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Low Density Nucleonic Matter in Fermi Energy Collisions. J.B. Natowitz. Few Body Syst.Suppl. 14 (2003) 361-366 Eur.Phys.J. A22 (2004) 261-269. Perfect Liquid?. Perfect Gas ?. Correlations – Cluster Formation Bose Condensates Efimov States Superfluidity.

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## J.B. Natowitz

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**Low Density Nucleonic Matter in Fermi Energy Collisions**J.B. Natowitz**Few Body Syst.Suppl. 14 (2003) 361-366**Eur.Phys.J. A22 (2004) 261-269 Perfect Liquid? Perfect Gas ? Correlations – Cluster Formation Bose Condensates Efimov States Superfluidity**The Symmetry Energy Problem**Constraining the density dependence of the symmetry energy is a complex problem- The Nuclei Always Solve the Problem Exactly For Us There is always a model dependence Requires close synergy between theorists and experimentalists**While low density situation would appear to be easier to**constrain- cluster formation changes the medium (leads to additional complexity opportunity)**Cluster Formation and The Equation of State of Low-Density**Nuclear Matter Cluster Formation and The Virial Equation of State of Low-Density Nuclear Matter C.J. Horowitz and A. Schwenk Nucl. Phys. A776 (2006) 55-79 Relativistic Equation of State of Nuclear Matter for Supernova and Neutron StarH.Shen, H.Toki, K. Oyamatsu and K. Sumiyoshi Nucl.Phys. A637 (1998) 435-450**Calculation -Private Communication – O’Connor, Schwenk,**Horowitz 2008 Data- Kowalski et al., Phys. Rev. C, 75 014601 (2007)**C. J. Horowitz and A. Schwenk nucl-th/0507033**Calculation -Private Communication – O’Connor, Schwenk, Horowitz 2008 What is the composition, EOS and neutrino response of nuclear matter near the neutrinosphere?**Light Charged Particle Emission Studies**• 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 NIMROD 4 Pi Charged Particles 4 Pi Neutrons Reaction System List Thesis – L. Qin TAMU- 2008**Velocity PlotsLight Charged Particles**From Fitting Velocity Plot Protons 40Ar+124Sn PLF Experiment Sampling the GAS-early emission faster particles NN V perpendicular NN Sum of Source Fits V parallel TLF Evaporation-like Sampling the Liquid – late emission**Reaction Tomography**LIQUID lAB GAS Fsym ═αT / {(4)[(Z/A)21 – (Z/A)22]}**TRANSPORT CALCULATIONS**For Us - Antisymmetrized Molecular Dynamics - ONO Constrained Molecular Dynamics - Bonasera NUCLEAR MATTER CALCULATIONS Beth-Uhlenbeck Cluster Mean Field Approach- Roepke ISOSCALING ANALYSIS Tsang et al. There is always a model dependence**“The Quantum Nature of a Nuclear Phase Transition.A.**Bonasera ,Z. Chen , R. Wada , K. Hagel , J. B. Natowitz, P. Sahu , L. Qin , S. Kowalski , Th. Keutgen, T. Materna ,T. Nakagawa, “ Physical Review Letters, 101. 122702 (2008)**L.Qin et al. In Progress**LIQUID Data - Surface, T Corrected**Average Density Determination**Coalescence ModelNon-Dissipative Analyses Expanding Fermi Gas Model 47A MeV LIQUID REGION K. Hagel et al. Phys. ReV. C 62 034607 (2000) J.B. Natowitz et al., Phys.Rev. C 66 031601 (2002)**Clusterization in Very Low Density Nuclear Matter**PRC 75, 014601 (2007)**LCP Isoscaling Analyses and Symmetry Energy**LOW DENSITY CHEMICAL EQUILIBRIUM MODEL(Albergo) THHe = 14.3/ [ln (1.59R)] Temperature [ Yd ] [ Y4He ] R = [ Yt ] [ Y3He ] Density ρn = 0.0062 x 1036 T3/2 exp[- 20.6/T] Y(4He)/ Y(3He) fm-3 ρp = 0.0062 x 1036 T3/2 exp[ -19.8/T] Y(4He)/ Y(3H) fm-3 ρnucl tot = ρp + ρn + 2 ρd + 3 ρt + 3 ρ3He + 4 ρα**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**Medium Modifications - Gerd Roepke et al.