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

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

Exploring The Nuclear Matter Phase Diagram With Collisional Heating 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. AMD Calculation TIMETIME Dynamic Evolution Excitation Energy ? Temperatures ? Degree of expansion Composition ? Chemical and Thermal Equilibrium ? Equation of State ? Liquid-gas phase transition?

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

Event Selection Neutron + Charged Particle multiplicity distribution for 64 Zn+ 124 Sn. Bin4 corresponds to the most violent collision events Most Violent Collision 30% Top Highest Multiplicity MnMn M CP

Source Analysis of Emission ( Energy, Angle) Source Fitting – 4 He from 40 Ar Sn PLF Angular Distribution NNTLF Elab, MeV 

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

T C =16.6  0.86 MeV Critical Temperature of Symmetric Nuclear Matter Phys.Rev.Lett. 89 (2002) Phys.Rev. C65 (2002) employing Skyrme interactions with the  = 1/6 density dependence, this value of T c leads 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 = 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.

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

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

C.J. HorowitzC.J. Horowitz, A. Schwenk nucl-th/ A. Schwenk

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

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/ C.J. HorowitzA. Schwenk

. nucl-th/ The Virial Equation of State of Low-Density Neutron Matter C.J. Horowitz and A. SchwenkC.J. HorowitzA. Schwenk Clustered Gas VEOS SFSF SESE T/2 Skyrme, Fermi gas etc. SYMMETRY ENERGY(T,  )

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

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

Isoscaling Analyses and Symmetry Energy 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 M.B. TsangM.B. Tsang, W.A. Friedman, C.K. Gelbke, W.G. Lynch,W.A. FriedmanC.K. GelbkeW.G. Lynch G. VerdeG. Verde and H.S. Xu, Phys.Rev. C64 (2001) H.S. Xu F sym

T  α ═ (4F / T)[(Z/A) 2 1 – (Z/A) 2 2 ]  n = 0.62 x T 3/2 exp[- 20.6/T] Y( 4 He)/ Y( 3 He) cm -3  p = 0.62 x T 3/2 exp[ -19.8/T] Y( 4 He)/ Y( 3 H) cm -3  nuc tot =  p +  n + 2  d + 3  t + 3  3He + 4   Density LOW DENSITY CHEMICAL EQUILIBRIUM MODEL(Albergo) Temperature T HHe = 14.3/ [ln (1.59R)] R = [ Y d ] [ Y 4 He ] [ Y t ] [ Y 3 He ] [ Y t ] [ Y 3 He ] Isoscaling Analyses and Symmetry Energy

Clusterization in Low Density Nuclear Matter

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

Neutron Rich Proton Rich

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

V par cm/ns V perp cm/ns Significant Temperature Evolution With Velocity Relatively Small Changes with Projectile Size DOUBLE ISOTOPE RATIO T HHe CHEMICAL EQUILIBRIUM TEMPERATURES T HHe = 14.3/ [ln (1.59R)] (albergo) R = [ Y d ] [ Y 4 He ] [ Y t ] [ Y 3 He ] [ Y t ] [ Y 3 He ] Reaction Tomography-Temperatures

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

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

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

E sym(nuclides) = E sym(NM) ( /A 1/3 ) P. Danielewicz

Few Body Syst.Suppl. 14 (2003) Eur.Phys.J. A22 (2004) M. Beyer, G. Roepke et al., Phys.Lett. B488, (2000) IN MEDIUM BINDING ENERGIES and MOTT TRANSITION

Alpha Mass Fractions

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

Correlations Bose Condensates Superfluidity Efimov States

E. Bell 1, M. Cinausero 2, Y. El Masri 6,D. Fabris 3, K. Hagel 1, J. Iglio 1, A. Keksis 1, T. Keutgen 6, M. Lunardon 3, Z. Majka 4, A. Martinez-Davalos, 5 A. Menchaca-Rocha 5, S. Kowalski 1,T. Materna 1, S. Moretto 3, J. B. Natowitz 1, G. Nebbia 3, L. Qin 1, G. Prete, 2 R. Murthy 1, S. Pesente 3, V. Rizzi, 3 D. V. Shetty 1, S. Soisson 1, B. Stein 1, G. Souliotis 1, P. M. Veselsky 1,A. Wieloch 1, G. Viesti 3, R. Wada 1, J. Wang 1, S. Wuenshel 1, and S. J. Yennello 1 1 Texas A&M University, College Station, Texas 2 INFN Laboratori Nazionali di Legnaro, Legnaro, Italy 3 INFN Dipartimento di Fisica, Padova, Italy 4 Jagellonian University, Krakow, Poland 5 UNAM, Mexico City, Mexico 6 UCL, Louvain-la-Neuve, Belgium

Major Contributors 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. Natowitz L. Qin, S. Pesente, G. Prete, V. Rizzi, P. Sahu, S. ShlomoJ. Wang, G. ViestiM. CinauseroZ. ChenD. FabrisY. El MasriK. HagelT. KeutgenS. KowalskiM. LunardonS. MorettoG. NebbiaJ. NatowitzL. QinS. PesenteG. PreteV. RizziG. Viesti S. Shlomo, A. Ono, G. Roepke A. Schwenk, E. O’Connor AND THE NIMROD COLLABORATION TAMU, PADOVA, LEGNARO, KRAKOW, LOUVAIN la NEUVE, CATANIA, LANZHOU