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Physical Review Letters

Structure of Nuclear Matter

A. W. Overhauser

Published Apr 15, 1960• 173 citations
Publisher

Abstract

Equations for explicit Hartree states of energy lower than that of conventional ground states for noninteracting Fermi gases are given for Fermi gases with attractive interactions. One-dimensional and three-dimensional cases are treated. Large static density waves are shown to exist in such Fermi gases, and the binding energy is derived therefrom. If the density waves are used with the variational theorem, their contribution to the binding energy is greater, and it is concluded that density waves are of great importance in nuclear matter. In the limit of weak attractive interactions, the Fermi surface will become a manyfaced polyhedron, each pair of opposite faces arising from a density wave. (D.L.C.)

DOI
10.1103/physrevlett.4.415

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The Hartree-Fock theory for many fermions with plane-wave orbitals but with abnormal occupation is studied. A one-dimensional problem with an interparticle interaction of finite range which saturates the NNN body system at a fixed density and finite binding energy is solved explicitly. A direct variation of the resulting Hartree-Fock energy with respect to the additional variational parameters introduced is carried out numerically and results reminiscent of a gas-to-liquid phase transition are found.NUCLEAR STRUCTURE plane-wave Hartree-Fock; model calculation; nuclear matter.
It was suggested that the ground stute of an interacting gas of fermions has giart density or spin-density fluctuations and that the Hartree and Hartree- Fcck equations of a one-dimensional gas have solutions which give lower enengies than customary plane wave solutions. Arguments are set forth for the view that for sufficiently weak interactions the Hartree (and Hartree-Fcck) ground stutes in two or more dimensions are the familiar plane wave states. It is concluded that for weak interactions the Hartree equations have a nontnivial ground stute only in one dimension. There is little doubt that this is also tnne for the HartreeFock equation. (B.O.G.)
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.
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