Van der Waals Excluded Volume Model of Multicomponent Hadron Gas

A generalization of the Van der Waals excluded volume procedure for the multicomponent hadron gas is proposed. The derivation is based on the grand canonical partition function for the system of particles of several species interacting by hard core potentials. The obtained formulae for thermodynamical quantities are consistent with underlying principles of statistical mechanics as well as with thermodynamical identities. The model can be applied to the analysis of experimental data for particle number ratios in relativistic nucleus-nucleus collisions.Comment: 8 page

Simbol-X Hard X-ray Focusing Mirrors: Results Obtained During the Phase A Study

Simbol-X will push grazing incidence imaging up to 80 keV, providing a strong improvement both in sensitivity and angular resolution compared to all instruments that have operated so far above 10 keV. The superb hard X-ray imaging capability will be guaranteed by a mirror module of 100 electroformed Nickel shells with a multilayer reflecting coating. Here we will describe the technogical development and solutions adopted for the fabrication of the mirror module, that must guarantee an Half Energy Width (HEW) better than 20 arcsec from 0.5 up to 30 keV and a goal of 40 arcsec at 60 keV. During the phase A, terminated at the end of 2008, we have developed three engineering models with two, two and three shells, respectively. The most critical aspects in the development of the Simbol-X mirrors are i) the production of the 100 mandrels with very good surface quality within the timeline of the mission; ii) the replication of shells that must be very thin (a factor of 2 thinner than those of XMM-Newton) and still have very good image quality up to 80 keV; iii) the development of an integration process that allows us to integrate these very thin mirrors maintaining their intrinsic good image quality. The Phase A study has shown that we can fabricate the mandrels with the needed quality and that we have developed a valid integration process. The shells that we have produced so far have a quite good image quality, e.g. HEW <~30 arcsec at 30 keV, and effective area. However, we still need to make some improvements to reach the requirements. We will briefly present these results and discuss the possible improvements that we will investigate during phase B.Comment: 6 pages, 3 figures, invited talk at the conference "2nd International Simbol-X Symposium", Paris, 2-5 december, 200

Particle Freeze-out and Discontinuities in Relativistic Hydrodynamics

Freeze-out of particles in relativistic hydrodynamics is considered across a 3-dimensional space-time hypersurface. The conservation laws for time-like parts of the freeze-out hypersurface require different values of temperature, baryonic chemical potential and flow velocity in the fluid and in the final particle spectra. We analyze this freeze-out discontinuity and its connection to the shock-wave phenomena in relativistic hydrodynamics.Comment: 6 figure

Second Cluster Integral and Excluded Volume Effects for the Pion Gas

The quantum mechanical formula for Mayer's second cluster integral for the gas of relativistic particles with hard-core interaction is derived. The proper pion volume calculated with quantum mechanical formula is found to be an order of magnitude larger than its classical evaluation. The second cluster integral for the pion gas is calculated in quantum mechanical approach with account for both attractive and hard-core repulsive interactions. It is shown that, in the second cluster approximation, the repulsive pion-pion-interactions as well as the finite width of resonances give important but almost canceling contributions. In contrast, an appreciable deviation from the ideal gas of pions and pion resonances is observed beyond the second cluster approximation in the framework of the Van der Waals excluded-volume model.Comment: 29 pages, Latex, 9 PS-figure

Multiplicity Fluctuations in Hadron-Resonance Gas

The charged hadron multiplicity fluctuations are considered in the canonical ensemble. The microscopic correlator method is extended to include three conserved charges: baryon number, electric charge and strangeness. The analytical formulae are presented that allow to include resonance decay contributions to correlations and fluctuations. We make the predictions for the scaled variances of negative, positive and all charged hadrons in the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS and AGS to SPS and RHIC.Comment: 19 pages, 4 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

Quark Gluon Bags as Reggeons

The influence of the medium dependent finite width of QGP bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags from a variety of the lattice QCD data and get that the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that besides sigma T**4 term the lattice QCD pressure contains T-linear and T**4 ln T terms in the range of temperatures between 240 MeV and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at hight temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures they obey the lower bound of the Regge trajectory asymptotics (the square root one). Since the model explicitly contains the Hagedorn mass spectrum, it allows us to remove an existing contradiction between the finite number of hadronic Regge families and the Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.Comment: One section removed, a few references added, the Regge trajectories of free QGP bags are considere

On the Deconfinement Phase Transition in the Resonance Gas

We obtain the constraints on the ruling parameters of the dense hadronic gas model at the critical temperature and propose the quasiuniversal ratios of the thermodynamic quantities. The possible appearence of thermodynamical instability in such a model is discussed.Comment: 7 pages, plain LaTeX, BI-TP 94/4

The High E_T Drop of J/psi to Drell-Yan Ratio from the Statistical c anti-c Coalescence Model

The dependence of the J/psi yield on the transverse energy E_T in heavy ion collisions is considered within the statistical c anti-c coalescence model. The model fits the NA50 data for Pb+Pb collisions at the CERN SPS even in the high-E_T region (E_T > 100 GeV). Here E_T-fluctuations and E_T-losses in the dimuon event sample naturally create the celebrated drop in the J/psi to Drell-Yan ratio.Comment: 14 pages, REVTeX, 1 PS-figure. v2: References are corrected and update

Local Thermal and Chemical Equilibration and the Equation of State in Relativistic Heavy Ion Collisions

Thermodynamical variables and their time evolution are studied for central relativistic heavy ion collisions from 10.7 to 160 AGeV in the microscopic Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). The UrQMD model exhibits drastic deviations from equilibrium during the early high density phase of the collision. Local thermal and chemical equilibration of the hadronic matter seems to be established only at later stages of the quasi- isentropic expansion in the central reaction cell with volume 125 fm$^{3}$. distributions at all collision energies for $t\geq 10 fm/c$ with a unique Baryon energy spectra in this cell are approximately reproduced by Boltzmann rapidly dropping temperature. At these times the equation of state has a simple form: $P \cong (0.12-0.15) \epsilon$. At 160 AGeV the strong deviation from chemical equilibrium is found for mesons, especially for pions, even at the late stage of the reaction. The final enhancement of pions is supported by experimental data.Comment: 17 Pages, LaTex, 8 eps figures. Talk given at SQM'98 conference, 20-24 July 1998, Padova, Italy, submitted to J. Phys.