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.

No abstract

The reactions 12 Cϩ 116 Sn, 22 NeϩAg, 40 Arϩ 100 Mo, and 64 Znϩ 89 Y have been studied at 47A MeV projectile energy. For these reactions the most violent collisions lead to increasing amounts of fragment and light particle emission as the projectile mass increases. This is consistent with quantum molecular dynamics ͑QMD͒ model simulations of the collisions. Moving source fits to the light charged particle data have been used to gain a global view of the evolution of the particle emission. Comparisons of the multiplicities and spectra of light charged particles emitted in the reactions with the four different projectiles indicate a common emission mechanism for early emitted ejectiles even though the deposited excitation energies differ greatly. The spectra for such ejectiles can be characterized as emission in the nucleon-nucleon frame. Evidence that the 3 He yield is dominated by this type of emission and the role of the collision dynamics in determining the 3 H/ 3 He yield ratio are discussed. Self-consistent coalescence model analyses are applied to the light cluster yields, in an attempt to probe emitter source sizes and to follow the evolution of the temperatures and densities from the time of first particle emission to equilibration. These analyses exploit correlations between ejectile energy and emission time, suggested by the QMD calculations. In this analysis the degree of expansion of the emitting system is found to increase with increasing projectile mass. The double isotope yield ratio temperature drops as the system expands. Average densities as low as 0.36 0 are reached at a time near 100 fm/c after contact. Calorimetric methods were used to derive the mass and excitation energy of the excited nuclei which are present after preequilibrium emission. The derived masses range from 102 to 116 u and the derived excitation energies increase from 2.6 to 6.9 MeV/nucleon with increasing projectile mass. A caloric curve is derived for these expanded Aϳ110 nuclei. This caloric curve exhibits a plateau at temperatures near 7 MeV. The plateau extends from ϳ3.5 to 6.9 MeV/nucleon excitation energy.PACS number͑s͒: 25.70.Mn, 24.10.Lx