Laboratory Tests of Low Density Astrophysical Equations of State

Clustering in low density nuclear matter has been investigated using the NIMROD multi-detector at Texas A&M University. Thermal coalescence modes were employed to extract densities, $\rho$, 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. The yields of $d$, $t$, $^{3}$He, and $^{4}$He have been determined at $\rho$ = 0.002 to 0.032 nucleons/fm$^{3}$ and $T$= 5 to 10 MeV. The experimentally derived equilibrium constants for $\alpha$ 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.Comment: 5 pages, 3 figure

Evidence of Critical Behavior in the Disassembly of Nuclei with A ~ 36

A wide variety of observables indicate that maximal fluctuations in the disassembly of hot nuclei with A ~ 36 occur at an excitation energy of 5.6 +- 0.5 MeV/u and temperature of 8.3 +- 0.5 MeV. Associated with this point of maximal fluctuations are a number of quantitative indicators of apparent critical behavior. The associated caloric curve does not appear to show a flattening such as that seen for heavier systems. This suggests that, in contrast to similar signals seen for liquid-gas transitions in heavier nuclei, the observed behavior in these very light nuclei is associated with a transition much closer to the critical point.Comment: v2: Major changes, new model calculations, new figure

Critical Behavior in Light Nuclear Systems: Experimental Aspects

An extensive experimental survey of the features of the disassembly of a small quasi-projectile system with $A \sim$ 36, produced in the reactions of 47 MeV/nucleon $^{40}$Ar + $^{27}$Al, $^{48}$Ti and $^{58}$Ni, has been carried out. Nuclei in the excitation energy range of 1-9 MeV/u have been investigated employing a new method to reconstruct the quasi-projectile source. At an excitation energy $\sim$ 5.6 MeV/nucleon many observables indicate the presence of maximal fluctuations in the de-excitation processes. The fragment topological structure shows that the rank sorted fragments obey Zipf's law at the point of largest fluctuations providing another indication of a liquid gas phase transition. The caloric curve for this system shows a monotonic increase of temperature with excitation energy and no apparent plateau. The temperature at the point of maximal fluctuations is $8.3 \pm 0.5$ MeV. Taking this temperature as the critical temperature and employing the caloric curve information we have extracted the critical exponents $\beta$, $\gamma$ and $\sigma$ from the data. Their values are also consistent with the values of the universality class of the liquid gas phase transition. Taken together, this body of evidence strongly suggests a phase change in an equilibrated mesoscopic system at, or extremely close to, the critical point.Comment: Physical Review C, in press; some discussions about the validity of excitation energy in peripheral collisions have been added; 24 pages and 32 figures; longer abstract in the preprin

Experimental Determination of In-Medium Cluster Binding Energies and Mott Points in Nuclear Matter

In medium binding energies and Mott points for $d$, $t$, $^3$He and $\alpha$ clusters in low density nuclear matter have been determined at specific combinations of temperature and density in low density nuclear matter produced in collisions of 47$A$ MeV $^{40}$Ar and $^{64}$Zn projectiles with $^{112}$Sn and $^{124}$Sn target nuclei. The experimentally derived values of the in medium modified binding energies are in good agreement with recent theoretical predictions based upon the implementation of Pauli blocking effects in a quantum statistical approach.Comment: 5 pages, 3 figure

Tracing the Evolution of Temperature in Near Fermi Energy Heavy Ion Collisions

The kinetic energy variation of emitted light clusters has been employed as a clock to explore the time evolution of the temperature for thermalizing composite systems produced in the reactions of 26A, 35A and 47A MeV $^{64}$Zn with $^{58}$Ni, $^{92}$Mo and $^{197}$Au. For each system investigated, the double isotope ratio temperature curve exhibits a high maximum apparent temperature, in the range of 10-25 MeV, at high ejectile velocity. These maximum values increase with increasing projectile energy and decrease with increasing target mass. The time at which the maximum in the temperature curve is reached ranges from 80 to 130 fm/c after contact. For each different target, the subsequent cooling curves for all three projectile energies are quite similar. Temperatures comparable to those of limiting temperature systematics are reached 30 to 40 fm/c after the times corresponding to the maxima, at a time when AMD-V transport model calculations predict entry into the final evaporative or fragmentation stage of de-excitation of the hot composite systems. Evidence for the establishment of thermal and chemical equilibrium is discussed.Comment: 9 pages, 5 figure

A Ghoshal-like Test of Equilibration in Near-Fermi-Energy Heavy Ion Collisions

Calorimetric and coalescence techniques have been employed to probe equilibration for hot nuclei produced in heavy ion collisions of 35 to 55 MeV/u projectiles with medium mass targets. Entrance channel mass asymmetries and energies were selected in order that very hot composite nuclei of similar mass and excitation would remain after early stage pre-equilibrium particle emission. Inter-comparison of the properties and de-excitation patterns for these different systems provides evidence for the production of hot nuclei with decay patterns relatively independent of the specific entrance channel.Comment: 7 pages, 2 figure

Properties of the Initial Participant Matter Interaction Zone in Near Fermi-Energy Heavy Ion Collisions

The sizes, temperatures and free neutron to proton ratios of the initial interaction zones produced in the collisions of 40 MeV/nucleon $^{40}$Ar + $^{112}$Sn and 55 MeV/nucleon$^{27}$Al + $^{124}$Sn are derived using total detected neutron plus charged particle multiplicity as a measure of the impact parameter range and number of participant nucleons. The size of the initial interaction zone, determined from a coalescence model analysis, increases significantly with decreasing impact parameter. The temperatures and free neutron to proton ratios in the interaction zones are relatively similar for different impact parameter ranges and evolve in a similar fashion.Comment: 7 pages, 8 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

The Nuclear Matter Symmetry Energy at 0.03≤ρ/ρ0≤0.20.03\leq \rho/\rho_0\leq 0.2

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, $\rho$, 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 $0.03 \leq \rho/\rho_0 \leq 0.2$ 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.Comment: 6 pages, 6 figure

Deformation effects in 56^{56}Ni nuclei produced in 28^{28}Si+28^{28}Si at 112 MeV

Velocity and energy spectra of the light charged particles (protons and $\alpha$-particles) emitted in the $^{28}$Si(E$_{lab}$ = 112 MeV) + $^{28}$Si reaction have been measured at the Strasbourg VIVITRON Tandem facility. The ICARE charged particle multidetector array was used to obtain exclusive spectra of the light particles in the angular range 15 - 150 degree and to determine the angular correlations of these particles with respect to the emission angles of the evaporation residues. The experimental data are analysed in the framework of the statistical model. The exclusive energy spectra of $\alpha$-particles emitted from the $^{28}$Si + $^{28}$Si compound system are generally well reproduced by Monte Carlo calculations using spin-dependent level densities. This spin dependence approach suggests the onset of large deformations at high spin. A re-analysis of previous $\alpha$-particle data from the $^{30}$Si + $^{30}$Si compound system, using the same spin-dependent parametrization, is also presented in the framework of a general discussion of the occurrence of large deformation effects in the A$_{CN}$ ~ 60 mass region.Comment: 25 pages, 6 figure