Second Cluster Integral and Excluded Volume Effects for the Pion Gas

Abstract

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.

29 pages, Latex, 9 PS-figures

References in corpus (5)

• Chemical Equilibration in Pb+Pb Collisions at the SPS
• The analysis of particle multiplicities in Pb+Pb collisions at 158A GeV/c within hadron gas models
• Van der Waals Excluded Volume Model of Multicomponent Hadron Gas
• Van der Waals Excluded Volume Model for Lorentz Contracted Rigid Spheres
• Chiral symmetry and the pion gas virial expansion

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• Beth-Uhlenbeck approach for repulsive interactions between baryons in a hadron gas
• Excluded-volume effects for a hadron gas in Yang-Mills theory
• Hadron resonance gas with van der Waals interactions
• Equation of state and sound velocity of hadronic gas with hard-core interaction
• Limiting temperature of pion gas with the van der Waals equation of state
• Chiral Hadronic Mean Field Model including Quark Degrees of Freedom
• Interacting Constituents in Cosmology
• A consistent quasiparticle picture of Quark-Gluon plasma and the velocity of sound