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The nuclear liquid gas phase transition

NM phase diagram. fm -3. fm -3. C.Ducoin et al 2005. The nuclear liquid gas phase transition. Francesca Gulminelli LPC Caen and Institut Universitaire de France. The status of the art The isospin degree of freedom transition observables new phenomena

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The nuclear liquid gas phase transition

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  1. NM phase diagram fm-3 fm-3 C.Ducoin et al 2005 The nuclear liquid gas phase transition Francesca Gulminelli LPC Caen and Institut Universitaire de France • The status of the art • The isospin degree of freedom • transitionobservables • new phenomena • what do we need from Eurisol • Conclusions Eurisol Workshop @ ECT*

  2. The status of the art Eurisol Workshop @ ECT*

  3. multi fragmentation P.J.Siemens Nature 1983 Boiling nuclei • Motivations: • nuclear thermometry • interdisciplinary connections • dense matter and stars Eurisol Workshop @ ECT*

  4. p+Xe 80-350 GeV Self similarity and scalings A-2.64 Fisher 1967 J.Finn et al PRL1982 nA=q0A-texp(- c0eAs) T IsIs PRL2002 Multics PRC2003 EoS PRC2003 Au Liquid-Gas t2.20.12.196 0.024 s0.710.02 0.647 0.006 g1.120.05 1.24 0.01 b0.3 0.10.305 0.005 Eurisol Workshop @ ECT*

  5. Texas A&M PRC2003 Aladin PRL1995 Caloric Curve Temperature (Degrees) Heat (Calories per grams) Eurisol Workshop @ ECT*

  6. one source Isis E900A all Fluctuations and negative heat capacity INDRA NPA 2002 Nimrod PRC 2004 INDRA-Aladin nucl-ex 2005 Eurisol Workshop @ ECT* Multics NPA 2003

  7. Au+Au 80 A.MeV INDRA@GSI data "reservoir" Z2 Bimodality Z1 Z1 T 197Au 197Au order parameter: charge asymmetry Z1-Z2 Z1-Z2 B.Tamain et al. 2005 Eurisol Workshop @ ECT*

  8. rp Sc’= Sc+bmtsr Spinodal Decomposition Spontaneous fluctuation growth inside an Instability region rn Eurisol Workshop @ ECT*

  9. Spinodal Decomposition G.Tabacaru et al., EPJA18(2003)103 t Eurisol Workshop @ ECT*

  10. The status of the art Multifragmentation: • An (out of equilibrium) phase transition • First or second order • If first order, most probably driven by spinodal instabilities • WCI 2003-2005 • world-wide review of the field of dynamics and thermodynamics with nucleonic degrees of freedom • http://cyclotron.tamu.edu/wci3/ Eurisol Workshop @ ECT*

  11. The phase transition with Eurisol Eurisol Workshop @ ECT*

  12. Z N Muller Serot PRC 1995 Changing the isospin content (N/Z) the Coulomb properties of the fragmenting source: an extra dimension Eurisol Workshop @ ECT*

  13. From supernovae to neutron stars Eurisol Workshop @ ECT*

  14. Gas: + asymmetric 1 Y Spinodal C.Ducoin nucl-th 2005 Liquid: + symmetric 0 Equilibrium -1 -1 1 0 Y=(N-Z)/A Neutron rich nuclei: isospin fractionation New phenomena Eurisol Workshop @ ECT*

  15. Isospin fractionation C.Ducoin et al nucl-th 2005 Gas: + asymmetric v/c (x100) 1 Y I Spinodal Equilibrium Liquid: + symmetric 0 Z counts -1 0 -1 1 Y=(N-Z)/A r(fm) Eurisol Workshop @ ECT* V.Baran et al. PR 2005

  16. NIMROD PRC 2003 Sn+Sn 28 A.MeV LASSA + Miniball PRL 2000 Sn+Sn 50 A.MeV 11B/11C 7Li/7Be 20 t/3He ratio 11B/11C 20 15 ratio 11B/11C 7Li/7Be 10 10 7Li/7Be 5 5 t/3He t/3He 1.3 1.4 1.5 2 N/Z 124Sn + 124Sn 112Sn + 112Sn 1 0 2 0 1 2 1 DB(MeV) Isospin fractionation rn/rp5.5 for N/Z=1.48 but thermodynamic characterization needed Eurisol Workshop @ ECT*

  17. Y2(N,Z) Y1(N,Z) = C exp(aN+bZ) Fractionation observables: isoscaling Lassa+Miniball PRL 2001 FRS nucl-ex 2005 a Texas A&M PRC 2004 • Pre-equilibrium effects • Sequential decay (?) • approximately cancel out Eurisol Workshop @ ECT*

  18. Ono PRC 2003 T.X.Liu et al. PRC 2004 a=1.83 C secondary 15 A 10 a=1.60 Y2(N,Z) Y1(N,Z) = C exp(aN+bZ) primary A Fractionation observables: isoscaling Sensitive to the EOS symmetry properties Eurisol Workshop @ ECT*

  19. Ono PRC 2003 a=1.83 a=1.60 Y2(N,Z) Y1(N,Z) = C exp(aN+bZ) Fractionation observables: isoscaling ~(N-Z)/A Sensitive to the isotopic content of fragments Sensitive to the EOS symmetry properties Eurisol Workshop @ ECT*

