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arXiv:1807.00596 · Physical Review C

Microscopic predictions of the nuclear matter liquid-gas phase transition

Arianna Carbone, A. Polls, Arnau Rios

Published Aug 28, 2018• 44 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevc.98.025804

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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 Tc=16\ifmmode±\else\textpm\fi2{T}_{c}=16\ifmmode\pm\else\textpm\fi{}2Tc​=16\ifmmode±\else\textpm\fi2 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.
The properties of hot symmetric nuclear matter for a wide range of densities and temperatures are investigated by employing the AV14A{V}_{14}AV14​ potential within the lowest order constrained variational (LOCV) method with the inclusion of a phenomenological three-body force as well as relativistic corrections. The relativistic corrections of many-body kinetic energies as well as the boot interaction corrections are presented for a wide range of densities and temperatures. The free energy, pressure, incompressibility, and other thermodynamic quantities of symmetric nuclear matter are obtained and discussed. The critical temperature is found, and the liquid-gas phase transition is analyzed both with and without the inclusion of three-body forces and relativistic corrections in the LOCV approach. It is shown that the critical temperature is strongly affected by the three-body forces but does not depend on the relativistic corrections. Finally, the results obtained in the present study are compared with other many-body calculations and experimental predictions.
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 calculations of the energy per particle of pure neutron and symmetric nuclear matter with simplified Argonne nucleon-nucleon potentials for different many-body theories. We compare critically the Brueckner-Hartree-Fock results to other formalisms, such as the Brueckner-Bethe-Goldstone expansion up to third order, self-consistent Green's functions, auxiliary field diffusion Monte Carlo, and Fermi hypernetted chain. We evaluate the importance of spin-orbit and tensor correlations in the equation of state and find these to be important in a wide range of densities.
Abstract This chapter discusses the significance of two body interactions to many-body properties, beginning with a schematic model showing the relevance of short-range correlations beyond those of the Fermi gas. These correlations are studied within Brueckner theory and the help of the Bethe-Goldstone equation, mainly for nuclear matter proper but extensions to finite temperature are presented. Effective forces of Skyrme type are derived through an expansion of the G-matrix to small relative momenta. This scheme hinges essentially on the Brueckner-Hartree-Fock approximation, for which results for binding energy and equilibrium density are presented. An alternative variational method based on Jastrow functions is sketched, which demonstrates the necessity for considering effective three body forces. The concept of the nuclear equation of state is presented and parameterized by Skyrme forces with density dependent parameters. Finally, a semi-classical transport theory is presented which accounts for statistical collisions of the nucleons.
Dense nucleonic matter is of vital importance for understanding compact stars and inferring the transition into deconfined quark phase. We present ab initio exact calculations of infinite nucleonic matter with the state-of-the-art full configuration-interaction quantum Monte Carlo method, enabling us to rigorously benchmark many-body methods and assess the degree to which the nucleonic matter is correlated. Our method has been numerically validated against exact diagonalization within a small model space. Calculations of nucleonic matter using chiral nuclear forces reveal that symmetric nuclear matter is strikingly strongly correlated, raising questions on previous ab initio calculations of nuclear matter with many-body expansion truncations and offering insights into simultaneous descriptions of finite nuclei and infinite nucleonic matter from first principles.
Realistic nucleon-nucleon interactions induce correlations to the nuclear many-body system, which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this fragmentation affects the thermodynamical properties of nuclear matter. In particular, we show that the entropy can be computed with the help of a spectral function, which can be evaluated in terms of the self-energy obtained in the self-consistent Green's function approach. Results for the density and temperature dependences of the entropy per particle for symmetric nuclear matter are presented and compared to the results of lowest order finite-temperature Brueckner-Hartree-Fock calculations. The effects of correlations on the calculated entropy are small, if the appropriate quasiparticle approximation is used. The results demonstrate the thermodynamical consistency of the self-consistent TTT-matrix approximation for the evaluation of the Green's functions.