1. …..viewed through ALADiN
Experimental Signature of the Nuclear Liquid-Gas Phase Transition
…..viewed through ALADiN
Concettina Sfienti
for the ALADiN2000 Collaboration
The nuclear phase-diagram
The ALADiN Recipes
Consensus Experimental Signatures
Discussed Experimental Signatures
Phase Transitions in Asymmetric Matter

2. How it all begun emulsion data Bo Jakobsson@NUFRA2007
The nuclear phase-diagram

3. The liquid-gas phase transition of nuclear matter
QGP
MeV
Gas
Temperature
Liquid ?
Density r/r0
The nuclear phase-diagram

4. The liquid-gas phase transition of nuclear matter
QGP
MeV
Ions
Collisions
Gas
Heavy
Temperature
Liquid ?
Density r/r0
The nuclear phase-diagram

5. The liquid-gas phase transition of nuclear matter
QGP
MeV
Ions
Collisions
Gas
Heavy
Temperature
Liquid
W. Trautmann et al., NN2000 Strasbourg ?
Density r/r0
The nuclear phase-diagram

6. Making boiling nuclei Disadvantages: Typical Incident Energy  30AMeV
Flow
scentralcollision  0
Overlap Participant & Spectators
Spectators can be heated !
Advantages of the Recipe
Typical Incident Energy  1 AGeV
(almost) no flow
Source well localized in rapidity
Equilibrated System
Easy 4p coverage for fragments
Disadvantages of the Recipe
Varying Size of the system by varying Excitation Energy.
The ALADiN Recipes

7. Projectile fragmentation with ALADiN
Int. Conf. on Nucleus-Nucleus Collisions, 1982
Nucl. Phys. A 400 (1983) 565
ALADiN2000
Z, tracking and ToF
multi-hit recognition
The ALADiN Recipes

8. The ALADiN Spectrometer
ALL Fragments (Z 2)
Isotope Resolution
Protons...(but TOF)
The ALADiN Recipes

9. UNIVERSALITY of Spectator Fragmentation
Charge partition (I)
UNIVERSALITY of Spectator Fragmentation
Consensus Experimental Signatures

10. Charge partition (II)
Consensus Experimental Signatures

11. Charge partition (III)
Self Similarity and Scaling
Fisher 1967
Multics PRC2003
IsIs PRL2002
Au Liquid-Gas
t =2.2 0.024
Consensus Experimental Signatures

12. Bimodality of the magnetization in a finite Ising ferromagnet at
From Charge Partition to Bimodality L∞
order parameter M
Binder & Landau PRB30 (1984)
L finite
Field H
Bimodality of the magnetization
in a finite Ising ferromagnet at
phase transition
Characteristic of a finite system
slope at Hc  Ld/T
LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February,
Transition point
Discussed Experimental Results

13. Bimodality as a Signature of NM- Phase Transition?
Results from
Reaction centrality
Source Size (A)
Bimodal variable
INDRA
Central
~200
Z1-Z2
Zliq-Zgas
INDRA*
~100
Asym12
Peripheral
MULTICS/ MINIBALL
~180
NIMROD
24-40
Discussed Experimental Results

14. D-Scaling (I) Identifying the order parameter:
Varying a control parameter (eg. Temperature)
 The order parameter m exhibits a change of Δ-scaling regime
Ordered system
Disordered system
Discussed Experimental Results

15. Identifying the order parameter:
D-Scaling (II)
Ordered Phase (D~1/2)
Disordered Phase (D~1)
Discussed Experimental Results

16. Δ~0.5
Δ~1.
Discussed Experimental Results

17. Heat (Calories per grams) Temperature (degrees)
Some more things that we think we know
Consensus Experimental Signatures

18. Nuclear Thermometer
Central question: At which time do we measure the temperature with each thermometer?
Consensus Experimental Signatures

19. S.Albergo et al. Il Nuovo Cimento A (1985)
Some History….
S.Albergo et al. Il Nuovo Cimento A (1985)
X.Campi et al. PRC50(1994)2680
Consensus Experimental Signatures

20. Community Consensus Caloric Curves
From the existing data Caloric curves can be defined in different mass regions
Results from quite varied entrance channel systems, reaction dynamics and projectile energy ranges appear to be consistent.
J.B. Natowitz et al., Phys.Rev. C (2002)
Consensus Experimental Signatures

21. Bauer, Gelbke, Pratt, Annu.Rev.Nuc.Part.Sci. 42, 77 (1992)
Intensity interferometry
Information from interferometry:
Two-particle correlation are sensitive to space-time extension of emitting source
C(P,q)=∫d3x Fp(r) |f(r,q)|2
C(q)
Relative Momentum, q
Bauer, Gelbke, Pratt, Annu.Rev.Nuc.Part.Sci. 42, 77 (1992)
Discussed Experimental Results

