Equation of State for the Two-component Van der Waals Gas with Relativistic Excluded Volumes

TL;DR

This paper derives and analyzes two two-component Van der Waals models with relativistic excluded volumes, showing their differences from one-component models and their impact on particle densities and yields in high-energy physics experiments.

Contribution

It introduces two new two-component Van der Waals models with relativistic effects and compares them to existing models, highlighting their improved accuracy for different particle sizes.

Findings

Reduced suppression of particle densities in two-component models

Relativistic contraction enhances lighter particle yields

Models better fit high-energy collision data

Abstract

A canonical partition function for the two-component excluded volume model is derived, leading to two different van der Waals approximations. The one is known as the Lorentz-Berthelot mixture and the other has been proposed recently. Both models are analysed in the canonical and grand canonical ensemble. In comparison with the one-component van der Waals excluded volume model the suppression of particle densities is reduced in these two-component formulations, but in two essentially different ways. Presently used multi-component models have no such reduction. They are shown to be not correct when used for components with different hard-core radii. For high temperatures the excluded volume interaction is refined by accounting for the Lorentz contraction of the spherical excluded volumes, which leads to a distinct enhancement of lighter particles. The resulting effects on pion yield ratios are studied for AGS and SPS data.