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heaviest fragment of partitions => order parameter

The prominent role of the heaviest fragment in multifragmentation and phase transition for hot nuclei. heaviest fragment of partitions => order parameter Size/charge of the heaviest fragment => good estimator of E* and of the freeze-out volume

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heaviest fragment of partitions => order parameter

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  1. The prominent role of the heaviest fragment in multifragmentation and phase transition for hot nuclei heaviest fragment of partitions => order parameter Size/charge of the heaviest fragment => good estimator of E* and of the freeze-out volume bimodal behavior of the heaviest fragment distribution => generic signal of first order phase transition for finite systems Bernard Borderie

  2. INDRA@GANIL and INDRA-ALADIN@GSI Bernard Borderie

  3. Two ways to heat nuclei in H.I. collisions at int. energies Bernard Borderie

  4. The heaviest fragment of multifragmentation partitions is recognized as order parameter Universal fluctuations: Δ-scaling laws R. Botet and M. Ploszajczak Lecture Notes in Physics vol 65 (2002) Gaussian shape Gumbel shape J.D. Frankland et al., PRC 71 (2005) 034607 Bernard Borderie

  5. The size of the heaviest fragment QP: Au + Au 80 AMeV <Zs> : 79 - 65 QF: Xe + Sn 25-50 AMeV <Zs> : 90 - 80 E.Bonnet et al.,NPA 816 (2009) 1 Its size/charge estimates E* but only for heavy hot nuclei (Z>=60) B. B., MF Rivet, PPNP 61 (2008) 551 Fragment formation stage: we can think that the size of the heaviest fragment is correlated with the particle density and can give information on freeze-out density/volume Bernard Borderie

  6. A complete simulation to derive information at freeze-out • built event by event from all the available experimental information (LCP spectra, average and standard deviation of frag. velocity spectra and calorimetry) • F.O. partitions are built by dressing fragments with particles • Excited fragments and particles at F.O. undergo propagation (Coulomb+ thermal kin. E) during which fragments evaporate particles • 4 free parameters to recover the data: - percentage of particles evaporated from primary frag. - radial collective energy - minim. distance between the surfaces of products at F.O. -limiting temperature for fragments (vanishing of the level density at high E*- S.E. Koonin and J. Randrup A474 1987,173) Bernard Borderie

  7. Comparison data-simulation (asymptotic values) QF: Xe + Sn 32-50AMeV frag.-frag. correlations A limiting temperature of 9 MeV is mandatory to reproduce the measured widths S. Piantelli et al., NPA 809 (2008) 111 Bernard Borderie

  8. The normalized heaviest fragment Z1/ZS is used to calibrate the F.O. volume F.O.Volumes for QF sources (Xe+Sn 32-50 AMeV) taken from the simulation Piantelli et al. (NPA 809, 2008, 111) Calibrate F.O. volumes with the relation V/V0 = f(Z1/ZS) for QF, and derive freeze-out volumes for QP’s QP: Au + Au 80 AMeV QF: Xe + Sn 25-50AMeV At a given E*, QP volumes are smaller than QF volumes E.Bonnet et al.,NPA 816 (2009) 1 Bernard Borderie

  9. At fixed reduced Mfrag and fixed E*the size of Z1 is determined QP: Au + Au 80,100 AMeV QF: Xe + Sn 25-45 AMeV E. Bonnet et al., PRL to be submitted Bernard Borderie

  10. X extensive variable (E, N, V) Conjugate intensive variable (X)=S /  X (1/T, - μ/T, P/T) Finite syst. and first order phase transition NEGATIVE HEAT CAPACITY BIMODALITY μcanonical sampling (Fixed value of X) Canonical-Gaussian sampling P(X)  exp(S(X)- X) Ph. Chomaz et al., Phys. Rep. 389 SPINODAL INSTABILITY Bernard Borderie

  11. Bimodal behavior of the heaviest fragment distribution ? Recent observations: bimodal behavior of the distribution of the asymmetry between the charges of the two heaviest fragments M.Pichon et al., NPA 779 (2006) 267 M. Bruno et al., NPA 807 (2008) 48 and for the heaviest fragment Z1/Zs (related to F.O. volume) ? QP: Au+Au 60,80,100 AMeV Bernard Borderie

  12. Bimodal behavior of the heaviest fragment distribution in Quasi-Projectile fragmentation To select QPs with negligible neck contribution (mid-rapidity emission) 2 different procedures (I): eliminating events with size hierarchy (heaviest fragment the most forward, PRC 67 064603) (II): keeping compact events in velocity space, NPA 816 1 Bernard Borderie

  13. How to compare data to predictions of the canonical ensemble comparison of normalized correlations (Z1 versus E*) F. Gulminelli, NPA 791 (2007) 165 Bernard Borderie

  14. Normalized distributions measured ones => normalized ones => Bernard Borderie

  15. Fit procedure to extract parameter values (common E* range) (II) as exemple Correlation coeff. ρ=σZ1E*/σZ1σE* Zi, σZi, Ei, σEi i=L,G Bernard Borderie

  16. Bimodal behavior of the heaviest fragment distribution as signature of a first order phase transition in finite systems Z1 versus E* using the deduced parameter values latent heat of the phase transition (EG-EL) for heavy nuclei Z~ 70 8.1 (±0.4)stat (+1.2 -0.9)syst AMeV syst. error: different QP selections E.Bonnet, D. Mercier et al, PRL August 2009 Bernard Borderie

  17. Summary THE PROMINENT ROLE OF THE HEAVIEST FRAGMENT IN MULTIFRAGTATION AND PHASE TRANSITION OF HOT NUCLEI IS ESTABLISHED - early recognized as order parameter (universal fluctuation theory) id large class of transitions involving complex clusters from percolation to gelation, nucleation,aggregation - representative of E* and of the F.O. volume - bimodal behavior of its distribution => generic signal expected in finite systems for a first order phase transition => estimate of the latent heat of the transition for Z~70and possibly for other sizes of nuclei in the future Bernard Borderie

  18. Selection of QF nuclei: compact single sources in velocity space using the kinetic energy tensor and the flow angle (Өflow >= 60o) Өflot≥60° Bernard Borderie

  19. Selection of QP nuclei : compactness criterion in velocity space Bernard Borderie

  20. Other estimators (normalized dist.) Bernard Borderie

  21. X extensive variable (E, N, V) Conjugate intensive variable (X)=S /  X (1/T, - μ/T, P/T) Finite syst. and first order phase transition BIMODALITY Canonical-Gaussian sampling P(X)  exp(S(X)- X) Bernard Borderie

  22. Observation of a fossil signal with a confidence level of 3-4 σ (QF Xe+Sn 32-50 AMeV) B.B. et al. PRL 86 (2001) 3252 Bernard Borderie

  23. Finite syst. and first order phase transition X extensive variable (E, N, V) Conjugate intensive variable (X)=S /  X (1/T, - μ/T, P/T) NEGATIVE HEAT CAPACITY μcanonical sampling (Fixed value of X) Bernard Borderie

  24. Caloric curves, heat capacity and config. energy fluctuations Bernard Borderie

  25. Negative microcanonical heat capacity QF QP N. Le Neindre et al., NPA 795 (2007) 47 N. Le Neindre et al., NPA 699 (2002) 795 Bernard Borderie

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