A. Z. Mekjian

The thermodynamic model for relativistic heavy ion collisions

Abstract The collision between two heavy ions at high energies is discussed within the framework of a statistical model which is developed step by step so that it can be followed by a reader unfamiliar with this approach. As we hope to show, the statistical model forms a comprehensive framework for investigating various aspects of such collisions. When statistical thermodynamics is coupled with a one and two fireball model or a firestreak model, single particle and multiparticle inclusive cross sections can be evaluated. Specifically, single particle proton, deuteron, triton and pion cross sections are calculated and compared with experiment. Two particle correlations are discussed using the microcanonical ensemble. Multiplicity distributions are evaluated using the canonical ensemble and composite particle formation is simply obtained from the grand canonical ensemble. The power law behaviour of composite particle cross sections is studied. The thermodynamic model is justified by calculating various reaction rates. Many comparisons with experimental data are made.

The thermodynamic model for nuclear multifragmentation

Abstract A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and number of particles in the system are kept fixed), canonical ensemble (temperature and number of particles are kept fixed) or grand canonical ensemble (fixed temperature and a variable number of particles but with an assigned average). This paper deals with calculations with canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in intermediate energy heavy ion collision, to study the caloric curves for nuclei and to explore the possibility of negative specific heat because of the finiteness of nuclear systems. The model can also be used for detailed calculations of other observables not connected with phase transitions, such as populations of selected isotopes in a heavy ion collision. The model also serves a pedagogical purpose. For the problems at hand, both the canonical and grand canonical solutions are obtainable with arbitrary accuracy hence we can compare the values of observables obtained from the canonical calculations with those from the grand canonical. Sometimes, very interesting discrepancies are found. To illustrate the predictive power of the model, calculated observables are compared with data from the central collisions of Sn isotopes.

Phase transition in a statistical model for nuclear multifragmentation

We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of particles. This enables us to study a phase transition in the model. A first order phase transition can be tracked down. There are significant differences between this phase transition and some other well-known cases. {copyright} {ital 1998} {ital The American Physical Society}

Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

Abstract A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K − / K + ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K − / K + ratio using the equilibrium theory, even though the production processes for K + s and K − s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.

Analog state resonances

Abstract A theory of analog state resonances is presented based on a K -matrix formulation of the shell-model theory of nuclear reactions. After deriving the detailed structure of the analog state and the “configurational states” of Lane and Soper, we discuss the “internal” mixing of the analog state to the configurational states. A shell-model description of “external” mixing is then given. In contradiction to earlier suggestions that internal mixing is unimportant, we conclude that internal mixing cannot be neglected. We also derive the distribution of partial widths for the fine structure resonances. The structure of the fine structure states is discussed, and the various coupling mechanisms that can exist between the analog state and these states are established. The internal and external mixing of these different isospin states is treated on an equal footing, and the effect on each on the distribution of widths is discussed. Expressions for the average cross section for the one- and many-open channel cases are derived. A numerical discussion of the p 3 2 analog resonance in 41 K is given.

Liquid-Gas Phase Transition in Nuclear Multifragmentation

Heavy-ion collisions allow one to pump energy into a nuclear system. In central collisions of equal size nuclei one can also create a significant amount of compression using high energy nuclear beams. The possibility of studying nuclei far from normal conditions raises the question: can we study phase transitions in nuclei similar, for instance, to the way, one can study phase transition in water? This is the subject of the present article.

Nuclear fragmentation and its parallels

A model for the fragmentation of a nucleus is discussed. A general framework for obtaining the canonical ensemble partition function for a fragmentation process is developed based on simple recursive techniques. Parallels of the description of this process with other areas are shown which include Feynmans theory of the [lambda] transition in liquid helium, Bose condensation, and Markov process models. These parallels are used to generalize and further develop a previous exactly solvable model of nuclear fragmentation. A comparsion with other models is also given and one of these models is generalized to include a tuning parameter which contains the underlying physical quantities associated with the fragmentation process. A discussion of the behavior of the partion function and phase transitions is given in terms of Lee-Yang zeros of the partition function. An analysis of some experimental data is given.

Direct interaction, classical thermodynamic and quantum statistical theories of heavy ion collisions

Abstract Various theories of composite-particle formation are developed and compared. One theory is a nonequilibrium final-state interaction model, while another theory is based on equilibrium thermodynamics. A version of the equilibrium model is developed which is classical - analogous to the Rayleigh-Jeans limit of black-body radiation. Recent experiments suggest that the nonclassical equilibrium predictions are in better agreement with data than the results of the nonequilibrium picture or the classical thermodynamic view.

Liquid-gas phase transition in the nuclear equation of state

A canonical ensemble model is used to describe a caloric curve of the 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 possible initial temperatures for a given total reaction energy, the first order characteristics of the liquid-gas phase transition is smeared out to a smooth transition. Two experiments, one at low energy and one at high energy, show different caloric behaviors and are discussed. {copyright} {ital 1997} {ital The American Physical Society}

Coulomb mixing of isospin states

Abstract The Coulomb mixing of an analog state into states of different isospin and also into states of the same isospin is calculated. The dynamic distortion and isospin impurity of the analog state wave function is discussed. The sum of the squares of the matrix elements between the analog and states of the same and different isospin is given for various statistical model distributions of the nuclear matter density. These include a constant density model, a Thomas-Fermi model and a quadratic surface peaked model. The sum is also calculated using harmonic oscillator wave functions. The mixing of the analog to the configuration states is compared with with the total transition strength of the analog into states of normal isospin. The transition strength to the configuration states is found to be only one percent or so of the sum rule. The energy of the configuration states is then compared with the c.m. energy of the normal isospin states which mix with the analog. The contribution of the configuration states to the spreading width of an analog is calculated. A statistical model calculation of the spreading, which takes into account the total transition strength of the analog, is also given. The conspiracies which enter into the statistical model description are discussed.