Hot Nuclei and Phase Transitions Karnaukhov V.A. & FASA Collaboration: S.P. Avdeyev1, H. Oeschler2, A. Budzanowski3, A.S.Botvina4 , E.A. Cherepanov1 , W. Karcz3, V. Kirakosyan1, E.A. Kuzmin5, E.Norbeck5, P.A.Rukoyatkin1, I. Skwirczyńska3 1Joint Institute for Nuclear Research, Dubna, Russia; 2 Institut für Kernphysik, University of Technology, Darmstadt, Germany; 3 H.Niewodniczanski Institute of Nuclear Physics, Cracow, Poland; 4 Institute for Nuclear Research, Moscow, Russia 5Kurchatov Institute, Moscow,Russia; 5 University of Iowa, Iowa City, USA;

A. L. Goodman et al., Phys. Rev.C 30 (1984) 851

From Nuclear Matter to Quark-Gluon Plasma ( by heating ) (S. Nagamia , Nucleus-Nucleus III, 1988)

mJ/Y = 3097 MeV t @ 10-20 s 1986 Start of CERN heavy ion program 1988 The first claim of QGP observation 1996 The second claim. The dashed line corresponds to a model where a J/Y is absorbed in nuclear matter 2003 Latest data

Proposed nuclear phase diagram Proposed nuclear phase diagram. Critical temperature for the liquid-gas phase transition, Tc , is on the top of spinodal region. Hagedorn-temperature TH - is critical temperature for the phase transition to the quark-gluon plasma.

A. Goodman et al., Phys. Rev. C30,(1984)851 J.B. Silva et al., Phys. Rev. C69,(2004)024606 Fig.: P. Napolitani et al., PRC 70 (2004) 055607 7

Classical & Nuclear Equations of State Van der Waals system -1875 & nuclear system (Skyrme, 1961) (relative units: V/Vc; p/pc ;T/Tc ) ■The spinodal region: ■Top of spinodal is Tc – critical temperature for liquid –gas phase transition( surface tension vanishes here) H. Jaqaman et al., Phys. Rev. C 27 (1983)2782 G. Sauer et al., Nucl. Phys. A264 (1976) 221 8

Nuclear Equation of State

Critical temperature for liquid-gas phase transition from multifragmentation data

The IMF charge distributions for p(8. 1GeV)+Au collisions The IMF charge distributions for p(8.1GeV)+Au collisions. Symbols are data. Solid lines are calculated (INC+SMM) assuming Tc= 18 MeV and break-up volumes indicated. Green and blue lines are for Tc= 7 and 11MeV.

Critical temperature from multifragmentation in p(8 Critical temperature from multifragmentation in p(8.1GeV)+Au collision (lines are calc.with INC+SMM)

Experimental Results τem ≈ 1.5∙10-22 s p (8.1 GeV) + Au, 4π-setup FASA, Nuclotron, Dubna Tc = (17 ± 2) MeV Two-characteristic volumes Mean decay time τem ≈ 1.5∙10-22 s Spinodal decomposition= liquid-fog phase transition

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Critical temperature for liquid-gas phase from fission data

Temperature dependence of liquid - drop fission barrier of 188Os for different parameterizations of surface tension.

The symbols are taken from G. Sauer, G. Chandra H. and U. Mosel, Nucl The symbols are taken from G. Sauer, G. Chandra H. and U. Mosel, Nucl. Phys. A264 (1976) 221. 19

Fission probability of 188Os as a function of the excitation energy Fission probability of 188Os as a function of the excitation energy. Data – from L.G. Moretto et al., 1972: 4He + 184W Curves are calculated assuming different values of critical temperature. Surface tension is taken according to D.G. Ravenhall et al., Nucl. Phys. A40 (1983) 71.

(1) Tc = (19.5 ± 1.2) MeV (2) Tc = (16.5 ± 1.0) MeV Fission probabilities for 188Os at excitation energy 40 MeV. The calculated values are given for different parameterizations of surface tension. (1) Tc = (19.5 ± 1.2) MeV (2) Tc = (16.5 ± 1.0) MeV

Thanks for ATTENTION

Determination of break-up volume from IMF charge distribution FASA data, 2004 Vt = (2.6  0.3)V0 or  t = (0.38  0.04) 0

Determination of the freeze-out volume from energy spectrum of carbon produced in p(8 GeV)+Au collisions ( FASA, 2004 ) Vf = (5  0.5)V0 or  f = (0.2  0.02) 0

Similarity of Multifragmentation and Nuclear Scission J.A. Lopez & J. Randrup, NP A512 (1990) 345 Qualitative presentation of the potential energy of hot nucleus (with excitation energy Eo*) as a function of the system radius. Schematic view of the multi-fragmentation process and its time scale.

200 fm/c 100 fm/c 50 fm/c 0 fm/c

Fissility of 188Os at E*=40 MeV, experiment and theory

Relative value of fissility parameter for l88Os as a function of temperature for different parameterization of surface tension.

Temperature as a function of the excitation energy per nucleon Temperature as a function of the excitation energy per nucleon. The data are from J. Pochodzalla et al. (PRL.B 1995). The line is calculated within the statistical model of multifragmentation assuming Tc = 16 MeV (J.P. Bondorf et al., NP A, 1985) 32