Spin-isospin density fluctuations in nuclear collisions

The possible build-up of the spin-isospin fluctuation strength in nuclear collisions is investigated. In lack of quantum mechanical methods we rely on assumptions usually applied for heavy ion collisions. Based on a fluid dynamical picture we present our ‘isospin coupling in a nucleon cascade’. Within this framework it is possible to describe the mean isospin value as a function of the number of participants in a heavy ion collision and it is possible to study the effect of neutron excess. Since the pion field couples to the spin-isospin density a substantial size of this quantity gives rise to pion bremsstrahlung, the dominant subthreshold pion production mechanism.     

Non-equilibrium hadronisation and event-by-event fluctuations of rapidity distributions

During the transition from deconfined to hadronic stage the firaball in ultrarelativistic nuclear collisions can fragment. We propose a method which uses the Kolmogorov-Smirnov test to identify whether the fireball has fragmented or not. We test the method on artificial data generated by a Monte Carlo event generator which simulates particle emission from a fragmented fireball.     

Non-extensive statistics, fluctuations and correlations in high-energy nuclear collisions

Starting from the experimental evidence that high-energy nucleus–nucleus collisions cannot be described in terms of superpositions of elementary nucleon–nucleon interactions, we analyze the possibility that memory effects and long-range forces imply a non-extensive statistical regime during high-energy heavy-ion collisions. The relevance of these statistical effects and their compatibility with the available experimental data are discussed. In particular, we show that theoretical estimates obtained in the framework of the generalized non-extensive thermostatistics, can reproduce the shape of the pion transverse mass spectrum and explain the different physical origin of the transverse momentum correlation function of the pions emitted during the central Pb + Pb and during the p +p collisions at 158 GeV. Received: 6 June 1999 / Published online: 21 December 1999     

Can the fluctuations in head-on ultra-relativistic nuclear collisions be large?

We apply the Low-nussinov model of hadron-hadron collisions to nucleus-nucleus collisions. We show that fluctuations in the multiplicity are larger than those for models which assume that the nucleons interact incoherently. The dependence of the total multiplicity onA is difficult to estimate. String formation and breaking is discussed using classical chromodynamic equations to describe the gluon fields. These equations display amusing collective phenomena.     

On chemical equilibrium in nuclear collisions

The data on average hadron multiplicities in central A+A collisions measured at CERN SPS are analysed with the ideal hadron gas model. It is shown that the full chemical equilibrium version of the model fails to describe the experimental results. The agreement of the data with the off–equilibrium version allowing for partial strangeness saturation is significantly better. The chemical freeze–out temperature of about 180 MeV seems to be independent of the system size (from S+S to Pb+Pb) and in agreement with that extracted in , and collisions. The strangeness suppression is discussed at both hadron and valence quark level. It is found that the hadronic strangeness saturation factor increases from about 0.45 for interactions to about 0.7 for central A+A collisions with no significant change from S+S to Pb+Pb collisions indicating that the strangeness enhancement in heavy ion collisions cannot be fully attributed to the increased system size. The quark strangeness suppression factor is found to be about 0.2 for elementary collisions and about 0.4 for heavy ion collisions independently of collision energy and type of colliding system. Received: 31 October 1997 / Published online: 26 February 1998     

Traces of thermalization from p(t) fluctuations in nuclear collisions

Scattering of particles produced in high energy nuclear collisions can wrestle the system into a state near local thermal equilibrium. I illustrate how measurements of the centrality dependence of the mean transverse momentum and its fluctuations can exhibit this thermalization.     

On the dynamics of statistical fluctuations in heavy ion collisions

We show how statistical fluctuations can be treated within the collective approach to heavy ion reactions. In the classical limit, the equation of motion for the distribution d in the collective variables Q_μ and their conjugate momenta P_μ turns out to be a Fokker-Planck equation. We briefly describe the connection of this equation to one of the Smoluchowski type for a distribution in Q_μ only, often used in heavy ion physics. For anharmonic motion our general Fokker-Planck equation is simplified to be linear in the deviations of the Q_μ mand P_μ from their mean values. The solution of this equation is discussed in terms of a simple Gaussian. The parameters of this Gaussian are determined completely by the first and second moments in Q_μ mand P_μ. The equations for the first moments are identical to the Newton equations including frictional forces. Those for the second moments are linear differential equations of first order and hence easily solvable. The whole derivation is completely analogous to that for the Newton equation reported recently. Here the starting point is the quantum mechanical von Neumann equation rather than the Heisenberg equations. As an intermediate result we obtain and discuss briefly a quantal equation for the reduced density operator d which includes frictional effects.     

Ericson fluctuations in dissipative collisions

We generalize Ericson's theory of fluctuations to deep inelastic reactions. Following Ericson we assume that theS-matrixS _βα(E, l) can be written as a sum of pole terms in the complex energy plane, but the dependence ofS _βα (E, l) on the angular momentuml is assumed to be coherent. Semi-classical approximations for the summation of the angular momenta lead to a simple formula for the energy autocorrelation function. It contains the average widthΓ(l) describing the lifetimeτ(l) of the intermediate dinuclear system and the numberN _eff of unresolved primary channels. These quantities can be determined from a measurement of the autocorrelation function.     

