A consistent formulation of the excluded volume effect in hadron gas at high densities

Abstract

Thermodynamics of a gas of nucleons and antinucleons at nonzero temperatureT and nonzero chemical potential μ is formulated by taking into account the nuclear repulsive force as an excluded volume effect. A thermodynamical potential Ω(T, μ, V) is constructed by replacing the true volumeV of the system with the effective volume in a formula which is valid for a free pointlike hadron gas. The general thermodynamical relationV −1∂Ω/∂μ=−n (n is the net baryon number density) yields a differential equation forn. The equation is solved in a compact integral form. The behavior of the solution is examined numerically for typical ranges ofT and μ which are relevant to the hadron-quark phase transition. The numerical results show that our previous formalism of the excluded volume effect is a good approximation of the present rigorous formalism. The baryon number susceptibility ∂n/∂μ|μ=0 is also calculated numerically, and is compared with the result from the QCD Monte Carlo simulation by Gottlieb et al. [5].