Liquid-gas phase transition in nuclei in the relativistic Thomas-Fermi theory

The equation of state (EOS) of finite nuclei is constructed in the relativistic Thomas-Fermi theory using the non-linear $\sigma-\omega -\rho$ model. The caloric curves are calculated by confining the nuclei in the freeze-out volume taken to be a sphere of size about 4 to 8 times the normal nuclear volume. The results obtained from the relativistic theory are not significantly different from those obtained earlier in a non-relativistic framework. The nature of the EOS and the peaked structure of the specific heat $C_v$ obtained from the caloric curves show clear signals of a liquid-gas phase transition in finite nuclei. The temperature evolution of the Gibbs potential and the entropy at constant pressure indicate that the characteristics of the transition are not too different from the first-order one.Comment: RevTex file(19 pages) and 12 psfiles for fugures. Physical Review C (in Press

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

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

Equation of state and phase transitions in asymmetric nuclear matter

The structure of the 3-dimension pressure-temperature-asymmetry surface of equilibrium of the asymmetric nuclear matter is studied within the thermal Thomas-Fermi approximation. Special attention is paid to the difference of the asymmetry parameter between the boiling sheet and that of the condensation sheet of the surface of equilibrium. We derive the condition of existence of the regime of retrograde condensation at the boiling of the asymmetric nuclear matter. We have performed calculations of the caloric curves in the case of isobaric heating. We have shown the presence of the plateau region in caloric curves at the isobaric heating of the asymmetric nuclear matter. The shape of the caloric curve depends on the pressure and is sensitive to the value of the asymmetry parameter. We point out that the experimental value of the plateau temperature T \approx 7 MeV corresponds to the pressure P = 0.01 MeV/fm^3 at the isobaric boiling.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Caloric Curves and Nuclear Expansion

Nuclear caloric curves have been analyzed using an expanding Fermi gas hypothesis to extract average nuclear densities. In this approach the observed flattening of the caloric curves reflects progressively increasing expansion with increasing excitation energy. This expansion results in a corresponding decrease in the density and Fermi energy of the excited system. For nuclei of medium to heavy mass apparent densities ~ 0.4 rho_0 are reached at the higher excitation energies.Comment: 4 pages, 3 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

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

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

Caloric curves and critical behavior in nuclei

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

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