  20. First results Indra-Aladin PRL 2005 Decreasing a with centrality Reduced symmetry energy or increased fractionation disentangle with transport observables • We need: • IMF isotopic resolution • 4p detection for event sorting • Neutron rich nuclei • E/A>30 MeV Eurisol Workshop @ ECT*

  21. Bonche Vautherin NPA 1984 Z Gas: + asymmetric 1 Y N Spinodal C.Ducoin nucl-th 2005 Liquid: + symmetric 0 Equilibrium -1 -1 1 0 Y=(N-Z)/A Neutron rich nuclei: isospin fractionation New phenomena Proton rich nuclei: vanishing limiting temperatures Eurisol Workshop @ ECT*

  22. SMM by Raduta2 Z=23, A=50 4 200Pb Probability bC = 0 Uncharged 3 0 4 8 12 Coulomb interaction VC Energy Coulomb interaction VC bC= Uncharged 2 2 Spinodal 1.6 1.2 1 bC = bNCharged 0.8 bC=bNCharged 0.4 Energy Energy 0 2 4 6 8 10 12 14 0 2 4 6 8 10 14 12 Coulomb effects on the phase transition FG PRL 2003 • Rotation of the order parameter • Reduction of the coexistence zone • New decay channels (cf.fission) • Cross over Eurisol Workshop @ ECT*

  23. Bonche Vautherin NPA 1984 Z Gas: + asymmetric 1 Y N Spinodal C.Ducoin nucl-th 2005 Liquid: + symmetric 0 Equilibrium -1 -1 1 0 Y=(N-Z)/A Ono et al PRC 2004 Neutron rich nuclei: isospin fractionation New phenomena In medium modification of cluster properties Proton rich nuclei: vanishing limiting temperatures Eurisol Workshop @ ECT*

  24. In medium modification of cluster properties Ono PRC 2004 Botvina PRL 2005 Reduction of the volume symmetry term for clusters? Reduction of the the surface symmetry term at finite temperature? Wide isotopic distributions Eurisol Workshop @ ECT*

  25. C/A E/A (A.MeV) Conclusions Multics NPA 2003 • The physics of hot nuclei • a unique laboratory for the thermodynamics • of open, finite, off-equilibrium systems • a quantitative nuclear metrology • What do we need • 4p detection • wide isotopic resolution • wide asymmetry range for the compound • wide asymmetry range for the QP • 30-100 A.MeV beams • (AZ4p collaboration - • FAZIA concept • of the EURISOL report) Eurisol Workshop @ ECT*

  26. Eurisol Workshop @ ECT*

  27. Superfluidité dans les noyaux Siem-PRC65(2002)044318 1.2 (MeV) 172Yb 0.8 Brechignac et al, PRL81(98)4612 0.4 Temperature • L’ensemble évaporatif 0 0 1 2 3 4 5 6 Excitation Energy (MeV) Statistical mechanics of small quantum systems A.Ono, PRC 59(98)853 • Collisions d’ions lourds rélativistes • Transition solide-liquide dans les agrégats Schmidt et al, PRL 79(1997)99 (eV/K) 0 0.8 0.4 Heat Capacity 0 200 100 300 400 Temperature (K) Eurisol Workshop @ ECT*

  28. Clusterization properties at b-equilibrium  Most instable mode: k0(rn, rp) (min. of k2C<) Path at b-equilibrium for mn=100 MeV Slya SGIISIII Affects cluster size l0/2 = p/k0 k0 (MeV) T=10 MeV Slya rn (fm-3) Instability dir.  Isospin fractionation: drn/drp < rn/rp Direction of constant Z/A Affects cluster composition (less n-rich) Direction of instability drn/ drp Instability direction: Eigen-vector corresponding to C< Eurisol Workshop @ ECT* rn (fm-3)

  29. Eurisol Workshop @ ECT*

  30. Eurisol Workshop @ ECT*

  31. BPAL32 SLy230b 20 Symmetry energy (MeV) 10 SkM* 0.2 0.4 0.6 matter density (fm-3) Equation of state at T=0: symmetry energy E=E1(r) + Esym(r) (rn-rp)2/r2 Muller Serot PRC 1995 Theoretical uncertainty on the density dependence Eurisol Workshop @ ECT*

  32. 112 112 Sn + Sn 50 A.MeV 124 124 isospin transport ratio 2xi-x124+124-x112+112 x124+124-x112+112 x = a isospin sensitive variable Ri = no diffusion no diffusion isoscaling Y2(N,Z) Y1(N,Z) = C exp(aN+bZ) symmetry energy and isospin diffusion LASSA-Miniball PRL 2004 data data equilibration Eurisol Workshop @ ECT*

  33. 112 112 Sn + Sn 50 A.MeV 124 124 LASSA-Miniball PRL 2004 symmetry energy and isospin diffusion Better agreement with asy-stiff but • emission time scales: • correlations needed! BPAL32 SLy230b 20 Symmetry energy (MeV) data data 10 SkM* 0.2 0.4 0.6 matter density (fm-3) Eurisol Workshop @ ECT*

  34. Phase transition and equilibrium NM Skyrme Sly4b T=cte Sc= S-b E+bmtr Equilibrium Spinodal Coalescence Phase coexistence deduced from bimodality does not bear any information on the fragment production mechanism Camille Ducoin, Thèse 2006 Eurisol Workshop @ ECT*

  35. σ2/T2 Abnormal fluctuations Ph.Chomaz, F.G. PRL 2000 p = cte T V = cte pressure energy The caloric curve depends on the transformation Fluctuations are unique Eurisol Workshop @ ECT*

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