Thermodynamics of a finite system of classical particles with short and long range interactions and nuclear fragmentation

We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked out in the framework of the grand canonical ensemble. It is shown that the system experiences a phase transition at fixed average density in the thermodynamic limit. The phase diagram and the caloric curve are constructed and compared with numerical simulations. The implications of our results concerning the caloric curve are discussed in connection with the interpretation of corresponding experimental data.Comment: 11pages, LaTeX, 6 figures. Major change : A new section dealing with numerical simulations in the framework of a cellular model has been adde

Incorporating Radial Flow in the Lattice Gas Model for Nuclear Disassembly

We consider extensions of the lattice gas model to incorporate radial flow. Experimental data are used to set the magnitude of radial flow. This flow is then included in the Lattice Gas Model in a microcanonical formalism. For magnitudes of flow seen in experiments, the main effect of the flow on observables is a shift along the $E^*/A$ axis.Comment: Version accepted for publication in Phys. Rev. C, Rapid Communicatio

Isotope thermometery in nuclear multifragmentation

A systematic study of the effect of fragment$-$fragment interaction, quantum statistics, $\gamma$-feeding and collective flow is made in the extraction of the nuclear temperature from the double ratio of the isotopic yields in the statistical model of one-step (Prompt) multifragmentation. Temperature is also extracted from the isotope yield ratios generated in the sequential binary-decay model. Comparison of the thermodynamic temperature with the extracted temperatures for different isotope ratios show some anomaly in both models which is discussed in the context of experimentally measured caloric curves.Comment: uuencoded gzipped file containing 20 pages of text in REVTEX format and 12 figures (Postscript files). Physical Review C (in press

Anatomy of nuclear shape transition in the relativistic mean field theory

A detailed microscopic study of the temperature dependence of the shapes of some rare-earth nuclei is made in the relativistic mean field theory. Analyses of the thermal evolution of the single-particle orbitals and their occupancies leading to the collapse of the deformation are presented. The role of the non-linear $\sigma-$field on the shape transition in different nuclei is also investigated; in its absence the shape transition is found to be sharper.Comment: REVTEX file (13pages), 12 figures, Phys. Rev. C(in press), \documentstyle[aps,preprint]{revtex

Temperature induced shell effects in deformed nuclei

The thermal evolution of the shell correction energy is investigated for deformed nuclei using Strutinsky prescription in a self-consistent relativistic mean-field framework. For temperature independent single-particle states corresponding to either spherical or deformed nuclear shapes, the shell correction energy $\Delta_{sc}$ steadily washes out with temperature. However, for states pertaining to the self-consistent thermally evolving shapes of deformed nuclei, the dual role played by the single-particle occupancies in diluting the fluctuation effects from the single-particle spectra and in driving the system towards a smaller deformation is crucial in determining $\Delta_{sc}$ at moderate temperatures. In rare earth nuclei, it is found that $\Delta_{sc}$ builds up strongly around the shape transition temperature; for lighter deformed nuclei like $^{64}Zn$ and $^{66}Zn$, this is relatively less prominent.Comment: 6 pages revtex file + 4 ps files for figures, Phys. Rev. C (in press

Rare isotope production in statistical multifragmentation

Producing rare isotopes through statistical multifragmentation is investigated using the Mekjian method for exact solutions of the canonical ensemble. Both the initial fragmentation and the the sequential decay are modeled in such a way as to avoid Monte Carlo and thus provide yields for arbitrarily scarce fragments. The importance of sequential decay, exact particle-number conservation and the sensitivities to parameters such as density and temperature are explored. Recent measurements of isotope ratios from the fragmentation of different Sn isotopes are interpreted within this picture.Comment: 10 eps figure

Effect of Flow on Caloric Curve for Finite Nuclei

In a finite temperature Thomas-Fermi theory, we construct caloric curves for finite nuclei enclosed in a freeze-out volume few times the normal nuclear volume, with and without inclusion of flow. Without flow, the caloric curve indicates a smooth liquid-gas phase transition whereas with flow, the transition may be very sharp. We discuss these results in the context of two recent experiments, one for heavy symmetric system (Au + Au at 600A MeV) and the other for highly asymmetric system (Au + C at 1A GeV) where different behaviours in the caloric curves are seen.Comment: 11 pages revtex; 4 figs; version to appear in Phys. Rev. Let

Application of Information Theory in Nuclear Liquid Gas Phase Transition

Information entropy and Zipf's law in the field of information theory have been used for studying the disassembly of nuclei in the framework of the isospin dependent lattice gas model and molecular dynamical model. We found that the information entropy in the event space is maximum at the phase transition point and the mass of the cluster show exactly inversely to its rank, i.e. Zipf's law appears. Both novel criteria are useful in searching the nuclear liquid gas phase transition experimentally and theoretically.Comment: 5 pages, 5 figure

Tracking the phase-transition energy in disassembly of hot nuclei

In efforts to determine phase transitions in the disintegration of highly excited heavy nuclei, a popular practice is to parametrise the yields of isotopes as a function of temperature in the form $Y(z)=z^{-\tau}f(z^{\sigma}(T-T_0))$, where $Y(z)$'s are the measured yields and $\tau, \sigma$ and $T_0$ are fitted to the yields. Here $T_0$ would be interpreted as the phase transition temperature. For finite systems such as those obtained in nuclear collisions, this parametrisation is only approximate and hence allows for extraction of $T_0$ in more than one way. In this work we look in detail at how values of $T_0$ differ, depending on methods of extraction. It should be mentioned that for finite systems, this approximate parametrisation works not only at the critical point, but also for first order phase transitions (at least in some models). Thus the approximate fit is no guarantee that one is seeing a critical phenomenon. A different but more conventional search for the nuclear phase transition would look for a maximum in the specific heat as a function of temperature $T_2$. In this case $T_2$ is interpreted as the phase transition temperature. Ideally $T_0$ and $T_2$ would coincide. We invesigate this possibility, both in theory and from the ISiS data, performing both canonical ($T$) and microcanonical ($e=E^*/A$) calculations. Although more than one value of $T_0$ can be extracted from the approximate parmetrisation, the work here points to the best value from among the choices. Several interesting results, seen in theoretical calculations, are borne out in experiment.Comment: Revtex, 10 pages including 8 figures and 2 table

Isospin-rich nuclei in neutron star matter

Stability of nuclei beyond the drip lines in the presence of an enveloping gas of nucleons and electrons, as prevailing in the inner crust of a neutron star, is studied in the temperature-dependent Thomas-Fermi framework. A limiting asymmetry in the isospin space beyond which nuclei cannot exist emerges from the calculations. The ambient conditions like temperature, baryon density and neutrino concentration under which these exotic nuclear systems can be formed are studied in some detail.Comment: Submitted to Phy. Rev. C: Revtex version of manuscript 22 pages and 10 PS-files for figure