1. 16/1/06Eurisol Workshop @ ECT*1 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 what do we need from Eurisol Conclusions fm -3 NM phase diagram C.Ducoin et al 2005

2. 16/1/06Eurisol Workshop @ ECT*2 The status of the art

3. 16/1/06Eurisol Workshop @ ECT*3 Boiling nuclei multi fragmentation Motivations: nuclear thermometry interdisciplinary connections dense matter and stars P.J.Siemens Nature 1983

4. 16/1/06Eurisol Workshop @ ECT*4 Self similarity and scalings Au Liquid-Gas             n A =q 0 A -  exp(- c 0  A  ) T IsIs PRL2002 EoS PRC2003 Multics PRC2003 J.Finn et al PRL1982 p+Xe 80-350 GeV A -2.64 Fisher 1967

5. 16/1/06Eurisol Workshop @ ECT*5 Caloric Curve Aladin PRL1995 Heat (Calories per grams) Temperature (Degrees) Texas A&M PRC2003

6. 16/1/06Eurisol Workshop @ ECT*6 INDRA NPA 2002 Multics NPA 2003 Isis E900A all one source INDRA-Aladin nucl-ex 2005 Fluctuations and negative heat capacity Nimrod PRC 2004

7. 16/1/06Eurisol Workshop @ ECT*7 Bimodality B.Tamain et al. 2005 Z1Z1 Z2Z2 "reservoir" T 197 Au Au+Au 80 A.MeV INDRA@GSI data order parameter:  charge asymmetry Z 1 -Z 2 Z1Z1

8. 16/1/06Eurisol Workshop @ ECT*8 Spinodal Decomposition S c ’= S c +  ts  pp nn Spontaneous fluctuation growth inside an Instability region

9. 16/1/06Eurisol Workshop @ ECT*9 Spinodal Decomposition G.Tabacaru et al., EPJA18(2003)103 t

10. 16/1/06Eurisol 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/

11. 16/1/06Eurisol Workshop @ ECT*11 The phase transition with Eurisol

12. 16/1/06Eurisol Workshop @ ECT*12 Changing the isospin content (N/Z) the Coulomb properties of the fragmenting source: Muller Serot PRC 1995 N Z an extra dimension

13. 16/1/06Eurisol Workshop @ ECT*13 From supernovae to neutron stars

14. 16/1/06Eurisol Workshop @ ECT*14 New phenomena Neutron rich nuclei: isospin fractionation Y=(N-Z)/A 0 0 1 1 Gas: + asymmetric Liquid: + symmetric Equilibrium Spinodal Y C.Ducoin nucl-th 2005

15. 16/1/06Eurisol Workshop @ ECT*15 Isospin fractionation Y=(N-Z)/A 0 0 1 1 Gas: + asymmetric Liquid: + symmetric Equilibrium Spinodal Y C.Ducoin et al nucl-th 2005 Z counts I r(fm) v/c (x100) V.Baran et al. PR 2005

16. 16/1/06Eurisol Workshop @ ECT*16 Isospin fractionation 112 Sn + 112 Sn 124 Sn + 124 Sn 5 20 10 2 0 1 2012 1 t/ 3 He 11 B/ 11 C 7 Li/ 7 Be t/ 3 He 7 Li/ 7 Be 11 B/ 11 C ratio  B(MeV) LASSA + Miniball PRL 2000 Sn+Sn 50 A.MeV 11 B/ 11 C 7 Li/ 7 Be t/ 3 He 1.31.41.5 N/Z ratio 5 10 15 20 NIMROD PRC 2003 Sn+Sn 28 A.MeV  n /  p  5.5 for N/Z=1.48 but thermodynamic characterization needed

17. 16/1/06Eurisol Workshop @ ECT*17 Fractionation observables: isoscaling Y 2 (N,Z) Y 1 (N,Z) = C exp(  N+  Z) Lassa+Miniball PRL 2001 Texas A&M PRC 2004 FRS nucl-ex 2005  Pre-equilibrium effects Sequential decay (?) approximately cancel out

18. 16/1/06Eurisol Workshop @ ECT*18 Fractionation observables: isoscaling Y 2 (N,Z) Y 1 (N,Z) = C exp(  N+  Z) T.X.Liu et al. PRC 2004 A primary C 10 15 secondary A Ono PRC 2003   Sensitive to the EOS symmetry properties

19. 16/1/06Eurisol Workshop @ ECT*19 Fractionation observables: isoscaling Y 2 (N,Z) Y 1 (N,Z) = C exp(  N+  Z) Ono PRC 2003   Sensitive to the EOS symmetry properties ~(N-Z)/A Sensitive to the isotopic content of fragments

20. 16/1/06Eurisol Workshop @ ECT*20 First results Reduced symmetry energy or increased fractionation disentangle with transport observables Indra-Aladin PRL 2005 Decreasing  with centrality We need: IMF isotopic resolution 4  detection for event sorting Neutron rich nuclei E/A>30 MeV

