Symmetry energy of dilute warm nuclear matter

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 (QS) 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.Comment: 4 pages, 2 figures, 1 tabl

Isocaling and the Symmetry Energy in the Multifragmentation Regime of Heavy Ion Collisions

The ratio of the symmetry energy coefficient to temperature, $a_sym/T$, in Fermi energy heavy ion collisions, has been experimentally extracted as a function of the fragment atomic number using isoscaling parameters and the variance of the isotope distributions. The extracted values have been compared to the results of calculations made with an Antisymmetrized Molecular Dynamics (AMD) model employing a statistical decay code to account for deexcitation of excited primary fragments. The experimental values are in good agreement with the values calculated but are significantly different from those characterizing the yields of the primary AMD fragments.Comment: 12 pages, 6 figure

The Quantum Nature of a Nuclear Phase Transition

In their ground states, atomic nuclei are quantum Fermi liquids. At finite temperatures and low densities, these nuclei may undergo a phase change similar to, but substantially different from, a classical liquid gas phase transition. As in the classical case, temperature is the control parameter while density and pressure are the conjugate variables. At variance with the classical case, in the nucleus the difference between the proton and neutron concentrations acts as an additional order parameter, for which the symmetry potential is the conjugate variable. 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/Z dependence of the phase transition and discuss possible implications of these observations in terms of the Landau Free Energy description of critical phenomena.Comment: 5 pages, 4 figure

Cluster emission and phase transition behaviours in nuclear disassembly

The features of the emissions of light particles (LP), charged particles (CP), intermediate mass fragments (IMF) and the largest fragment (MAX) are investigated for $^{129}Xe$ as functions of temperature and 'freeze-out' density in the frameworks of the isospin-dependent lattice gas model and the classical molecular dynamics model. Definite turning points for the slopes of average multiplicity of LP, CP and IMF, and of the mean mass of the largest fragment ($A_{max}$) are shown around a liquid-gas phase transition temperature and while the largest variances of the distributions of LP, CP, IMF and MAX appear there. It indicates that the cluster emission rate can be taken as a probe of nuclear liquid--gas phase transition. Furthermore, the largest fluctuation is simultaneously accompanied at the point of the phase transition as can be noted by investigating both the variances of their cluster multiplicity or mass distributions and the Campi scatter plots within the lattice gas model and the molecular dynamics model, which is consistent with the result of the traditional thermodynamical theory when a phase transition occurs.Comment: replace nucl-th/0103009 due to the technique problem to access old versio

Density determinations in heavy ion collisions

The experimental determination of freeze-out temperatures and densities from the yields of light elements emitted in heavy ion collisions is discussed. Results from different experimental approaches are compared with those of model calculations carried out with and without the inclusion of medium effects. Medium effects become of relevance for baryon densities above $\approx 5 \times 10^{-4}$ fm$^{-3}$. A quantum statistical (QS) model incorporating medium effects is in good agreement with the experimentally derived results at higher densities. A densitometer based on calculated chemical equilibrium constants is proposed.Comment: 5 pages, 3 figure

Towards the critical behavior for the light nuclei by NIMROD detector

The critical behavior for the light nuclei with A$\sim 36$ has been investigated experimentally by the NIMROD multi-detectors. The wide variety of observables indicate the critical point has been reached in the disassembly of hot nuclei at an excitation energy of 5.6$\pm$0.5 MeV/u.Comment: 4 pages, 2 figures; Proceeding of 18th Nuclear Physics Division Conference of the Euro. Phys. Society (NPDC18) "Phase transitions in strongly interacting matter", Prague, 23.8.-29.8. 2004. To be published in Nuclear Physics

Measuring the Temperature of Hot Nuclear Fragments

A new thermometer based on fragment momentum fluctuations is presented. This thermometer exhibited residual contamination from the collective motion of the fragments along the beam axis. For this reason, the transverse direction has been explored. Additionally, a mass dependence was observed for this thermometer. This mass dependence may be the result of the Fermi momentum of nucleons or the different properties of the fragments (binding energy, spin etc..) which might be more sensitive to different densities and temperatures of the exploding fragments. We expect some of these aspects to be smaller for protons (and/or neutrons); consequently, the proton transverse momentum fluctuations were used to investigate the temperature dependence of the source

Critical behavior of the isotope yield distributions in the Multifragmentation Regime of Heavy Ion Reactions

Isotope yields have been analyzed within the framework of a Modified Fisher Model to study the power law yield distribution of isotopes in the multifragmentation regime. Using the ratio of the mass dependent symmetry energy coefficient relative to the temperature, $a_{sym}/T$, extracted in previous work and that of the pairing term, $a_{p}/T$, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields have been corrected for these effects. For a given I = N - Z value, the corrected yields of isotopes relative to the yield of $^{12}C$ show a power law distribution, $Y(N,Z)/Y(^{12}C) \sim A^{-\tau}$, in the mass range of $1 \le A \le 30$ and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted $\tau$ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple de-excitation model, which the power law distribution of the primary isotopes is determined to $\tau^{prim} = 2.4 \pm 0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at or very near the critical point.Comment: 5 pages, 5 figure

The Isospin Dependence Of The Nuclear Equation Of State Near The Critical Point

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 4He-3He 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.Comment: 14 pages, 18 figure

Dissipation of angular momentum in light heavy ion collision

The inclusive energy distributions of fragments (4$\leq$Z$\leq$7) emitted in the reactions $^{16}$O (116 MeV) + $^{27}$Al, $^{28}$Si, $^{20}$Ne (145 MeV) + $^{27}$Al, $^{59}$Co have been measured in the angular range $\theta_{lab}$= 10$^\circ$ - 65$^\circ$. Fusion-fission and deep inelastic components of the fragment emission have been extracted from the experimental data. The angular mometum dissipations in fully damped deep inelastic collisions have been estimated assming exit channel configuration similar to those for fusion-fission process. It has been found that, the angular momentum dissipations are more than those predicted by the empirical sticking limit in all cases. The deviation is found to increase with increasing charge transfer (lighter fragments). Qualitatively, this may be due to stronger friction in the exit channel. Moreover, for the heavier system $^{20}$Ne + $^{59}$Co, the overall magnitude of deviation is less as compared to those for the lighter systems, {\it i.e.}, $^{16}$O + $^{27}$Al, $^{28}$Si, $^{20}$Ne + $^{27}$Al. This may be due to lesser overlap in time scales of fusion and deep inelastic time scales for heavier systems.Comment: 15 pages, 9 figures, accepted for publication in Phys. Rev.