16/1/06Eurisol 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

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

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

16/1/06Eurisol 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 GeV A Fisher 1967

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

16/1/06Eurisol 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

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

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

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

16/1/06Eurisol 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 world-wide review of the field of dynamics and thermodynamics with nucleonic degrees of freedom

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

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

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

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

16/1/06Eurisol ECT*15 Isospin fractionation Y=(N-Z)/A 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

16/1/06Eurisol ECT*16 Isospin fractionation 112 Sn Sn 124 Sn Sn 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 N/Z ratio NIMROD PRC 2003 Sn+Sn 28 A.MeV  n /  p  5.5 for N/Z=1.48 but thermodynamic characterization needed

16/1/06Eurisol 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

16/1/06Eurisol 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 secondary A Ono PRC 2003   Sensitive to the EOS symmetry properties

16/1/06Eurisol 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

16/1/06Eurisol 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

16/1/06Eurisol 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 Gas: + asymmetric Liquid: + symmetric Equilibrium Spinodal Y C.Ducoin nucl-th 2005

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

16/1/06Eurisol 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 Gas: + asymmetric Liquid: + symmetric Equilibrium Spinodal Y C.Ducoin nucl-th 2005 In medium modification of cluster properties Ono et al PRC 2004

16/1/06Eurisol 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?

16/1/06Eurisol 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 A.MeV beams

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

16/1/06Eurisol 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 <

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

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

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

16/1/06Eurisol 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 

16/1/06Eurisol 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