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J. B. Natowitz

Experimental Investigations of The Equation of State of Low Density Nuclear Matter. J. B. Natowitz Department of Chemistry and Cyclotron Institute

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J. B. Natowitz

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  1. Experimental Investigations of The Equation of State of Low Density Nuclear Matter J. B. Natowitz Department of Chemistry and Cyclotron Institute , Texas A&M University, College Station

  2. HAPPY 75th BIRTHDAY, YURI AND MANY MANY MORE !

  3. Exploring The Nuclear Matter Phase Diagram With Collisional Heating AMD Calculation • Dynamic Evolution • Excitation Energy ? • Temperatures ? • Degree of expansion • Composition ? • Chemical and Thermal Equilibrium ? • Equation of State ? • Liquid-gas phase transition? T I M E • Collisions of normal density nuclei create initially compressed and excited systems, which expand and cool. • During this process, the properties of the expanding system is manifested in the matter flow, in the energy spectra, and in the yield patterns and nature of produced species which emerge from the collision zone.

  4. Light Charged Particle Emission - High Total Multiplicity Collisions NIMROD 4 Pi Charged Particles 4 Pi Neutrons

  5. Event Selection Most Violent Collision Events @ 30% Top Highest Multiplicity MCP Neutron + Charged Particle multiplicity distribution for 64Zn+124Sn. Bin4 corresponds to the most violent collision events Mn

  6. Source Analysis of Emission ( Energy, Angle) Angular Distribution 1 2 3 PLF NN TLF 4 5 6 7 8 9 10 11 12 Elab, MeV  Source Fitting – 4He from 40Ar + 124Sn

  7. Reaction Tomography-Particles From Fitting Velocity Plot Protons 40Ar+124Sn PLF Experiment Sum of Sources Evaporation-like NN V perpendicular NN Coalescence V parallel TLF Evaporation-like

  8. Critical Temperature of Symmetric Nuclear Matter Phys.Rev. C65 (2002) 034618 Phys.Rev.Lett. 89 (2002) 212701 TC =16.6  0.86 MeV employing Skyrme interactions with the  = 1/6 density dependence, this value of Tcleads to K = 232  22 MeV. Using Gogny interactions with  = 1/3 leads to K = 233  37 MeV. These results for K lead to m* value = 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.

  9. Derived Average Freeze-Out Densities Coalescence ModelNon-Dissipative Analyses Expanding Fermi Gas 47A MeV J.B. Natowitz et al., Phys.Rev. C 66 031601 (2002) K. Hagel et al. Phys. ReV. C 62 034607 (2000)

  10. STARS Giant Nuclei And Sites of Nucleosynthesis Large Changes in Temperature, Density, Proton/Neutron content SUPERNOVA NEUTRON STAR R ~ 10 km

  11. C.J. Horowitz, A. Schwenk nucl-th/0507033

  12. ASTROPHYSICAL EQUATIONS OF STATE AT LOW DENSITY DOMINATED BY ALPHA CLUSTERING Density

  13. Cluster Formation and The Equation of State of Low-Density Nuclear Matter symmetric nuclear matter, T=2, 4, 8 MeV C.J. Horowitz, A. Schwenk nucl-th/0507033

  14. . nucl-th/0507064 • The Virial Equation of State of Low-Density Neutron MatterC.J. Horowitz and A. Schwenk SYMMETRY ENERGY(T,) Clustered Gas VEOS SF T/2 Skyrme, Fermi gas etc. T/2 SE

  15. Many Nucear and Astrophysical Phenomena Strongly Affected by the Symmetry Energy At Normal Density aa ~ 23 MeV for Finite Nuclei ~30 MeV for Symmetric Nuclear Matter

  16. NN SOURCE EMISSION- Experimental Data and Calculated Yields from AMD and Chimera QMD Codes COALESCENCE Average Freeze-out Density 64Zn + 124Sn ~ 0.06 fm-3 “Gas” density ~ ANN/(Atot-ANN) * 0.06 fm-3 ~ 0.01 fm-3

  17. Isoscaling Analyses and Symmetry Energy M.B. Tsang, W.A. Friedman, C.K. Gelbke, W.G. Lynch, G. Verde and H.S. Xu, Phys.Rev. C64 (2001) 041603 Fsym A Comparison of the Yields of Emitted Species for Two Different Sources of Similar Excitation Energy and Temperature but Differing in Their Neutron to Proton Ratios