22. Results from particle-particle correlations
S. Fritz et al., Phys. Lett. B 461 (1999) 315
S. Pratt
Discussed Experimental Results

23. A real challenge... Correlations 1+R(q) q (MeV/c)
S. Pratt
1+R(q)
q (MeV/c)
Correlations
L.Beaulieu et al, Phys.Rev.Lett. 84 (2000)
Space-time (resolution?)
Flow
Finite Size Coulomb
Sequential Decays
Discussed Experimental Results

24. New directions Changing: of the fragmenting source
Muller Serot PRC 1995
Changing:
The isospin content (N/Z)
The Coulomb properties
of the fragmenting source
 An extra dimension
Phase Transitions in Asymmetric Matter

25. Phase Transitions in Asymmetric Matter
Muller Serot PRC 1995
Neutron rich nuclei:
isospin distillation
Bonche Vautherin NPA 1984
(asymmetry rp/rn)
Proton rich nuclei:
vanishing limiting temperatures
Phase Transitions in Asymmetric Matter

26. Bonche, Levit, Vautherin, NPA 436, 265 (1985)
Some History….
Bonche, Levit, Vautherin, NPA 436, 265 (1985)
Temperature-dependent Hartree-Fock in a box: the nucleus in equilibrium with its surrounding vapor
Proton rich nuclei:
vanishing limiting temperatures
limits of stability
Phase Transitions in Asymmetric Matter

27. Hunting for Limiting Effects
M.Baldo et al. Phys. Rev. C (2004)
Tc ≥ 15 MeV
Testing microscopic calculations
Phase Transitions in Asymmetric Matter

28. Conclusions….
For the most recent review: EPJA 30 (2006) Special Issue
Freeze-out in the coexistence region: fragments, temperature, density
The largest fragment as order parameter first or second order ?
Limiting temperatures and the nucleus in equilibrium with its vapor ?

29. The
2000 Collaboration
S.Bianchin, K.Kezzar, A.Le Fèvre, J.Lühning J.Lukasik, U.Lynen, W.F.J. Müller, H.Orth, A.N.Otte, H.Sann, C.Sfienti, C.Schwarz, W.Trautmann, J. Wiechula, M.Hellström, D.Henzlova, K.Sümmerer, H.Weick, P.Adrich, T.Aumann, H.Emling, Y.Leifels, R.Palit, H.Simon, H.Johansson, M.De Napoli, G.Imme', G.Raciti, E.Rapisarda, R.Bassini, C.Boiano,I.Iori, A.Pullia, W.G.Lynch, M.Mocko, M.B.Tsang, M.Wallace, G. Verde, C.O.Bacri, A.Boudard, J-E.Ducret, A. Lafriakh, E.Le Gentil, C.Volant, A. Chibihi, J. D. Frankland, T. Barczyk, J.Brzychczyk, J.Cibor, Z.Majka, A.Mykulyak, P.Pawlowski, A.Wieloch, B. Zwieglinski, B.Czech and A.S.Botvina

30. The phase diagram of strongly interacting matter
Source: NUCLEAR SCIENCE, A Teacher’s Guide to the Nuclear Science Wall Chart, Figure 9-2
The nuclear phase-diagram

31. Zbound .vs. Excitation Energy
A. Schüttauf et al., Nucl. Phys. A607(1996)457
Universality of fragment partition assures universality of Zbound.vs.,<Eo>/<Ao> correlation
J. Pochodzalla et al., Phys. Rev. Lett. 75(1995)1040
Things that we know, we know

32. Neutrons Multiplicities
(N/Z) projectile
 neutron initial
(by P.Pawlowski)
● ● ● SMM ensemble calculations for γ=14, preliminary
Things that we thought we didn’t know…

33. Bonche, Levit, Vautherin, NPA 436, 265 (1985)
Limiting Temperature
Bonche, Levit, Vautherin, NPA 436, 265 (1985)
Temperature-dependent Hartree-Fock in a box: the nucleus in equilibrium with its surrounding vapor
J.B. Natowitz et al., Phys.Rev. C (2002)
limits of stability
Phase Transitions in Asymmetric Matter

34. Small Isotopic effects .vs. Isotopic temperature Small effects Small
Phase Transitions in Asymmetric Matter

35. Hunting for Limiting Effects
 Initial System
 System at breakup
Discriminant analysis
J. Łukasik et al., NIMA 587(2008) 413
Heavy Residue disappearance
 Limiting Temperature case
Phase Transitions in Asymmetric Matter