J.B. Natowitz

Correlations – Cluster Formation Bose Condensates Efimov States Superfluidity Perfect Liquid? Perfect Gas ? Few Body Syst.Suppl. 14 (2003) Eur.Phys.J. A22 (2004)

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)

Relativistic Equation of State of Nuclear Matter for Supernova and Neutron Star H.Shen, H.Toki, K. Oyamatsu and K. Sumiyoshi Nucl.Phys. A637 (1998) Cluster Formation and The Virial Equation of State of Low-Density Nuclear Matter C.J. Horowitz and A. Schwenk Nucl. Phys. A776 (2006) Cluster Formation and The Equation of State of Low-Density Nuclear Matter

Data- Kowalski et al., Phys. Rev. C, (2007) Calculation -Private Communication – O’Connor, Schwenk, Horowitz 2008

C. J. Horowitz and A. Schwenk nucl-th/ 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 Thesis – L. Qin TAMU Reaction System List

Velocity Plots Light Charged Particles TLF NN Experiment From Fitting Velocity Plot Protons 40 Ar+ 124 Sn PLF V parallel V perpendicular NN Sum of Source Fits Sampling the GAS-early emission faster particles Sampling the Liquid – late emission Evaporation-like

F sym ═ α T / {(4)[(Z/A) 2 1 – (Z/A) 2 2 ]} lAB LIQUID GAS Reaction Tomography

ISOSCALING ANALYSIS TRANSPORT CALCULATIONS For Us - Antisymmetrized Molecular Dynamics - ONO Constrained Molecular Dynamics - Bonasera NUCLEAR MATTER CALCULATIONS Beth-Uhlenbeck Cluster Mean Field Approach- Roepke 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, (2008)

L.Qin et al. In Progress Data - Surface, T Corrected LIQUID

K. Hagel et al. Phys. ReV. C (2000) J.B. Natowitz et al., Phys.Rev. C (2002) Average Density Determination Coalescence Model Non-Dissipative Analyses Expanding Fermi Gas Model 47A MeV LIQUID REGION

Clusterization in Very Low Density Nuclear Matter PRC 75, (2007)

ρ n = x T 3/2 exp[- 20.6/T] Y( 4 He)/ Y( 3 He) fm -3 ρ p = x T 3/2 exp[ -19.8/T] Y( 4 He)/ Y( 3 H) fm -3 ρ nucl tot = ρ p + ρ n + 2 ρ d + 3 ρ t + 3 ρ 3He + 4 ρ α Density LOW DENSITY CHEMICAL EQUILIBRIUM MODEL(Albergo) Temperature T HHe = 14.3/ [ln (1.59R)] [ Y d ] [ Y 4 He ] [ Y t ] [ Y 3 He ] [ Y t ] [ Y 3 He ] LCP Isoscaling Analyses and Symmetry Energy R =

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

K, fm -1 Binding Energy, MeV Medium Modifications - Gerd Roepke et al. Work in Progress Free B.E.

Alpha Mass Fraction Density nuc/fm 3 Virial (no A=3) T = 5 A=3 Included No Medium Effects Medium Effects No Additional Momentum of cluster relative to the medium

Temperature Corrections Surface Corrections

GAS LIQUID L.Qin et al. In Preparation

Virial Orig T=5 Density nuc/fm 3 Alpha Mass Fraction

K, fm -1 Binding Energy, MeV Why Mott Point Not Seen? Effect of Momentum Relative to the Medium ? Free B.E.

Isoscaling Evolution  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 ( run) 61µm+300µm+1000µm+1000µm ( run & run) Fig. 1 CsI detectorsFig. 3 Demon detectors (right)Fig. 2 Demon detectors (left) Z. Chen, R. Wada, M. Huang et al ---in Progress See Talk of Z. Chen

(1) AMeV 64 Zn beam on 58 Ni, 64 Ni, 112 Sn, 124 Sn, 197 Au targets (2) AMeV 64 Zn beam on 112 Sn target 40 AMeV 70 Zn beam on 58 Ni, 64 Ni, 112 Sn, 124 Sn, 197 Au, 232 Th targets (3) AMeV 64 Ni beam on 58 Ni, 64 Ni, 112 Sn, 124 Sn, 197 Au, 232 Th targets Reaction systems studied

Isotope resolution Z=4 Z=6 Z=8 Z=10 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( 64 Ni+ 124 Sn)/ Y( 64 Zn+ 112 Sn) Time=2000 fm/cTime=300 fm/c

Fragment –Particle Correlations to Explore Effects of Secondary Decay S. Hudan et al.

40 MeV/u 64 Zn Sn Z. Chen, R. Wada, M. Rodrigues et al. Work in Progress

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. ViestiM. CinauseroZ. ChenY. El MasriD. FabrisK. HagelT. KeutgenS. KowalskiM. LunardonS. MorettoG. NebbiaJ. Natowitz L. QinS. PesenteG. Prete V. RizziG. Viesti Texas A&M, Padova, Legnaro, Krakow, Katowice,Louvain la Neuve, Lanzhou 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

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, (2007)).

We Hope To Be Able To Welcome Y’ALL to NN 2012 In San Antonio, Texas Torch-of-Friendship River-Walk-Dining Shrine of Texas Liberty Henry B. Gonzalez Convention Center

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

Fig. 9 Isotopic yield ratios for 64 Ni+ 124 Sn/ 64 Zn+ 112 Sn are shown for α parameter (upper) and β(lower). Fig. 10 Similar plot as Fig.9, but for ( 64 Ni+ 197 Au )/ ( 64 Ni+ 112 Sn)

summary Exp.AMD 300fm/c AMD 2000fm/c LP, NN, Y( 64 Ni+ 124 Sn)/ Y( 64 Zn+ 112 Sn) α = 0.31+/ β = / α = 0.35+/ β = / α = 0.26+/ β = / LP, NN+PLF, Y( 64 Ni+ 124 Sn)/ Y( 64 Zn+ 112 Sn) α = 0.34+/ β = / LP, with coulomb Y( 60 Ca+ 60 Ca)/ Y( 40 Ca+ 40 Ca) α = 3.08+/ β = / α = 2.17+/ β = / LP, without coulomb Y( 60 Ca+ 60 Ca)/ Y( 40 Ca+ 40 Ca) α =1.36 +/ β = /-0.12 α = 1.70+/ β = /-0.08 LP, Lijun’s exp. Y( 40 Ar+ 124 Sn)/ Y( 40 Ar+ 112 Sn) α = 0.41+/ β = /-0.11 IMF, Y( 64 Ni+ 124 Sn)/ Y( 64 Zn+ 112 Sn) α = 0.28+/ β = /-0.01 α = 0.42+/ β = /-0.13 α = 0.29+/ β = /-0.13 IMF, with coulomb Y( 60 Ca+ 60 Ca)/ Y( 40 Ca+ 40 Ca) α = 3.39+/-3.64 β = /-4.40 α =1.88 +/ β = /-0.21 IMF, without coulomb Y( 60 Ca+ 60 Ca)/ Y( 40 Ca+ 40 Ca) α = 3.19+/ β = /-0.59 α = 1.66+/-0.22 β = /-0.31 IMF, Lijun’s exp. Y( 40 Ar+ 124 Sn)/ Y( 40 Ar+ 112 Sn) α = 0.31+/ β = /-0.34

Experimental setup  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 ( run) 61µm+300µm+1000µm+1000µm ( run & run) Fig. 1 CsI detectorsFig. 3 Demon detectors (right)Fig. 2 Demon detectors (left) See Talk of Z. Chen