1. 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;

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

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

4. mJ/Y = 3097 MeV
t @ 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

5. 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.

7. 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) 7

8. Classical & Nuclear Equations of State
Van der Waals system &
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

9. Nuclear Equation of State

11. Critical temperature for liquid-gas phase transition from multifragmentation data

13. 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.

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

15. 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

16. 16

17. Critical temperature for liquid-gas phase
from fission data

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

19. 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

20. 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 W
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.

21. (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

24. Thanks for ATTENTION

25. 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

26. 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

27. 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.

29. 200 fm/c
100 fm/c
50 fm/c
0 fm/c

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

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

32. 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