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Bimodalities

This compilation discusses the theoretical foundations, experimental observations, and models of bimodalities in finite systems. Topics include phase transitions, order parameters, and bimodalities in different collision scenarios. The text language is English.

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Bimodalities

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  1. Bimodalities A compilation of models and data O. Lopez, M.F. Rivet WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  2. Bimodalities part 1 Theoretical bases LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  3. Bimodalities : foundation Characteristic of a finite system slope at Hc Ld/T Bimodality of the magnetization in a finite Ising ferromagnet at phase transition Binder & Landau PRB30 (1984) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  4. 2/ Inverted curvature of thermodynamical potential Chomaz, Colonna, Randrup, Phys. Rep. 389 (2004) Bimodality of order parameter distribution new definition of a 1st order phase transition in finite system Chomaz et al. PRE64 (2001) 1/ Equivalent to Yang-Lee theorem (stand. def. at thermodynamic limit) Chomaz/Gulminelli Physica A330 (2003) and to 3/ If X=E*, negative heat capacity LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  5. Phase transition definition and statistical ensembles C<0 : the order parameter (E* ) must be controlled microcanonical ensemble Bimodality and Yang-Lee Th.: extensive variable (E*, V ) should be free to fluctuate Canonical ensemble LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  6. Relaxed condition: Gaussian ensemble as interpolating ensemble N particles in sample, N’ in heat bath, vary N’ from 0 to ∞ a  1/N’ Bimodality obtained for large N’ (small a) ≈ canonical and not for small N’ ≈ μcanonical Challa & Hetherington PRL60 (1988) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  7. LG Phase transitions : different possible order parameters Order parameters are : • V (rliq-rgas) • Energy E • any linear comb. of E,V Canonical Lattice gas model in the first order phase transition region. Chomaz et al. PRE 64 (2001) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  8. Bimodalities part 2 Experimental facts LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  9. Bellaize et al, Nucl. Phys A709 (2002) INDRA collaboration 32/52/90 MeV/nucleon 58Ni+197Au A ~ 160-180, Central collisions (PCA) Zone 1 Zone 2 DZ E*/A ≠ (1) E*/A (MeV) (calorimetry) 52 MeV/nucleon E* differs from 1 MeV/nucleon Bimodalities: experimental overview Observation of a bimodality in fragment size asymmetry for E*~4 (32) and E*~5 (52) MeV/n (from SMM) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  10. SMF simulation (BOB) Xe+Sn 32A MeV Passage through the coexistence region Bimodalities: experimental overview Borderie et al, Journal of Physics G (2002) R217 INDRA collaboration 32-50 MeV/nucleon 129Xe+natSn A ~ 180-220, Central collisions (qflow) Ratio between “Liquid” and “Gas” phase LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  11. SMM GEMINI (Z1-<Z>)2+ (Z1-<Z>)2+ (Z2-<Z>)2 Asym123 = 6<Z> Bimodalities: experimental overview Lautesse et al, PRC 2005, in press INDRA collaboration 32 MeV/nucleon 58Ni+natNi A ~ 100, central collisions (DFA) • Data exhibit 2 fragmentation patterns: • Evaporation-Residue (GEMINI-like) • multifragmentation (SMM-like) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  12. “canonical” sorting Etrans12QT bins Zasym>0.7 E* ≠ Zasym<0.3 Equal T Compatibility with the LG phase transition Bimodalities: experimental overview M. Pichon, Thèse LPC Caen (2004) http://tel.ccsd.cnrs.fr/documents/archives0/00/00/74/51 80 MeV/nucleon 197Au + 197Au A =160-180, peripheral reactions (QP) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  13. QT light particles transverse energy Bimodalities: experimental overview D'Agostino et al, 5th Italy-Japan Symposium – Naples 2004 MULTICS-MINIBALL collaboration 35 MeV/nucleon 197Au+197Au A ~180, peripheral reactions (QP) The same signal is observed LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  14. Trautmann et al, private communication (2005) ALADIN collaboration Zbound=53-55 Zbound Zb3 Same behavior Interpreted as a 2nd order PT ? Bond percolation (53), pb=0.328 Bimodalities: experimental overview 1000 MeV/nucleon 197Au+197Au A ~130, peripheral collisions (QP) Wait final remarks … LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  15. Excitation energy is deduced from 3-sources fits and calorimetry Bimodalities: experimental overview Ma et al, Nucl-ex/0410018 NIMROD Collaboration 47MeV/nucleon 40Ar+27Al,48Ti,58Ni A = 24-40, peripheral reactions (QP) A crossover between “gas” and “liquid” phase for E*/A ~ 5.5 MeV (exc5-6) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  16. Bimodalities part 3 Models and simulations LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  17. nucl-th/0412111 N. Buyukcizmeci, R. Ogul, A.S. Botvina - Amax>2A0/3 : residue-evaporation - Amax< A0/3 : multifragmentation They correspond to different caloric curves (liquid and gas type) Bimodalities: Statistical Multifragmentation Model Calculations for different nuclei From E*A=2-20 MeV 2 classes of events are seen depending on the size of Amax (A) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  18. D. Cussol Private communication (2005) Bimodalities: Classical Molecular Dynamics Bimodality in A1-A2 is observed for 3 simulation sets : - central collisions (b<0.1) - peripheral collisions (QP) - thermalized systems (r0/r=8) The transition is located at different excitation energies Eleastbound < E*/N < 2Eleastbound What is its meaning ? Role of the deposited energy ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  19. Lopez and Lacroix, Preliminary results (2005) 20-30 hbar ~ 60-80 hbar Bimodality: Heavy Ion Phase Space Exploration Van Lauwe et al, PRC 69, 054604 (2004) 80 MeV/nucleon Xe+Sn, Et12QC bins (QP) The transition is governed by the transferred spin to the QP source Bimodality and Phase Transition (not LG) LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  20. Bimodalities part 4 Questions and (some) answers LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  21. (*) Zliq= sum of Z>2, Zgas= sum of Z<=2 (**) Zliq= sum of Z>12, Zgas= sum of Z<=12 Bimodalities: general overview of experimental data Amax: a better order parameter ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  22. In experiments, we never observe a bimodality of Amax, but for some asymmetry parameter (Aasym, Z1-Z2, …) , Why ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  23. Event sorting is not enough canonical ? Heat Bath β = βtr No Heat Bath E  Etr = (SA30- SA2-30)/As Lattice-gas F. Gulminelli Bimodality is observed in Aasym but not in Amax LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  24. What is the influence of out-of-equilibrium effects ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  25. F. Gulminelli Phase coexistence in Nuclei Habilitation Université de Caen (2003) Bimodality: Lattice-gas model and out-of-equilibrium effects Bimodality and radial flow Bimodality is still present even for 100% of radial flow (as compared to E) Similar conclusions are observed in presence of transparency (longitudinal flow) F. Gulminelli and Ph. Chomaz Nucl. Phys. A734 (2004) 581 LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  26. What is the influence of Coulomb interaction ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  27. Bimodalities: Influence of Coulomb Gulminelli et al PRL 91, Number 20 (2003) Bimodality in IMMM (Isobar Microcanonical Multifragmentation Model) A multicanonical approach allows the mapping between Coulomb and uncharged systems Inclusion of Coulomb deforms the event probability structure of the phase space but the bimodal character still remains for small systems but not for the heavier ones … Size dependence ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  28. Is the asymmetry parameter a good order parameter ? LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  29. No PT 2nd PT 1st PT F. Gulminelli, private communication LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005 Bimodality of Amax (order parameter): only when there is a 1st order PT Aasy = (Amax –A2)/(Amax +A2) may lead to ambiguity on the order of the PT but not on the existence of a PT

