates • Superfluidity (Cooper pairs) • Fund. symmetries breakings (matter/antimatter, electroweak, …) • Nuclei ! …

  38. Boltzman-Langevin (Stochastic Mean-Field) T (MeV) Metastable regions 10-15 “GANIL” trajectory Spinodal region /0 0.3 1 A. Guarnera et al, Phys. Lett. B 403, 191 (1997) Privileged wavelength are formed : R ~10 fm R  10 fm Dynamics of the phase transitionSpinodal decomposition?

  39. Neutron-proton asymmetry is different between the bulk and surface for exotic nuclei Modified BW formula : E = -aVA + asA2/3 + ac + + d For A>>1, → asym, forsmall A → weakening of SE r(r) neutron proton r asym asym V V Symmetry Energy (future) (N-Z)2 Z2 A1/3 1 + A-1/3asym/asym V S A

  40. Multifragmentation as an equilibrated process… 129Xe+natSn at 50AMeV; Multifragmentation dN dcos(qcm) -1 cos (qcm) +1 Isotropic emission in cm frame From N. Marie et al., Phys. Lett. B 391, 15 (1996)

  41. Phase transition and critical phenomena • Power laws and scaling • Power law of the A-distribution : P(A) = A-t f(eAs) e = (T-Tc)/Tc • 3D Ising Model : t = 2.2 s = 0.66 • Experimentally : t = 2.12 ± 0.13 s = 0.64 ± 0.04 From M. D’Agostino et al., Nucl. Phys. A 650, 329 (1999)

  42. Bimodality : exp. results • Observed whatever the sorting • Characteristic of a 1st order phase transition

  43. 4He+116-124Sn E=180 MeV 124Ba 130Ba 138Ba E*/A ≈ 1.5 MeV From J. Brzychczyk et al., Phys. Rev. C 47, 1553 (1993) Statistical Models and drip lines • Enhancement of Carbon emission for p-rich nuclei • Hauser-Feshback calculations (BUSCO) for Ba isotopes 75,78,82Kr + 40Ca at E/A=5.5 MeV forming CN 115-122Ba !

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