Induced Surface and Curvature Tensions Equation of State of Hadrons with Relativistic Excluded Volumes and its Relation to Morphological Thermodynamics

Abstract

An analytical formula that accurately accounts for the Lorentz contraction of the excluded volume of two relativistic hadrons with hard-core repulsion is worked out. Using the obtained expression we heuristically derive the equation of state of Boltzmann particles with relativistic excluded volumes in terms of system pressure and its surface and curvature tension coefficients. The behavior of effective excluded volumes of lightest baryons and mesons is studied at very high temperatures (particle number densities) and for very large values of degeneracy factors. Several parameterizations of the obtained equation of state demonstrate a universal asymptotics of the effective excluded volume at high particle number densities. It is peculiar, that the found maximal packing fraction $\eta \simeq 0.75$ of Lorentz contracted particles is very close to the dense packing limit of classical hard spheres of same radius ${\eta }_{exc}\approx 0.74$. We show that the developed equation of state is the grand canonical formulation of the morphological thermodynamics approach applied to Lorentz contracted rigid spheres.

arXiv comment15 pages, 3 figures

References in corpus (16)

• The equation of state in (2+1)-flavor QCD
• Full result for the QCD equation of state with 2+1 flavors
• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Morphological Thermodynamics of Fluids: Shape Dependence of Free Energies
• The statistical multifragmentation model for liquid-gas phase transition with a compressible nuclear liquid
• Hadron Resonance Gas Model with Induced Surface Tension
• Van der Waals Excluded Volume Model for Lorentz Contracted Rigid Spheres
• The Van-der-Waals Gas EOS for the Lorentz Contracted Spheres
• The Flow Constraint Influence on the Properties of Nuclear Matter Critical Endpoint
• Hard-core Radius of Nucleons within the Induced Surface Tension Approach
• Self-consistent Treatment of Quantum Gases of D-dimensional Hard Spheres Beyond the Van der Waals Approximation
• Second virial coefficients of light nuclear clusters and their chemical freeze-out in nuclear collisions
• The concept of induced surface and curvature tensions and a unified description of the gas of hard discs and hard spheres
• Alternative Formulation of the Induced Surface and Curvature Tensions Approach
• Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics
• Resolution of hyper-triton chemical freeze-out puzzle in high energy nuclear collisions