  30. Limitations: Coulomb, … Bimodalities : some questions • What is the best order parameter: Amaxvs. (Amax-A2), (Amax-A2-A3), … ? • What about the event sorting: canonicalvs. X ? • Some alternative explanations may exist : • spin, geometry effect, boundary conditions, … LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  31. Influence of the size of the system (varying masses and energies) Peripheral (QP/QT) vs.central reactions Disentangle the entrance channel effects A+Avsn+A/A+n reactions Bimodalities : to go further from the exp. side Correlation between bimodality and the other proposed signals for the LG phase transition: Abnormal energy fluctuations (negative heat capacity) Scaling laws (universal fluctuations, Fisher’s, Zipf’s, …) Space-time correlations (emission times, correlation functions) Improve the validity of the signal LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  32. BIMODALITIES The discussion is now OPEN LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  33. Bimodalities : summary Definition: Bimodality is the presence of two components in an event probability distribution of an order parameter for a finite system; it is related to the coexistence of two phases for the considered system Generic features: It is related to the abnormal convexity of the entropy or other thermodynamical potentials It is then a 1st order phase transition It should be observed in a “canonical” treatment of data or at least in the framework of “gaussian” ensembles It is a signature of the liquid-gas phase transition in nuclear matter if Order parameter is the density (rliq-rgas) or Energy LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

  34. Bimodalities : what could be in the Consensus From the theoretical side : The relationship between phase coexistence and bimodality is clearly established for finite systems The order parameter for the Liquid-Gas phase transition is (rliq-rgas) or E and is related to the biggest fragment (Amax) for LG (but not only !) From the experiment side : Two decay modes are observed; they correspond to the fragmentation threshold and the route from residue-evaporation to multifragmentation They are observed both in peripheral and central collisions LOPEZ/RIVET, WCI3 Town Meeting, College Station (Texas) February, 12-17 2005

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