Data from a number of different experimental measurements have been used to construct caloric curves for five different regions of nuclear mass. These curves are qualitatively similar and exhibit plateaus at the higher excitation energies. The limiting temperatures represented by the plateaus decrease with increasing nuclear mass and are in very good agreement with results of recent calculations employing either a chiral symmetry model or the Gogny interaction. This agreement strongly favors a soft equation of state. Evidence is presented that critical excitation energies and critical temperatures for nuclei can be determined over a large mass range when the mass variations inherent in many caloric curve measurements are taken into account.Comment: In response to referees comments we have improved the discussion of the figures and added a new figure showing the relationship between the effective level density and the excitation energy. The discussion has been reordered and comments are made on recent data which support the hypothesis of a mass dependence of caloric curve

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

From experimental observations of limiting temperatures in heavy ion collisions we derive Tc, the critical temperature of infinite nuclear matter. The critical temperature is 16.6 ± 0.86 MeV. Theoretical model correlations between Tc, the compressibility modulus, K the effective mass, m * and the saturation density, ρs, are exploited to derive the quantity (K/m * )s . This quantity together with calculations employing Skyrme and Gogny interactions indicates a nuclear matter incompressibility in moderately excited nuclei that is in excellent agreement with the value determined from Giant Monopole Resonance data. This technique of extraction of K may prove particularly useful in investigations of very neutron rich systems using radioactive beams.PACS numbers: 24.10.i,25.70.Gh Improved knowledge of the nuclear equation of state and a coherent picture of the relationship between the properties of finite nuclei and bulk nuclear matter remains a key requirement in both nuclear physics and astrophysics. It is key, for example, to understanding nuclear structure, heavy ion collisions, supernova explosions and neutron star properties [1,2,3]. Significant effort has been devoted to the development of microscopic theoretical models which can provide reliable mathematical formulations of this equation of state [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Such calculations are usually specified for symmetric nuclear matter, a hypothetical system of equal numbers of neutrons and (uncharged) protons interacting through nuclear forces. Driven by the astrophysical problems and more recent laboratory excursions into the region of more exotic nuclei, the dependence of the equation of state on neutronproton asymmetry has also become a subject of significant interest. [21,22,23]. In this letter we employ data from experimental measurements of caloric curves in nuclear collisions, together with systematic trends and correlations derived from a number of theoretical investigations of nuclear matter, to derive the critical temperature and incompressibility of symmetric nuclear matter. The techniques employed offer a natural method to extend such investigations to more asymmetric systems.In a recent paper measurements of nuclear specific heats from a large number of experiments were employed to construct caloric curves for five different regions of nuclear mass [24]. Within experimental uncertainties each of these caloric curves exhibits a plateau region at higher excitation energy, i.e., a "limiting temperature" is reached. In Figure 1 these limiting temperatures from reference [24] are presented as a function of mass. As previously noted, they are observed to decrease with increasing mass. This decrease with increasing mass has long been predicted as resulting from Coulomb Instabilities of expanded and heated nuclei [25,26,27,28,29,30,31,32,33,34,35].The results employed in reference [24] were based upon temperature determinations derived from double isotope yield ratios and from slope measurements of particle spectra. More rece...

We discuss experimental evidence for a nuclear phase transition driven by the different concentration of neutrons to protons. Different ratios of the neutron to proton concentrations lead to different critical points for the phase transition. This is analogous to the phase transitions occurring in 4 He-3 He liquid mixtures. We present experimental results which reveal the N/A (or Z/A) dependence of the phase transition and discuss possible implications of these observations in terms of the Landau Free Energy description of critical phenomena.

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-