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WCI3 THERMOMETRY AND CALORIC CURVES

WCI3 THERMOMETRY AND CALORIC CURVES. 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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WCI3 THERMOMETRY AND CALORIC CURVES

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  1. WCI3 THERMOMETRY AND CALORIC CURVES

  2. 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

  3. 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)

  4. 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)

  5. A. Le Fevre et al., NPA 657, 446 (1999)

  6. 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, 1040–1043 (1995)

  7. G. Papp and W. Norenberg Hirschegg ’94 Multifragmentation p87

  8. J. Pochodzalla et al., Phys. Rev. C 35, 1695 (1987) V. Serfling et al., Phys. Rev. Lett. 80, 3928 (1998)

  9. Excitation of IMF N. Marie et al, PRC 58 256 (1998) S. Hudan, et al. Phys.Rev. C67 064613(2003) 136Xe + Sn

  10. A "Little Big Bang" Scenario of MultifragmentationAuthors:X. Campi, H. Krivine, E. Plagnol, N. SatorPhys.Rev. C67 (2003) 044610

  11. 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 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  12. 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

  13. J. Pochodzalla et al., • Phys. Rev. Lett. 75, 1040–1043 (1995) T. Odeh Thesis GSI 1999

  14. Double Isotope Temperatures • T = BE / ln( C*R) • 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

  15. K. Hagel et al., Phys. Rev. C 62, 034607 (2000)

  16. 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. • 38, 640 (1977); Phys. Lett. 89B, 177 (1980) • H. Sato and K. Yazaki, Phys. Lett. 98B, 153 (1981) • T. C. Awes, G. Poggi, C. K. Gelbke, B. B. Back, B. G. • Glagola, H. Breuer, and V. E. Viola, Jr., Phys. Rev. C 24, 89 • (1981) • J. Cibor, A. Bonasera, J.B. Natowitz, R. Wada, K. Hagel, M. • Murray, and T. Keutgen, Isospin Physics in Heavy-Ion Collisions • at Intermediate Energies, edited by B. A. Li and W. U. • Schroeder ~Nova Science

  17. J. Cibor et al, Phys. Lett. B 473, 20 (2000), K. Hagel et al, Phys. Rev. C 62, 4607 (2001)

  18. Temperature and Excitation Energy Measurements Included in Survey

  19. Caloric Curves T initial vs Ex/A Corrected

  20. 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)

  21. 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.

  22. Caloric Curves and Lyapunov Exponents in Molecular Dynamics CalculationsC.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.”

  23. A. Chernomoretz , C. O. Dorso , and J. A. López Phys. Rev. C 64, 044605 (2001)

  24. Takuya Furuta, Akira OnoProg.Theor.Phys.Suppl. 156 (2004) 147-148

  25. The Mass Dependence of Limiting Temperatures D. G. d’Enterria, Phys. Rev. Lett. 87, 22701 (2002).D. G. d'Enterria, , submitted to Phys. Lett., (2002). Temperatures Derived from Second Chance Nuclear Bremsstrahlung Show a Similar Mass Dependence to Those Determined from Other Techniques

  26. P. Napolitani et al., Phys.Atom.Nucl. 66 1471 (2003) Yad.Fiz. 66 1517 (2003)

  27. The Mass Dependence of Limiting Temperatures D. G. d’Enterria, Phys. Rev. Lett. 87, 22701 (2002).D. G. d'Enterria, , submitted to Phys. Lett., (2002). Temperatures Derived from Second Chance Nuclear Bremsstrahlung Show a Similar Mass Dependence to Those Determined from Other Techniques

  28. Coulomb instability in hot nuclei with Skyrme interactionH. Q. Song R. K. Su Phys. Rev. C 44, 2505–2511 (1991)

  29. Critical Temperature of Symmetric Nuclear Matter 16.6  0.86 MeV

  30. 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

  31. 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

  32. Relative Densities Derived Assuming Non-Dissipative Expanding Fermi Gas Using the usual expression for a, the Fermi gas level density parameter, a = (A/K(ρ )) =( π 2/4 є F(ρ )) K(ρ ), the inverse level density parameter for an expanded nucleus of equilibrium density, ρ eq,, may be written K(ρ eq )= T2 { ρ eq /ρ0 }2/3 {m*( ρ0) /m*( ρ eq)} єth where ρ0 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, ρ eq /ρ0 = ( K ρ eq/ K0)3/2(5) J.B. Natowitz et al., PRC in press, August 2002

  33. 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

  34. Caloric Curve for Mononuclear ConfigurationsL. G. Sobotka, R. J. Charity, J. Tõke, and W. U. SchröderPhys. Rev. Lett. 93, 132702 (2004)

  35. V. E. Viola et al. Phys. Rev. Lett. 93, 132701 (2004) 13

  36. J. Wang et al. nucl-ex/0408002 January 05 Hot Fermi Gas A ~ 2 APROJ

  37. Impact Parameter Dependence 40A MeV 40Ar + 112Sn J. Wang et al., In Progress

  38. 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)

  39. J.N. De et al. Phys. Rev. C55 (1997) 1641-1644 Note-Addition of Radial Flow Will Flatten the Curve

  40. 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

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