Phase transitions in nuclei: from fission to multifragmentation and back F.Gulminelli – LPC Caen

1. Phase transitions in nuclei: from fission to multifragmentation and backF.Gulminelli – LPC Caen • First multifragmentation models: ~1980 • (L.Moretto, J.Randrup, J.Bondorf, D.Gross) • First exclusive data on multifragmentation: ~1995 • (ALADIN, EOS, INDRA, IsIs)

2. V E* Multifragmentation: an extension of fission? q Extended fission coordinate in hyperspace Conjugated momentum =E* Partition dependent multi-dimensional fission barrier Transition current n and partial width G J. A. LOPEZ and J. RANDRUP: Nucl. Phys. A512(1990)345; A571(1994)379

3. E* Multifragmentation: an extension of fission? • In principle, a very complex many-body dynamics: • multi-dimensional deformations • pre-saddle emission • dissipation • post-saddle emission =E* Conditional saddle Scission ----------- Dissipation (Langevin) J. A. LOPEZ and J. RANDRUP: Nucl. Phys. A512(1990)345; A571(1994)379

4. E* Multifragmentation: an extension of fission? • In principle, a very complex many-body dynamics: • BUT: • saddle very close to scission =E* Conditional saddle Scission ----------- Dissipation (Langevin) Saddle configurations J. A. LOPEZ and J. RANDRUP: Nucl. Phys. A512(1990)345; A571(1994)379

5. E* Multifragmentation: an extension of fission? • Experimental evidence: time plays no role in the multi-fragmentation regime L.Beaulieu et al, Phys.Rev.Lett. 84 (2000) 5971-5974

6. The liquid-gas phase transition of nuclear matter QGP 20 200 MeV Gas Temperature Liquid 1 5? Density r/r0

7. The liquid-gas phase transition of nuclear matter QGP 20 200 MeV Ions Collisions Gas Heavy Temperature Liquid 1 5? Density r/r0

8. The liquid-gas phase transition of nuclear matter QGP 20 200 MeV Ions Collisions Gas Heavy Temperature Liquid 1 5? Density r/r0

9. Phase transitions in finite systems L o o order parameter M L finite Field H Transitionpoint Landau Binder PRB 1984

10. F F M M P F M M Phase transitions in finite systems L o o order parameter M L finite Field H Transitionpoint Landau Binder PRB 1984 K.C.Lee PRE 1996 F.Gulminelli Ph.Chomaz PRE 2001 Physica A 2003

11. Bimodalities in fragmentation distributions Au+Au 80 A.MeV INDRA@GSI data Z1 Z2 Z1 197Au 197Au Largest fragment Z1: typical order parameter in fragmentation phenomena Z1-Z2 M.Pichon et al. NPA 2006

12. C L G E.Bonnet et al. 2008 Liquid-Gas Transition versus data =Ebeam(MeV/A) Independent of the incident energy => of the entrance channel dynamics Lattice Gas Model : An exact model belonging to the LG Universality Class • Qualitative agreement • Quantitative disagreement !! 0 .2 .4 A/As

13. LGM with symmetry and Coulomb Z=54 N=75 L G F G.Lehaut et al. 2008

14. 0. .5 1 Z1/Zs 0. .5 1 Z1/Zs 0. .5 1 Z1/Zs 0. .5 1 0. .5 1 0. .5 1 0. .5 1 Z1/Zs LGM with symmetry and Coulomb Temperature L G F G.Lehaut et al. 2008

15. 4 200Pb bC = 0 Uncharged 3 Coulomb interaction VC 2 Spinodal 1 bC = bNCharged 0 2 4 6 8 10 12 14 Energy F.Gulminelli et al.PRL91(2003)202701 Nuclear statistical models : MMM ~Z1

16. Nuclear statistical models: CTM charged uncharged charged uncharged G.Chaudhuri et al. nucl-ex 2008

17. Conclusions • Charged systems at finite temperature have a generic fragmentation pattern with Z1~Ztot/2, Z2~Z1 • This hot (asymmetric) « fission » phenomenon can be interpreted as a first order transition • Contrary to fragmentation of neutral systems, this Coulomb-induced transition has no thermodynamic limit => it is not related to the LG universality class but closer to bimodality in fission • This may be what we experimentally observe through multi-fragmentation experiments (projectile fragmentation) (??)