WCI3

1

• WCI3
• THERMOMETRY
• AND
• CALORIC CURVES

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Shlomo S and Natowitz J B 1990 Phys. Lett. B 252
187 Shlomo S and Natowitz J B 1991 Phys. Rev. C
44 2878
S. Shlomo and V. Kolomietz Rep. Prog. Phys. 68 1
(2005) Hot Nuclei
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ISOSPIN DEPENDENCE OF LIMITING
TEMPERATURES
J. Besprovany and S. Levit Phys. Lett. B217 1
(1989)
Based on Temperature Dependent Hartree Fock
Calculations Of Bonche, Levit and Vautherin
Theoretical Coulomb Instability Temperatures
( SKM Interaction)
6
CALORIC CURVES
J. Bondorf et al., Phys. Lett B 162, 30
(1985) H.W. Barz et al., Phys. Lett. B 184 125
(1987)
D. Gross et al., Nucl. Phys. A461 668 (1987) Y.
Zheng et al., Phys. Lett. B 194 183 (1987)
R. Wada et al. Phys. Rev. C 39, 497 (1989)
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A. Le Fevre et al., NPA 657, 446 (1999)
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Double Isotope Ratio Temperature
S. Albergo, S. Costa, E. Costanzo, and A.
Rubbino, Nuovo Cimento A 89, 1 (1985)
J. Pochodzalla et al., Phys. Rev. Lett. 75,
10401043 (1995)
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G. Papp and W. Norenberg Hirschegg
94 Multifragmentation p87
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J. Pochodzalla et al., Phys. Rev. C 35, 1695
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V. Serfling et al., Phys. Rev. Lett. 80, 3928
(1998)
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Excitation of IMF

N. Marie et al, PRC 58 256 (1998)
S. Hudan, et al. Phys.Rev. C67 064613(2003)
136Xe Sn
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A "Little Big Bang" Scenario of
MultifragmentationAuthors X. Campi, H. Krivine,
E. Plagnol, N. Sator Phys.Rev. C67 (2003) 044610
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• H. Xi et al. Phys. Rev. C 57, R462 (1998)
• G. J. Kunde et al. Phys. Lett. B 416, 56 (1998)
• H. F. Xi et al Phys. Rev. C 58, R2636(1998)
• M. B. Tsang et al. Phys.Rev. Lett. 78, 3836
  (1997)
• V. E. Viola et al. Phys. Rev. C 59, 2660 (1999)
• AND MANY MORE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  !!!!!

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Z. Majka et al, Phys. Rev. C 55, 2991-2997
(1997)
F. Gulminelli and D. Durand Nucl. Phys. A 615 117
(1997)
Al. Raduta and Ad. Raduta Hirschegg
99 Multifragmentation p 231
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J. Pochodzalla et al., Phys. Rev. Lett. 75,
10401043 (1995)
T. Odeh Thesis GSI 1999
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Double Isotope Temperatures

• T ?BE / ln( CR)
• Caloric curves constructed from Raw
  Double Isotope Ratio Temperatures in different
  experiments differ greatly
• S. Das Gupta, A. Z. Mekjian and M. B. Tsang,
• arXiv nucl- th/ 0009033 v2.,23 Oct 2000

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K. Hagel et al., Phys. Rev. C 62, 034607 (2000)
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Coalescence Model References

• L. P. Csernai and J. I. Kapusta, Phys. Rep. 131,
  223 (1986)
• Z. Mekjian, Phys. Rev. C 17, 1051 (1978) Phys.
  Rev. Lett.
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• Glagola, H. Breuer, and V. E. Viola, Jr., Phys.
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• J. Cibor, A. Bonasera, J.B. Natowitz, R. Wada,
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• Murray, and T. Keutgen, Isospin Physics in
  Heavy-Ion Collisions
• at Intermediate Energies, edited by B. A. Li and
  W. U.
• Schroeder Nova Science

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J. Cibor et al, Phys. Lett. B 473, 20 (2000),
K. Hagel et al, Phys. Rev. C 62, 4607 (2001)
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Temperature and Excitation Energy Measurements
Included in Survey
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Caloric Curves T initial vs Ex/A Corrected