**Work in Progress Free B.E. Binding Energy, MeV K, fm-1**Virial (no A=3)**T = 5 A=3 Included No Medium Effects Alpha Mass Fraction Medium Effects Density nuc/fm3 No Additional Momentum of cluster relative to the medium**Temperature Corrections**Surface Corrections**L.Qin et al. In Preparation**LIQUID GAS**Virial Orig T=5**Alpha Mass Fraction Density nuc/fm3**Why Mott Point Not Seen?**Effect of Momentum Relative to the Medium ? Free B.E. Binding Energy, MeV K, fm-1**Isoscaling Evolution**Fig. 1 CsI detectors Fig. 2 Demon detectors (left) Fig. 3 Demon detectors (right) Z. Chen, R. Wada, M. Huang et al ---in Progress See Talk of Z. Chen • IMFs were measured by a Si quadrant telescope, backed by four CsI detectors (3cm) at 20°. The Si telescope consisted of four 5cm x 5cm area detectors, having thicknesses 129µm+300µm+1000µm+1000µm (021705 run) 61µm+300µm+1000µm+1000µm (040805 run &060605 run)**Reaction systems studied**• 021705 40 AMeV 64Zn beam on 58Ni, 64Ni, 112Sn, 124Sn, 197Au targets • 040805 40 AMeV 64Zn beam on 112Sn target 40 AMeV 70Zn beam on 58Ni, 64Ni, 112Sn, 124Sn, 197Au, 232Th targets (3) 060605 40 AMeV 64Ni beam on 58Ni, 64Ni, 112Sn, 124Sn, 197Au, 232Th targets**Isotope resolution**Z=10 Z=8 Z=6 Z=4 Fig. 4 Isotopes for Z=3 to 12 have been clearly identified in all Si-Si combinations Fig. 5 Linearized Z distribution**Isoscaling Evolution from AMD.Y(64Ni+124Sn)/ Y(64Zn+112Sn)**Time=300 fm/c Time=2000 fm/c**Fragment –Particle Correlations to Explore Effects of**Secondary Decay S. Hudan et al.**40 MeV/u 64Zn + 112Sn**Z. Chen, R. Wada, M. Rodrigues et al. Work in Progress**Texas A&M University, College Station, Texas INFN Laboratori**Nazionali di Legnaro, Legnaro, Italy INFN Dipartimento di Fisica, Padova, Italy Jagellonian University, Krakow, Poland UCL, Louvain-la-Neuve, Belgium • M. Barbui, A. Bonasera. C. Bottosso, M. Cinausero, Z. Chen, Y. El Masri, D. Fabris, K. Hagel, S. Kimura, T. Keutgen, S. Kowalski, M. Lunardon, Z. Majka, S. Moretto, G. Nebbia, J. Natowitz, A. Ono, L. Qin, S. Pesente, G. Prete, V. Rizzi, M. Rodrigues, G. Roepke, P. Sahu, S. Shlomo, R. Wada, J. Wang, G. Viesti Texas A&M, Padova, Legnaro, Krakow, Katowice,Louvain la Neuve, Lanzhou**Figure 2. The alpha-particle cluster**structure of the Hoyle-state in 12C, as predicted using Fermionic Molecular Dynamics (M. Chernykh, et al., Phys. Rev. Lett. 98, 032501 (2007)).**We Hope To Be Able To Welcome Y’ALL to NN2012**In San Antonio, Texas Torch-of-Friendship Henry B. Gonzalez Convention Center Shrine of Texas Liberty River-Walk-Dining**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**Fig. 9 Isotopic yield ratios for 64Ni+124Sn/64Zn+112Sn are**shown for α parameter (upper) and β(lower). Fig. 10 Similar plot as Fig.9, but for (64Ni+197Au )/ (64Ni+112Sn)**Experimental setup**Fig. 1 CsI detectors Fig. 2 Demon detectors (left) Fig. 3 Demon detectors (right) See Talk of Z. Chen • IMFs were measured by a Si quadrant telescope, backed by four CsI detectors (3cm) at 20°. The Si telescope consisted of four 5cm x 5cm area detectors, having thicknesses 129µm+300µm+1000µm+1000µm (021705 run) 61µm+300µm+1000µm+1000µm (040805 run &060605 run)

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