Equations of state for real gases on the nuclear scale

Abstract

The formalism to augment the classical models of equation of state for real gases with the quantum statistical effects is presented. It allows an arbitrary excluded volume procedure to model repulsive interactions, and an arbitrary density-dependent mean field to model attractive interactions. Variations on the excluded volume mechanism include van der Waals (VDW) and Carnahan-Starling models, while the mean fields are based on VDW, Redlich-Kwong-Soave, Peng-Robinson, and Clausius equations of state. The VDW parameters of the nucleon-nucleon interaction are fitted in each model to the properties of the ground state of nuclear matter, and the following range of values is obtained: a = 330 − 430 MeV fm 3 and b = 2.5 − 4.4 fm 3 . In the context of the excluded-volume approach, the fits to the nuclear ground state disfavor the values of the effective hard-core radius of a nucleon significantly smaller than 0.5 fm, at least for the nuclear matter region of the phase diagram. Modifications to the standard VDW repulsion and attraction terms allow to improve significantly the value of the nuclear incompressibility factor K0, bringing it closer to empirical estimates. The generalization to include the baryon-baryon interactions into the hadron resonance gas model is performed. The behavior of the baryon-related lattice QCD observables at zero chemical potential is shown to be strongly correlated to the nuclear matter properties: an improved description of the nuclear incompressibility also yields an improved description of the lattice data at µ = 0.

A Density-dependent van der Waals Model under the GW170817 Constraint

“…It is worth to mention that in the recent work of Ref. (Vovchenko 2017), the results pointed out that none of the other real gases models produces K 0 inside the aforementioned range for K 0 . Finally, it is also clear from Fig.…”

“…In order to avoid such limitations, the repulsive term was modified in Ref. (Vovchenko 2017), by applying the Carnahan-Starling (CS) (Carnahan & Starling 1969) method of excluded volume, in which the pressure of hard-core particles of radius r is given by P = ρT Z CS (η), with…”

“…By following this method, the first eight virial expansion coefficients are obtained, unlike the traditional vdW excluded volume procedure, where only two of them are recovered since for this case Z(η) = (1 − 4η) −1 . By taking the CS procedure to the vdW model, the nuclear matter energy density in the grand canonical ensemble is written as (Vovchenko 2017)…”

Constraints and correlations of nuclear matter parameters from a density-dependent van der Waals model

“…For the real gases models in the CS method, this value is in the range of 333 MeV K 0 601 MeV [14]. In Refs.…”

Self-consistent analysis of quantum gases of hard spheres beyond the Van der Waals approximation

“…Such a trick is employed in Ref. [10] to generalize the Carnahan-Starling EoS to the quantum case. One should, however, remember that at this stage of the derivation neither the pressure of the system p nor its derivatives (including n) are defined yet.…”