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Community Consensus Caloric Curves
From the existing data Caloric curves can be
defined in different mass regions Results from
quite varied entrance channel systems,
reaction dynamics and projectile energy ranges
appear to be consistent.
Only the lightest nuclei have been
investigated to very high excitation There
appears to be a mass dependence in the Caloric
Curves
J.B. Natowitz et al., Phys.Rev. C 65 034618
(2002)
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J.N. De et al. Phys. Rev. C55 (1997)
1641-1644
S.K. Samaddar et al. Phys.Rev.Lett. 79 4962
(1997)
Collisions between heavy nuclei at high energies
may generate a modest amount of compression even
for far-central impacts. We have therefore
repeated the calculations taking into account the
effect of flow energy with different values of
P0. If P0 is given, an estimate of the flow
energy per nucleon can be easily made if P0
-0.1 MeV fm-3, the average flow energy per
nucleon is ? 1.3 MeV. We find that with
increase in flow energy, the rise in temperature
is slower and when the pressure P0 -0.1 MeV
fm-3, the caloric curve shows a plateau at T ? 5
MeV in the excitation energy range of 5-10 MeV.
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Caloric Curves and Lyapunov Exponents in
Molecular Dynamics Calculations C.O. Dorso
and A. Bonasera, Eur. Phys. J. A, 421 (2001)
MLE reaches a maximum for that energy for which
the fluctuations are maximal and where we expect
to find critical behavior.
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A. Chernomoretz , C. O. Dorso , and J. A. López
Phys. Rev. C 64, 044605 (2001)
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Takuya Furuta, Akira OnoProg.Theor.Phys.Suppl.
156 (2004) 147-148
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D. G. dEnterria, Phys. Rev. Lett. 87,
22701 (2002). D. G. d'Enterria, ,
submitted to Phys. Lett., (2002).
The Mass Dependence of Limiting
Temperatures
Temperatures Derived from Second Chance
Nuclear Bremsstrahlung Show a Similar Mass
Dependence to Those Determined from
Other Techniques
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P. Napolitani et al., Phys.Atom.Nucl. 66 1471
(2003) Yad.Fiz. 66 1517 (2003)
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D. G. dEnterria, Phys. Rev. Lett. 87,
22701 (2002). D. G. d'Enterria, ,
submitted to Phys. Lett., (2002).
The Mass Dependence of Limiting
Temperatures
Temperatures Derived from Second Chance
Nuclear Bremsstrahlung Show a Similar Mass
Dependence to Those Determined from
Other Techniques
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Coulomb instability in hot nuclei with Skyrme
interactionH. Q. Song R. K. Su Phys. Rev.
C 44, 25052511 (1991)
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Critical Temperature of Symmetric Nuclear Matter
16.6 ? 0.86 MeV
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The Nuclear Incompressibility

Thus employing Skyrme interactions
with the ? 1/6 parameterization,
K 232 ? 22 MeV.
Using Gogny interactions with ? 1/3
leads to K 233 ? 37 MeV.
These results for K
lead to m values of 0.674 A value of K
231 ? 5 MeV, was derived by D. H. Youngblood,
H. L. Clark, and Y.-W. Lui, Phys. Rev. Lett.
82, 691 (1999) by comparison of data for the GMR
breathing mode energy of five different nuclei
with energies calculated employing the Gogny D1(?
1/3), D1S (? 2/3) and D250 (? 2/3)
interactions. Of J. P. Blaizot, J. F. Berger, J.
Decharge and M. Girod, Nucl. Phys. A591, 435
(1995) This Technique May Prove Useful To Probe
the Isospin Dependence of KNM
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Inverse Level Density Parameters
J. Natowitz et al., ArXiV
nucl-ex/0205005 (2002)
T 6 MeV
T 7 MeV
Above the Onset of The Plateau The Apparent K,
Derived from E(A/K)T2, Decreases
T 8 MeV
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Relative Densities Derived Assuming
Non-Dissipative Expanding Fermi Gas
Using the usual expression for a, the Fermi gas
level density parameter, a
(A/K(? )) ( p 2/4 ? F(? )) K(? ),
the inverse level density parameter for an
expanded nucleus of equilibrium density, ? eq,,
may be written K(? eq ) T2 ? eq /?0
2/3 m( ?0) /m( ? eq)
?th where ?0 is the normal nuclear density and
m is the ratio of the effective mass of the
nucleon to the mass of the free nucleon. At the
temperatures at which we are Interested in using
this expression m should be close to 1.Above
the excitation energy where m goes to 1, ?
eq /?0 ( K ? eq / K0)3/2 (5)  
J.B. Natowitz et al., PRC in press, August 2002
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Comparison to
Densities Derived With Other Techniques
Relative Densities Derived From Expanding
Fermi Gas Assumption are in Reasonable
Agreement With Those Determined Using
Thermal Coalescence Model Analysis J. Cibor
et al., Phys. Lett. B 473, 29 (2000) K. Hagel
et al. Phys. Rev. C 62 034607 (2000)
Those Derived From an Emission Barrier
Analysis Are Somewhat Lower
D. Bracken et al. ( ISiS Group)
Private Communication
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Caloric Curve for Mononuclear ConfigurationsL.
G. Sobotka, R. J. Charity, J. Tõke, and W. U.
SchröderPhys. Rev. Lett. 93, 132702 (2004)
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V. E. Viola et al. Phys. Rev.
Lett. 93, 132701 (2004)
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January 05
J. Wang et al. nucl-ex/0408002
Hot Fermi Gas A 2 APROJ
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Impact Parameter Dependence
40A MeV 40Ar 112Sn
J. Wang et al., In Progress
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Community Consensus Caloric Curves
From the existing data Caloric curves can be
defined in different mass regions Results from
quite varied entrance channel systems,
reaction dynamics and projectile energy ranges
appear to be consistent.
Only the lightest nuclei have been
investigated to very high excitation There
appears to be a mass dependence in the Caloric
Curves
J.B. Natowitz et al., Phys.Rev. C 65 034618
(2002)
49
J.N. De et al. Phys. Rev. C55 (1997)
1641-1644
Note-Addition of Radial Flow Will Flatten the
Curve
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J. Wang et al. Work in Progress
35 MeV/u 64Zn 92Mo 47 MeV/u 64Zn 92Mo 40
MeV/u 40Ar 112Sn 55 MeV/u 27Al 124Sn