Geometry, Scaling and Universality in the Mass Distributions in Heavy Ion Collisions

Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate the mass yields and the distribution of cluster sizes. Simple Malthusian dynamics and non-linear Verhulst dynamics are used to illustrate the approach. Nuclear cobwebbing, attractors of the dynamics, and Lyapanov exponents are discussed for the mass distribution. The self-similar property of the Malthusian orbit offers a new variable for the study of scale invariance using power moments of the mass distribution. Correlation lengths, exponents and dimensions associated with scaling relations are developed. Fourier transforms of the mass distribution are used to obtain power spectra which are investigated for a $1/f^{\beta}$ behavior.Comment: 29 pages in REVTEX, 9 figures (available from the authors), RU-92-0

Critical Exponents and Particle Multiplicity Distributions in High Energy Collisions

Data from the L3, Tasso, Opal and Delphi collaborations are analyzed in terms of a statistical model of high energy collisions. The model contains a power law critical exponent tau and Levy index alpha. These data are used to study values of tau and alpha. The very high multiplicity events in L3, Opal and Delphi are consistent with a model based on a Feynman-Wilson gas which has a tail exponent tau=3/2 and alpha=1/2.Comment: 10 pages, new table adde

Critical point multiplicities and multiplicity fluctuations in heavy ion collisions

An exactly solvable model of nuclear fragmentation is shown to lead to a simple connection between the critical point multiplicity $\langle m \rangle_{c}$ and the critical point exponent $\tau$ recently reported on in the EOS collaboration. The importance of multiplicity fluctuations on critical point behavior is also discussed.Comment: 6 pages (revtex), 1 fig. avail. on request, submitted to Phys. Lett.

Development of particle multiplicity distributions using a general form of the grand canonical partition function and applications to L3 and H1 Data

Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ with Fisher's critical exponent $\tau$ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent $\tau$. Various physical phenomena such as hierarchical structure, void scaling relations, KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent $\tau$. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. The mean, fluctuation and third cummulant of distribution determine three parameters $x$, $z$, $a$. We find that a generalized random work model fits the data better than the widely used negative binomial model.Comment: 7 figures include

A Bose-Einstein Model of Particle Multiplicity Distributions

A model of particle production is developed based on a parallel with a theory of Bose-Einstein condensation and similarities with other critical phenomena such as critical opalescence. The role of a power law critical exponent tau and Levy index alpha are studied. Various features of this model are developed and compared with other commonly used models of particle production which are shown to differ by having different values for tau, alpha. While void scaling is a feature of this model, hierarchical structure is not a general property of it. The value of the exponent tau=2 is a transition point associated with void and hierarchical scaling features. An exponent gamma is introduced to describe enhanced fluctuations near a critical point. Experimentally determined properties of the void scaling function can be used to determine tau.Comment: Accepted for publication in Nucl. Phys.

Model of multifragmentation, Equation of State and phase transition

We consider a soluble model of multifragmentation which is similar in spirit to many models which have been used to fit intermediate energy heavy ion collision data. We draw a p-V diagram for the model and compare with a p-V diagram obtained from a mean-field theory. We investigate the question of chemical instability in the multifragmentation model. Phase transitions in the model are discussed.Comment: Revtex, 9 pages including 6 figures: some change in the text and Fig.

Baryon phase-space density in heavy-ion collisions

The baryon phase-space density at mid-rapidity from central heavy-ion collisions is estimated from proton spectra with interferometry and deuteron coalescence measurements. It is found that the mid-rapidity phase-space density of baryons is significantly lower at the SPS than the AGS, while those of total particles (pion + baryon) are comparable. Thermal and chemical equilibrium model calculations tend to over-estimate the phase-space densities at both energies.Comment: 5 pages, 2 tables, no figure. RevTeX style. Accepted for publication in Phys. Rev. C Rapid Communicatio

Widths of Isobaric Analog Resonances: a microscopic approach

A self-consistent particle-phonon coupling model is used to investigate the properties of the isobaric analog resonance in $^{208}$Bi. It is shown that quantitative agreement with experimental data for the energy and the width can be obtained if the effects of isospin-breaking nuclear forces are included, in addition to the Coulomb force effects. A connection between microscopic model predictions and doorway state approaches which make use of the isovector monopole resonance, is established via a phenomenological ansatz for the optical potential.Comment: 18 pages, 1 figure. To appear on Phys. Rev. C (tentatively scheduled for June 1998

Universal features of the order-parameter fluctuations : reversible and irreversible aggregation

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the finite-size scaling analysis. The relation between order parameter, criticality and scaling law of fluctuations has been established and the connexion between the scaling function and the critical exponents has been found. We give examples in out-of-equilibrium aggregation models such as the Smoluchowski kinetic equations, or of at-equilibrium Ising and percolation models.Comment: 19 pages, 10 figure