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EPJ Web of Conferences

Liquid-gas phase transition in nuclear matter: Mean-field and beyond

Arnau Rios, Arianna Carbone, A. Polls, Isaac Vidaña

Published Jan 1, 2012• 0 citations
Publisher

Abstract

The liquid-gas phase transition in nuclear systems is a unique phenomenon, at the frontier of nuclear, many-body and statistical physics. We study this phase transition theoretically at the Hartree-Fock level and explore the available parameter space for the critical point by using several mean-field parametrizations. We find the latent heat of the transition and describe its temperature dependence from first principles. Using tools from many-body physics, we also describe the phase transition beyond the mean-field approximation and find a marked dependence on both the microscopic interaction and the many-body approximation scheme.

DOI
10.1051/epjconf/20123100003

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The liquid-gas phase transition in nuclear systems is a unique phenomenon, at the frontier of nuclear, many-body and statistical physics. We study this phase transition theoretically at the Hartree-Fock level and explore the available parameter space for the critical point by using several mean-field parametrizations. We find the latent heat of the transition and describe its temperature dependence from first principles. Using tools from many-body physics, we also describe the phase transition beyond the mean-field approximation and find a marked dependence on both the microscopic interaction and the many-body approximation scheme.
We present first-principles predictions for the liquid-gas phase transition in symmetric nuclear matter employing both two- and three-nucleon chiral interactions. Our discussion focuses on the sources of systematic errors in microscopic quantum many-body predictions. On the one hand, we test uncertainties of our results arising from changes in the construction of chiral Hamiltonians. We use five different chiral forces with consistently derived three-nucleon interactions. On the other hand, we compare the ladder resummation in the self-consistent Green's functions approach to finite-temperature Brueckner-Hartree-Fock calculations. We find that systematics due to Hamiltonians dominate over many-body uncertainties. Based on this wide pool of calculations, we estimate that the critical temperature is ${T}_{c}=16\ifmmode\pm\else\textpm\fi{}2$ MeV, in reasonable agreement with experimental results. We also find that there is a strong correlation between the critical temperature and the saturation energy in microscopic many-body simulations.
Abstract We discuss the dependence of the phase diagram of a hypothetical isotope of helium with nuclear mass less than 4 atomic mass units. We argue that with decreasing nucleus mass, the temperature of the superfluid phase transition (about 2.2 K in real 4 He) increases, while that of the liquid–gas critical point (about 5.2 K in real 4 He) decreases. We discuss various scenarios that may occur when the two temperatures approach each other and the order parameters of the superfluid and the liquid–gas phase transitions interact with each other. The simplest scenario, in which both order parameters become critical at particular values of the nuclear mass, temperature, and pressure, can be ruled out through on an analysis of the Landau theory. We argue that in the most likely scenario, as the nuclear mass decreases, first, a tricritical point appears on the line separating the superfluid and the normal fluid phase, then the critical point disappears under the first-order part of superfluid phase transition line, and in the end the tricritical point disappears. The last change in the phase diagram occurs when the two-body scattering length crosses zero, which corresponds to the nuclear mass of about 1.55 u. We develop a quantitative theory that allows one to determine the phase diagram in the vicinity of this point. Finally, we discuss several ways to physically realize such liquids.
This and the four next chapters are devoted to the study of several aspects of the theory of phase transition. This has been for more than one century, and still remains, a subject of intense experimental and theoretical activity, with important breakthroughs having impacts on different fields in physics but also on other disciplines such as mathematics, economics, sociology, biology In the first section of this chapter, the transition between the ferromagnetic and paramagnetic phases of the Ising system will be studied in the framework of a mean field approximation. The problem will first be addressed by means of the intuitive Weiss molecular field approximation ( Section 9.1.2 ) and then by means of the more detailed Bragg-Williams approximation ( Section 9.1.3 ) which will serve as a base to develop, in Section 9.2 , a general theory of continuous phase transitions: the Landau mean field theory for which the concept of order parameter will first be introduced. Other types of phase transitions will then be studied using the mean field approximation. Phase transitions in liquid crystals will be studied in Section 9.3 . These are systems with a tensor order parameter which exhibit a rich phenomenology. Finally, in Section 9.4 , a transition of a fairly more elaborate nature than a simple first or second order phase transition will be discussed.
This chapter describes the physics of phase transitions and critical phenomena. After introducing the thermodynamics of phase transitions, the general considerations are made explicit by presenting statistical mechanical calculations on a lattice gas model in the mean-field approximation. Phase transitions occur in macroscopic systems when one or more external parameters like temperature, pressure, electrical field, magnetic field, etc are varied. The chapter demonstrates the utility of the alternative formulations of thermodynamics and statistical mechanics in the context of phase transitions and shows how their use clarifies and unifies the theory of phase transitions. It deals with the basic thermodynamic description of a single component fluid. To understand different phases and associated transitions, one studies how the couplings flow in the parameter space under repeated Renormalization Group (RG) transformations. The flows around the fixed point are easily studied by linearizing the RG equations around the fixed points and determining the eigenvalues and eigenvectors of the linearized RG transformations.
Transformations among many of the diverse states of matter arise from microscopic interactions involving very many (approximately 10(23)) constituent particles and result in dramatic changes in macroscopic properties. The values of some physical parameters vanish, while others approach infinity. These changes and their evolution are strikingly similar in systems as apparently different as liquids, magnets, superconductors, ferroelectrics, and liquid crystals, which suggests that there is an underlying unity to phase transition phenomena. The basis and extent of this unity are reviewed for many-body systems in equilibrium, and analogies with instability phenomena in systems far from equilibrium (such as lasers, fluid flows, and avalanche electronic devices) are pointed out.