Experimental analyses of moderate temperature nuclear gases produced in the violent collisions of 35 MeV/nucleon 64 Zn projectiles with 92 Mo and 197 Au target nuclei reveal a large degree of alpha particle clustering at low densities. For these gases, temperature and density dependent symmetry energy coefficients have been derived from isoscaling analyses of the yields of nuclei with A ≤ 4. At densities of 0.01 to 0.05 times the ground state density of symmetric nuclear matter, the temperature and density dependent symmetry energies range from 9.03 to 13.6 MeV. This is much larger than those obtained in mean field Calculations and reflects the clusterization of low density nuclear matter. He are expected to be small and they are ignored in the calculation. In the work reported in reference [1] these virial coefficients were then used to make predictions for a variety of properties of nuclear matter over a range of density, temperature and composition. The authors view this virial equation of state, derived from experimental observables, as modelindependent, and therefore a benchmark for all nuclear equations of state at low densities. Its importance in both nuclear physics and in the physics of the neutrino sphere in supernovae is discussed in the VEOS paper [1]. A particularly important feature of the VEOS, emphasized in reference [1], is the natural inclusion of clustering which leads to large symmetry energies at low baryon density.In this paper we extend our investigations of the nucleon and light cluster emission that occurs in near-Fermi energy heavy ion collisions [2,3,4,5,6] to investigate the properties of the low density participant matter produced in such collisions. The data provide experimental evidence for a large degree of alpha clustering in this low density matter, in agreement with theoretical predictions [1,7,8,9]. Temperature and density dependent symmetry free energies and symmetry energies have been determined at densities of 0.05ρ 0 or less, where ρ 0 is the ground state density of symmetric nuclear matter, by application of an isoscaling analysis [10,11]. The symmetry energy coefficient values obtained, 9.03 to 13.6 MeV, are much larger then those derived from effective interactions in mean field models. The values are in reasonable agreement with those calculated in the VEOS treatment of reference [1]. EXPERIMENTAL PROCEDURESThe reactions of 35A MeV 64 Zn projectiles with 92 Mo and 197 Au target nuclei were studied at the K-500 SuperConducting Cyclotron at Texas A&M University, using the 4π detector array NIMROD [3]. NIMROD consists of a 166 segment charged particle array set inside a neu-

Clustering in low density nuclear matter has been investigated using the NIMROD multidetector at Texas A&M University. Thermal coalescence modes were employed to extract densities, ρ, and temperatures, T, for evolving systems formed in collisions of 47A MeV (40)Ar+(112)Sn, (124)Sn and (64)Zn+(112)Sn, (124)Sn. The yields of d, t, (3)He, and (4)He have been determined at ρ=0.002 to 0.03 nucleons/fm(3) and T=5 to 11 MeV. The experimentally derived equilibrium constants for α particle production are compared with those predicted by a number of astrophysical equations of state. The data provide important new constraints on the model calculations.

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Measurements of the density dependence of the Free symmetry energy in low density clustered matter have been extended using the NIMROD multi-detector at Texas A&M University. Thermal coalescence models were employed to extract densities, ρ, and temperatures, T , for evolving systems formed in collisions of 47 A MeV 40 Ar + 112 Sn , 124 Sn and 64 Zn + 112 Sn , 124 Sn. Densities of 0.03 ≤ ρ/ρ0 ≤ 0.2 and temperatures in the range 5 to 10 MeV have been sampled. The Free symmetry energy coefficients are found to be in good agreement with values calculated using a quantum statistical model. Values of the corresponding symmetry energy coefficient are derived from the data using entropies derived from the model.