There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

What are the thermodynamic properties of matter at extreme densities, even exceeding nuclear matter density severely? How can we describe the composition of matter for such conditions, the resulting pressure, and the maximum mass of cold neutron stars? How is this affected by finite temperatures, as they occur in core collapse supernovae and in compact star mergers? This review addresses these points within the framework of constraints from experiments as well as astronomical observations.

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Equations of state for supernovae and compact stars

Science is an effective way for man to know the world.With individual objects as direct research objects,and general existing state of the objects as targets,with the help of scientific suppositions their verification and other methods to surpass gap among experience and superexperience targets,it obtains the knowledge of the objects.The study on general process and methods for scientific knowledge proves that science,which is based on experience and beyoud experience,is a way and method to verify experience.

Nature of Science

In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.

http://iopscience.iop.org/article/10.1088/0034-4885/77/9/096302/pdf

Coupled-cluster computations of atomic nuclei

We extend the self-consistent Green's functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation-of-motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.

/pdf/self-consistent-green-s-functions-formalism-with-three-body-3aqxwnnnqm.pdf

Self-consistent Green's functions formalism with three-body interactions

We present calculations for symmetric nuclear matter using chiral nuclear interactions within the self-consistent Green's functions approach in the ladder approximation. Three-body forces are included via effective one-body and two-body interactions, computed from an uncorrelated average over a third particle. We discuss the effect of the three-body forces on the total energy, computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on single-particle properties. Saturation properties are substantially improved when three-body forces are included, but there is still some underlying dependence on the similarity renormalization group evolution scale.

Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach

The properties of symmetric nuclear and pure neutron matter are investigated within an extended self-consistent Green's function method that includes the effects of three-body forces. We use the ladder approximation for the study of infinite nuclear matter and incorporate the three-body interaction by means of a density-dependent two-body force. This force is obtained via a correlated average over the third particle, with an in-medium propagator consistent with the many-body calculation we perform. We analyze different prescriptions in the construction of the average and conclude that correlations provide small modifications at the level of the density-dependent force. Microscopic as well as bulk properties are studied, focusing on the changes introduced by the density-dependent two-body force. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sum rule. Our results validate previously used uncorrelated averages and extend the availability of chirally motivated forces to a larger density regime.

Correlated density-dependent chiral forces for infinite-matter calculations within the Green's function approach

We present the fundamental techniques and working equations of many-body Green’s function theory for calculating ground state properties and the spectral strength. Green’s function methods closely relate to other polynomial scaling approaches discussed in Chaps. 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.

Self-Consistent Green’s Function Approaches

We study the latent heat of the liquid-gas phase transition in symmetric nuclear matter using self-consistent mean-field calculations with a few Skyrme forces. The temperature dependence of the latent heat is rather independent of the mean-field parametrization and it can be characterized by a few parameters. At low temperatures, the latent heat tends to the saturation energy. Near the critical point, the latent heat goes to zero with a well-determined mean-field critical exponent. A maximum value of the latent heat in the range l similar to 25-30 MeV is found at intermediate temperatures, which might have experimental relevance. All these features can be explained from very basic principles.

Arianna Carbone

Papers

Self-consistent Green's functions formalism with three-body interactions

Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach

Correlated density-dependent chiral forces for infinite-matter calculations within the Green's function approach

Self-Consistent Green’s Function Approaches

Latent heat of nuclear matter