IWND09 Bernard Borderie 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
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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 - PowerPoint PPT Presentation
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IWND09 Bernard Borderie
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
IWND09 Bernard Borderie
INDRA@GANIL and INDRA-ALADIN@GSI
IWND09 Bernard Borderie
Two ways to heat nuclei in H.I. collisions at int. energies
IWND09 Bernard Borderie
The heaviest fragment of multifragmentation partitions is recognized as order parameter
Universal fluctuations: Δ-scaling lawsR. Botet and M. Ploszajczak Lecture Notes in Physics vol 65 (2002)
Gaussian shape Gumbel shape
J.D. Frankland et al., PRC 71 (2005) 034607
IWND09 Bernard Borderie
The size of the heaviest fragment
Its size/charge estimates E* but only for heavy hot nuclei (Z>=60)B. B., MF Rivet, PPNP 61 (2008) 551
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
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
IWND09 Bernard Borderie
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)
IWND09 Bernard Borderie
Comparison data-simulation (asymptotic values)
A limiting temperature of 9 MeV is mandatory to reproduce the measured widths
S. Piantelli et al., NPA 809 (2008) 111
QF: Xe + Sn 32-50AMeV frag.-frag. correlations
IWND09 Bernard Borderie
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-outvolumes for QP’s
At a given E*, QP volumes are smaller than QF volumes
E.Bonnet et al.,NPA 816 (2009) 1
QP: Au + Au 80 AMeVQF: Xe + Sn 25-50AMeV
IWND09 Bernard Borderie
QP: Au + Au 80,100 AMeV
QF: Xe + Sn 25-45 AMeV
At fixed reduced Mfrag and fixed E*
the size of Z1 is determined
E. Bonnet et al., PRL to be submitted
IWND09 Bernard Borderie
Finite syst. and first order phase transition X extensive variable
SPINODAL INSTABILITY Ph. Chomaz et al., Phys. Rep. 389
IWND09 Bernard Borderie
Bimodal behavior of the heaviest fragment distribution ?
Recent observations: bimodal behavior ofthe distribution of the asymmetry betweenthe 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
IWND09 Bernard Borderie
Bimodal behavior of the heaviest fragment distribution in Quasi-Projectile
fragmentationTo select QPs with negligibleneck contribution (mid-rapidityemission)