Van der Waals Equation of State with Fermi Statistics for Nuclear Matter

Abstract

The van der Waals (VDW) equation of state is a simple and popular model to describe the pressure function in equilibrium systems of particles with both repulsive and attractive interactions. This equation predicts an existence of a first-order liquid-gas phase transition and contains a critical point. Two steps to extend the VDW equation and make it appropriate for new physical applications are carried out in this paper: 1) the grand canonical ensemble formulation; 2) an inclusion of the quantum statistics. The VDW equation with Fermi statistics is then applied to a description of the system of interacting nucleons. The VDW parameters $a$ and $b$ are fixed to reproduce the properties of nuclear matter at saturation density $n_0=0.16$ fm${}^{-3}$ and zero temperature. The model predicts a location of the critical point for the symmetric nuclear matter at temperature $T_c\cong 19.7$ MeV and nucleon number density $n_c\cong 0.07$ fm${}^{-3}$.

20 pages, 5 figures, minor changes to match published version

References in corpus (5)

• Relativistic Mean-Field Theory and the High-Density Nuclear Equation of State
• Incompressibility in finite nuclei and nuclear matter
• Limiting temperatures and the Equation of State of Nuclear Matter
• Equation of state of hadron resonance gas and the phase diagram of strongly interacting matter
• Critical Temperature for the Nuclear Liquid-Gas Phase Transition

Cited by in corpus (64)

• van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD
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• Multicomponent van der Waals equation of state: Applications in nuclear and hadronic physics
• Future Physics Perspectives on the Equation of State from Heavy Ion Collisions to Neutron Stars
• Excluded-volume model for quarkyonic Matter: Three-flavor baryon-quark Mixture
• Equations of state for real gases on the nuclear scale
• Examination of the sensitivity of the thermal fits to heavy-ion hadron yield data to the modeling of the eigenvolume interactions
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• Chemical freeze-out conditions and fluctuations of conserved charges in heavy-ion collisions within quantum van der Waals model
• Excluded-volume model for quarkyonic matter II: Three-flavor shell-like distribution of baryons in phase space
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• Surprisingly large uncertainties in temperature extraction from thermal fits to hadron yield data at LHC
• Critical point fluctuations: Finite size and global charge conservation effects
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• Beth-Uhlenbeck approach for repulsive interactions between baryons in a hadron gas
• Quarkyonic Effective Field Theory, Quark-Nucleon Duality and Ghosts
• Critical parameters of consistent relativistic mean-field models
• Critical parameters of liquid-gas phase transition in thermal symmetric and asymmetric nuclear matter
• Non-congruent phase transitions in strongly interacting matter within the Quantum van der Waals model
• Hadron resonance gas with van der Waals interactions
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• Non-Gaussian particle number fluctuations in vicinity of the critical point for van der Waals equation of state
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• Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD
• Correlations between critical parameters and bulk properties of nuclear matter
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• Thermodynamics of a rotating hadron resonance gas with van der Waals interaction
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• Might Normal Nuclear Matter be Quarkyonic?
• Chemical freeze-out curve in heavy-ion collisions and the QCD critical point
• Equation of state of neutron star matter and its warm extension with an interacting hadron resonance gas
• Quarkyonic Mean Field Theory
• Self-consistent Treatment of Quantum Gases of D-dimensional Hard Spheres Beyond the Van der Waals Approximation
• Constraints and correlations of nuclear matter parameters from a density-dependent van der Waals model
• Higher order conserved charge fluctuations inside the mixed phase
• Effects of quantum statistics near the critical point of nuclear matter
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• Diffusion and fluctuations of open charmed hadrons in an interacting hadronic medium
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• Collision Energy Dependence of Particle Ratios and Freeze-out Parameters in Ultra Relativistic Nucleus Nucleus Collisions
• Thermoelectric effects of an interacting hadron gas in the presence of an external magnetic field
• Viscosity of a classical gas: The rare-collision versus the frequent-collision regime
• Quantum thermochemical engines
• Shear viscosity of nuclear matter
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• Van der Waals equation of state for asymmetric nuclear matter
• Quantum statistics effects near the critical point in systems with different inter-particle interactions
• Can charm fluctuation be a better probe to study QCD critical point?
• Fluctuations in heavy ion collisions and global conservation effects
• Phase transitions and finite-size effects in integrable virial statistical models
• Universal descriptions of chemical freeze-out based on pressure and specific heat
• A Chiral Mean-Field Equation-of-State in UrQMD: Effects on the Heavy Ion Compression Stage
• Correlations between nuclear incompressibility, liquid-gas critical point, and quarkyonic transition
• Lattice-based equation of state with a critical point from constant entropy contours and its comparison to effective QCD approaches
• Quark flavors in hot and dense holographic QCD: setup and comparison to data
• Bose-Einstein Condensation of Quantum Hard-Spheres as a Deposition Phase Transition and New Relations Between Bosonic and Fermionic Pressures
• Magneto-Thomson and transverse Thomson effects in an interacting hadron gas in the presence of an external magnetic field
• Particle-number fluctuations near the critical point of nuclear matter