The nuclear liquid gas phase transition Francesca Gulminelli

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 the properties of the EOS the observables of the transition • Conclusions 25/5/04 CERN-MW workshop 1

Boiling nuclei P. J. Siemens Nature 1983 multi fragmentation Motivations: • nuclear thermometry • dense matter and stars • interdisciplinary connections 25/5/04 CERN-MW workshop 2

J. Finn et al PRL 1982 p+Xe 80 -350 Ge. V Self similarity and scalings Multics PRC 2003 A-2. 64 Fisher 1967 Is. Is PRL 2002 n. A=q 0 A-texp(- c 0 e. As) T Eo. S PRC 2003 Au 25/5/04 CERN-MW workshop t 2. 2 0. 1 s 0. 71 0. 02 g 1. 12 0. 05 b 0. 3 0. 1 Liquid-Gas 2. 196 0. 024 0. 647 0. 006 1. 24 0. 01 0. 305 0. 005 3

Aladin PRL 1995 Temperature (Degrees) Caloric Curve Texas A&M PRC 2003 25/5/04 CERN-MW workshop Heat (Calories per grams) 4

Abnormal fluctuations Ph. Chomaz, F. G. PRL 2000 p = cte T V = cte σ2/T 2 e ener g y pr ur s es The caloric curve depends on the transformation 25/5/04 CERN-MW workshop Fluctuations are unique 5

fluctuations and negative heat capacity NIMROD PRC 2004 s. Z. 06. 04. 02. 6 1. 4 T/T 0 INDRA NPA 2002 25/5/04 CERN-MW workshop Multics NPA 2003 6

The phase transition with exotic beams Changing the isospin content (N/Z) the Coulomb properties of the fragmenting source: an extra dimension 25/5/04 CERN-MW workshop 7

Equation of state at T=0: symmetry energy Symmetry energy (Me. V) E=E 1(r) + Esym(r) (rn-rp)2/r 2 Muller Serot PRC 1995 BPAL 32 SLy 230 b 20 10 Sk. M* 0. 2 0. 4 0. 6 matter density (fm-3) Theoretical uncertainty on the density dependence 25/5/04 CERN-MW workshop 8

symmetry energy and isospin 112 diffusion 112 124 Sn +124 Sn 50 A. Me. V LASSA-Miniball PRL 2004 Better agreement with asy-stiff isospin transport butratio Symmetry energy Ri = 2 ai-a 124+124 -a 112+112 • emission a 124+124 -a 112+112 time no diffusion isoscaling BPAL 32 Y 2(N, Z) 20 = Y 1(N, Z) 10 SLy 230 b C exp(a. N+b. Z) data equilibration a : isospin Sk. M* sensitive variable 0. 2 0. 4 data 0. 6 matter density (fm-3) 25/5/04 scales: correlations needed! CERN-MW workshop no diffusion 9

Equation of state at T>0: phase transition Muller Serot PRC 1995 25/5/04 CERN-MW workshop 10

Phase transition: observables Neutron rich nuclei: isospin distillation Bonche Vautherin NPA 1984 pressure Muller Serot PRC 1995 asymmetry rp/rn Proton rich nuclei: vanishing limiting temperatures 25/5/04 CERN-MW workshop 11

Lattice Gas Model Isospin distillation ratio NIMROD PRC 2003 Sn+Sn 28 A. Me. V Ph. Chomaz, F. G. PLB 1999 15 LASSA + Miniball PRL 2000 Sn+Sn 50 A. Me. V ratio 11 B/11 C 20 11 B/11 C 10 7 Li/7 Be 5 t/3 He 2 112 Sn 1 0 1 25/5/04 + 112 Sn 2 0 20 11 B/11 C 7 Li/7 Be t/3 He 10 5 1. 3 1. 4 N/Z 1. 5 rn/rp 5. 5 for N/Z=1. 48 124 Sn + 124 Sn but thermodynamic characterization 1 2 DB(Me. V) needed CERN-MW workshop 12

Coulomb effects on the phase transition Statistical Multifragmentation Model F. Gulminelli et al PRL 2003 coulomb energy liquid From nuclear matter to heavily charged nuclei, the first order phase transition is expected to become a cross over qef=0 qef=e 25/5/04 gas total energy CERN-MW workshop 13

Multics NPA 2003 • The physics of hot nuclei • a unique laboratory for thermodynamics C/A conclusions of open, finite, off-equilibrium systems • a quantitative nuclear metrology WCI 2004 E/A (A. Me. V) world-wide review of the field of dynamics and thermodynamics with nucleonic degrees of freedom Multics E 1=2 0. 3 E 2=6. 5 0. 7 http: //cyclotron. tamu. edu/sjygroup/wci 2004/ Isis E 1=2. 5 E 2=7. Indra E 2=6. 0. 5 • What do we need • 4 p mass and charge detection (AZ 4 p collaboration FAZIA concept of the EURISOL report) • 20 -50 A. Me. V radioactive beams 25/5/04 CERN-MW workshop 14