Examining the necessity to include event-by-event fluctuations in experimental evaluations of elliptical flow

Elliptic flow at BNL RHIC is computed event by event with NeXSPheRIO. We show that when symmetry of the particle distribution in relation to the reaction plane is assumed, as usually done in the experimental extraction of elliptic flow, there is a disagreement between the true and reconstructed elliptic flows (15%-30% for eta=0, 30% for p perpendicular=0.5 GeV). We suggest a possible way to take into account the asymmetry and get good agreement between these elliptic flows.     

Measurement of nonrandom event-by-event fluctuations of average transverse momentum in square root of (sNN)=200 GeV Au+Au and p+p collisions

Event-by-event fluctuations of the average transverse momentum of produced particles near midrapidity have been measured by the PHENIX Collaboration in square root of (sNN)=200 GeV Au+Au, and p+p collisions at the Relativistic Heavy Ion Collider. The fluctuations are observed to be in excess of the expectation for statistically independent particle emission for all centralities. The excess fluctuations exhibit a dependence on both the centrality of the collision and on the pT range over which the average is calculated. Both the centrality and pT dependence can be well reproduced by a simulation of random particle production with the addition of contributions from hard-scattering processes.     

Multiplicity fluctuations in relativistic nucleus-nucleus collisions

We discuss the event-by-event multiplicity fluctuations in relativistic nucleus-nucleus collisions. Recent results of the transport and statistical approaches are presented and compared with existing data. The text was submitted by the author in English.     

Event-by-event fluctuations in heavy ion collisions

We discuss the physics underlying event-by-event fluctuations in relativistic heavy ion collision. We will emphasize how the fluctuations of particle ratios can be utilzed to explore the properties of the matter created in these collisions. In particular we will argue that the fluctutions of the ratio of positively over negatively charged particles may serve as a unique signature for the Quark-Gluon Plasma.     

Statistical fluctuations in dissipative heavy-ion collisions

We investigate statistical fluctuations in the relative motion of colliding heavy ions as well as in the nucleon transport. Approximate analytical expressions for the fluctuations in energy loss, scattering angle, and fragment charge number are derived from a Fokker-Planck equation and evaluated at the scission point using previously determined mean interaction times. In a detailed comparison with the data for¹³⁶Xe +²⁰⁹Bi and⁸⁶Kr +¹⁶⁶Er we can account for the observed multidifferential cross sections except at low energy loss where the calculated fluctuations in scattering angle are too small.     

Entropy in nuclear collisions

Data on the multiplicity of pions produced in nucleon-nucleon interactions and central collisions of identical nuclei are discussed using a statistical approach. It is argued that the suppression of the pion production observed at low energies (p _LAB <15>c per nucleon) is due to entropy transfer to baryons. The enhancement of the entropy production in central S+S collisions at 200 GeV/c per nucleon may be interpreted as manifestation of the increase, by a factor of about 3, of the effective number of degrees of freedom in the early stage of the collision.     

Entropy and specific heat as a measure of fluctuations in multiparticle production in relativistic nuclear collisions

An analysis to disentangle information about the occurrence of dynamical fluctuations in multiparticle production in high energy nucleus-nucleus collisions has been carried out in terms of fractal moments and entropy for the experimental and simulated data using FRITIOF, UrQMD and HIJING generators. Although there is a possibility to thermodynamically interpret the final state of multiparticle production by calculating the values of specific heat, c, using G _q - and F _q -moments. However, both these moments give markedly different values of c. The constancy observed in the values of specific heats calculated from either G _q - or F _q -moments is in accord with the predictions of constant specific heat approximation. Variations of multifractal and factorial moments and various other parameters calculated from these moments predict the presence of non-statistical fluctuations in high energy nuclear collisions.     

Correlation and fluctuations in relativistic nucleus-nucleus collisions

Correlation and fluctuations are now well accepted analysis techniques in heavy-ion collisions at relativistic energies. At the current stage of RHIC exploration, matter in bulk and many of the physics questions about the final stage of collisions are addressed with the help of correlation techniques. In the present work after a general introduction to the underlying formalism to the exotic phenomena of correlation and fluctuations, discussion on various parameters disentangling dynamical fluctuations is presented. Analysis to investigate dynamical fluctuations and correlation is carried out in terms of F _q - and G _q -moments. A study of various other parameters involving multiplicity and pseudorapidity of relativistic charged particles produced in high energy nuclear interactions reveals the presence of correlation and fluctuations in particle production in these collisions. The experimental data on 14.5A GeV/c ²⁸Si-nucleus interactions has been analyzed. A parallel analysis of correlation free data generated using MC-RAND Monte Carlo code, UrQMD data and for the HIJING generated events has also been carried out.