21. 16/1/06Eurisol Workshop @ ECT*21 New phenomena Proton rich nuclei: vanishing limiting temperatures Bonche Vautherin NPA 1984 N Z Neutron rich nuclei: isospin fractionation Y=(N-Z)/A 0 0 1 1 Gas: + asymmetric Liquid: + symmetric Equilibrium Spinodal Y C.Ducoin nucl-th 2005

22. 16/1/06Eurisol Workshop @ ECT*22 Coulomb effects on the phase transition Energy 1 2 3 4 Coulomb interaction V C 024681012 14  C  N  Charged  C  Uncharged Spinodal 200 Pb 0246810 12 14 Probability 04812 Energy  C =  N Charged  C =  Uncharged SMM by Raduta 2 Z=23, A=50 0.4 0.8 1.2 1.6 2 Coulomb interaction V C Rotation of the order parameter Reduction of the coexistence zone New decay channels (cf.fission) Cross over FG PRL 2003

23. 16/1/06Eurisol Workshop @ ECT*23 New phenomena Proton rich nuclei: vanishing limiting temperatures Bonche Vautherin NPA 1984 N Z Neutron rich nuclei: isospin fractionation Y=(N-Z)/A 0 0 1 1 Gas: + asymmetric Liquid: + symmetric Equilibrium Spinodal Y C.Ducoin nucl-th 2005 In medium modification of cluster properties Ono et al PRC 2004

24. 16/1/06Eurisol Workshop @ ECT*24 In medium modification of cluster properties Reduction of the the surface symmetry term at finite temperature? Wide isotopic distributions Ono PRC 2004 Botvina PRL 2005 Reduction of the volume symmetry term for clusters?

25. 16/1/06Eurisol Workshop @ ECT*25 Conclusions The physics of hot nuclei a unique laboratory for the thermodynamics of open, finite, off-equilibrium systems a quantitative nuclear metrology Multics NPA 2003 E/A (A.MeV) C/A What do we need 4  detection wide isotopic resolution (AZ4  collaboration - FAZIA concept of the EURISOL report) wide asymmetry range for the compound wide asymmetry range for the QP 30-100 A.MeV beams

26. 16/1/06Eurisol Workshop @ ECT*26

27. 16/1/06Eurisol Workshop @ ECT*27 Statistical mechanics of small quantum systems Collisions d’ions lourds rélativistes Excitation Energy (MeV) 1023456 Temperature (MeV) 0 0.4 0.8 1.2 172 Yb Siem-PRC65(2002)044318 Superfluidité dans les noyaux Schmidt et al, PRL 79(1997)99 Temperature (K) Heat Capacity (eV/K) 200 300 400 0 0.4 0.8 0 100 Transition solide-liquide dans les agrégats L’ensemble évaporatif Brechignac et al, PRL81(98)4612 A.Ono, PRC 59(98)853

28. 16/1/06Eurisol Workshop @ ECT*28 Clusterization properties at  -equilibrium Path at  -equilibrium for  =100 MeV  n (fm -3 ) k 0 (MeV)  n /  p  Direction of instability Instability dir. T=10 MeV Slya Isospin fractionation:  n /  p <  n /  p   n (fm -3 ) Affects cluster composition (less n-rich) Direction of constant Z/A Slya SGII SIII Most instable mode: k 0 (  n,  p ) (min. of k 2 C < ) Affects cluster size  /2 =  /k 0 Instability direction: Eigen-vector corresponding to C <

29. 16/1/06Eurisol Workshop @ ECT*29

30. 16/1/06Eurisol Workshop @ ECT*30

31. 16/1/06Eurisol Workshop @ ECT*31 Equation of state at T=0: symmetry energy E=E 1 (  ) + E sym  n  p     0.2 0.40.6 10 20 matter density (fm -3 ) Symmetry energy (MeV) BPAL32 SkM* SLy230b Theoretical uncertainty on the density dependence Muller Serot PRC 1995

32. 16/1/06Eurisol Workshop @ ECT*32 symmetry energy and isospin diffusion LASSA-Miniball PRL 2004 Sn + Sn 50 A.MeV 112 124 112 isoscaling Y 2 (N,Z) Y 1 (N,Z) = C exp(  N+  Z) isospin transport ratio 2x i -x 124+124 -x 112+112 x 124+124 -x 112+112 R i = x =  isospin sensitive variable no diffusion equilibration data

33. 16/1/06Eurisol Workshop @ ECT*33 symmetry energy and isospin diffusion LASSA-Miniball PRL 2004 Sn + Sn 50 A.MeV 112 124 112 0.2 0.40.6 10 20 matter density (fm -3 ) Symmetry energy (MeV) BPAL32 SkM* SLy230b Better agreement with asy-stiff but emission time scales: correlations needed! data

34. 16/1/06Eurisol Workshop @ ECT*34 Phase transition and equilibrium Equilibrium Spinodal Coalescence Phase coexistence deduced from bimodality does not bear any information on the fragment production mechanism NM Skyrme Sly4b T=cte Camille Ducoin, Thèse 2006 S c = S-  E+  t 

35. 16/1/06Eurisol Workshop @ ECT*35 Abnormal fluctuations T σ 2 /T 2 p = cte V = cte The caloric curve depends on the transformation Fluctuations are unique Ph.Chomaz, F.G. PRL 2000 energy pressure