  18. Isoscaling Analyses and Symmetry Energy T α═ (4F/T)[(Z/A)21 – (Z/A)22] Temperature  THHe = 14.3/ [ln (1.59R)] R = [ Yd ] [ Y4He ] LOW DENSITY CHEMICAL EQUILIBRIUM MODEL(Albergo) [ Yt ] [ Y3He ] Density n = 0.62 x 1036 T3/2 exp[- 20.6/T] Y(4He)/ Y(3He) cm-3 p = 0.62 x 1036 T3/2 exp[ -19.8/T] Y(4He)/ Y(3H) cm-3 nuc tot = p + n + 2d + 3t + 33He + 4

  19. Clusterization in Low Density Nuclear Matter

  20. C.J. Horowitz, A. Schwenk nucl-th/0507033 Private Communication O’Connor, Schwenk, Horowitz Manuscript in Preparation August 2007

  21. Proton Rich Neutron Rich

  22. Reaction System List Thesis – L. Qin TAMU • p + 112Sn and 124Sn • d + 112Sn and 124Sn • 3He + 112Sn and 124Sn • 4He + 112Sn and 124Sn • 10B + 112Sn and 124Sn • 20Ne + 112Sn and 124Sn • 40Ar + 112Sn and 124Sn • 64Zn+ 112Sn and 124Sn Projectile Energy - 47A Mev

  23. Reaction Tomography-Temperatures DOUBLE ISOTOPE RATIO THHe CHEMICAL EQUILIBRIUM TEMPERATURES THHe = 14.3/ [ln (1.59R)] (albergo) R = [ Yd ] [ Y4He ] [ Yt ] [ Y3He ] Vperp cm/ns Significant Temperature Evolution With Velocity Relatively Small Changes with Projectile Size Vpar cm/ns

  24. Reaction Tomography-Densities “Gas” Density TLF REMOVED L. Qin – PhD Thesis, In Progress Fm-3 CHEMICAL EQUILIBRIUM DENSITIES (Albergo) FROM ISOTOPE RATIOS

  25. 4He DERIVED VALUES OF Fsym as a FUNCTION of VELOCITY 47 MeV/u Projectiles on 112Sn, 124Sn 64Zn 10B V perpendicular 20Ne 40Ar NN V parallel

  26. Derived Average Freeze-Out Densities Coalescence ModelNon-Dissipative Analyses Expanding Fermi Gas J.B. Natowitz et al., Phys.Rev. C66 (2002) 031601 K. Hagel et al. PHYSICAL REVIEW C 62 034607 (2000)

  27. P. Danielewicz Esym(nuclides) = Esym(NM) (1 + 2.7/A 1/3)

  28. IN MEDIUM BINDING ENERGIES and MOTT TRANSITION M. Beyer, G. Roepke et al., Phys.Lett. B488, 247-253 (2000) Few Body Syst.Suppl. 14 (2003) 361-366 Eur.Phys.J. A22 (2004) 261-269

  29. Alpha Mass Fractions

  30. M. Beyer et al. nucl-th/0310055 Light Clusters in Nuclear Matter of Finite Temperature Note: Same at low density Rho LE ~.005 fm-3

  31. Correlations Bose Condensates Superfluidity Efimov States

  32. The NIMROD Collaboration E. Bell1,M. Cinausero2,Y. El Masri 6,D. Fabris3, K. Hagel1, J. Iglio1, A. Keksis1, T. Keutgen6,M. Lunardon3, Z. Majka4,A. Martinez-Davalos,5 A. Menchaca-Rocha5, S. Kowalski1,T. Materna1, S. Moretto3, J. B. Natowitz1, G. Nebbia3, L. Qin1, G. Prete,2 R. Murthy1, S. Pesente3, V. Rizzi,3 D. V. Shetty1, S. Soisson1, B. Stein1, G. Souliotis1, P. M. Veselsky1,A. Wieloch1, G. Viesti3,R. Wada1, J. Wang1, S. Wuenshel1, and S. J. Yennello1 1Texas A&M University, College Station, Texas 2INFN Laboratori Nazionali di Legnaro, Legnaro, Italy 3INFN Dipartimento di Fisica, Padova, Italy 4Jagellonian University, Krakow, Poland 5UNAM, Mexico City, Mexico 6UCL, Louvain-la-Neuve, Belgium

  33. Major Contributors • TAMU, PADOVA, LEGNARO, KRAKOW, LOUVAIN la NEUVE, CATANIA, LANZHOU • M. Barbui, A. Bonasera, C. Bottosso, M. Cinausero, Z. Chen, D. Fabris, Y. El Masri, K. Hagel, T. Keutgen, S. Kowalski, M. Lunardon, Z. Majka, S. Moretto, G. Nebbia, J. NatowitzL. Qin, S. Pesente, G. Prete, V. Rizzi, P. Sahu, S. ShlomoJ. Wang, G. Viesti • S. Shlomo, A. Ono, G. Roepke • A. Schwenk, E. O’Connor AND THE NIMROD COLLABORATION

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