Nuclear Multifragmentation Critical Exponents

We show that the critical exponents of nuclear multi-fragmentation have not been determined conclusively yet.Comment: 3 pages, LaTeX, one postscript figure appended, sub. to Phys.Rev.Lett. as a commen

Liquid-Gas Phase Transition in Nuclear Equation of State

A canonical ensemble model is used to describe a caloric curve of nuclear liquid-gas phase transition. Allowing a discontinuity in the freeze out density from one spinodal density to another for a given initial temperature, the nuclear liquid-gas phase transition can be described as first order. Averaging over various freeze out densities of all the possible initial temperatures for a given total reaction energy, the first order characteristics of liquid-gas phase transition is smeared out to a smooth transition. Two experiments, one at low beam energy and one at high beam energy show different caloric behaviors and are discussed.Comment: 12 pages in Revtex including two Postscript figure

Geochemical indices allow estimation of heavy metal background concentration in soils

Defining background concentrations for heavy metals in soils is essential for recognizing and managing soil pollution. However, background concentrations of metals in soils can vary naturally by several orders of magnitude. Moreover, many soils have also been subject to unquantifiable anthropogenic inputs of metals, in some cases, for centuries. Hence determination of heavy metal background concentrations in soils has to date been fraught with difficulty. Here we demonstrate that there are associations between the background heavy metal and Fe or Mn contents in soils which appear to be consistent for seven important heavy metals of environmental concern. The relationships are remarkably independent of both soil type and climatic setting. These observations provide the basis for a series of general equations from which it is proposed Southeast Asian including Australian, and possibly worldwide background concentrations for As, Cr, Co, Cu, Ni, Pb, and Zn in soils can be derived.R. E. Hamon, M. J. McLaughlin, R. J. Gilkes, A. W. Rate, B. Zarcinas, A. Robertson, G. Cozens, N. Radford and L. Bettena

Universal Behavior of Lyapunov Exponents in Unstable Systems

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic $^4He$ Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial "critical temperature". The largest Lyapunov exponents $\lambda$ are always positive and can be very well fitted near this "critical temperature" with a functional form $\lambda\propto |T-T_c|^{-\omega}$, where the exponent $\omega=0.15$ is independent of the system and mass number. At smaller temperatures we find that $\lambda\propto T~ ^{0.4498}$, a universal behavior characteristic of an order to chaos transition.Comment: 11 pages, RevTeX, 3 figures not included available upon reques

Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point

The event-by-event fluctuations of suitably chosen observables in heavy ion collisions at SPS, RHIC and LHC can tell us about the thermodynamic properties of the hadronic system at freeze-out. By studying these fluctuations as a function of varying control parameters, it is possible to learn much about the phase diagram of QCD. As a timely example, we stress the methods by which present experiments at the CERN SPS can locate the second-order critical endpoint of the first-order transition between quark-gluon plasma and hadron matter. Those event-by-event signatures which are characteristic of freeze-out in the vicinity of the critical point will exhibit nonmonotonic dependence on control parameters. We focus on observables constructed from the multiplicity and transverse momenta of charged pions. We first consider how the event-by-event fluctuations of such observables are affected by Bose-Einstein correlations, by resonances which decay after freeze-out and by fluctuations in the transverse flow velocity. We compare our thermodynamic predictions for such noncritical event-by-event fluctuations with NA49 data, finding broad agreement. We then focus on effects due to thermal contact between the observed pions and a heat bath with a given (possibly singular) specific heat, and due to the direct coupling between the critical fluctuations of the sigma field and the observed pions. We also discuss the effect of the pions produced in the decay of sigma particles just above threshold after freeze-out on the inclusive pion spectrum and on multiplicity fluctuations. We estimate the size of these nonmonotonic effects which appear near the critical point, including restrictions imposed by finite size and finite time, and conclude that they should be easily observable.Comment: 58 pages, 2 figures; to appear in Phys. Rev.

The liquid to vapor phase transition in excited nuclei

For many years it has been speculated that excited nuclei would undergo a liquid to vapor phase transition. For even longer, it has been known that clusterization in a vapor carries direct information on the liquid- vapor equilibrium according to Fisher's droplet model. Now the thermal component of the 8 GeV/c pion + 197Au multifragmentation data of the ISiS Collaboration is shown to follow the scaling predicted by Fisher's model, thus providing the strongest evidence yet of the liquid to vapor phase transition.Comment: four pages, four figures, first two in color (corrected typo in Ref. [26], corrected error in Fig. 4

Inclusive Soft Pion Production from 12.3 and 17.5 GeV/c Protons on Be, Cu and Au

Differential cross-sections are presented for the inclusive production of charged pions in the momentum range 0.1 to 1.2 GeV/c in interactions of 12.3 and 17.5 GeV/c protons with Be, Cu, and Au targets. The measurements were made by Experiment 910 at the Alternating Gradient Synchrotron in Brookhaven National Laboratory. The cross-sections are presented as a function of pion total momentum and production polar angle $\theta$ with respect to the beam.Comment: 14 pages, 8 figure

Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems

We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed.Comment: Contribution to the ``World Consensus Initiative III, Texas A & M University, College Station, Texas, USA, February 11-17, 2005, 21

Equation of State, Spectra and Composition of Hot and Dense Infinite Hadronic Matter in a Microscopic Transport Model

Equilibrium properties of infinite relativistic hadron matter are investigated using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model. The simulations are performed in a box with periodic boundary conditions. Equilibration times depend critically on energy and baryon densities. Energy spectra of various hadronic species are shown to be isotropic and consistent with a single temperature in equilibrium. The variation of energy density versus temperature shows a Hagedorn-like behavior with a limiting temperature of 130$\pm$10 MeV. Comparison of abundances of different particle species to ideal hadron gas model predictions show good agreement only if detailed balance is implemented for all channels. At low energy densities, high mass resonances are not relevant; however, their importance raises with increasing energy density. The relevance of these different conceptual frameworks for any interpretation of experimental data is questioned.Comment: Latex, 20 pages including 6 eps-figure