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AIP conference proceedings

Off-shell effects in nuclear matter from an EFT point of view

Boris Krippa

Published Jan 1, 2003• 0 citations
Publisher

Abstract

Effective field theory requires all observables to be independent of the representation used for the quantum field operators. Off‐shell parts of the in‐medium vertex functions depend on the partucular representation so that off‐shell properties of the interactions should not lead to any observable effects. We analyse this issue in the context of many‐body approaches to nuclear matter, where it should be possible to shift into three‐body force the contributions from purely off‐shell two‐body interactions. We show that none of the commonly used truncations of the two‐body scattering amplitude such as the ladder, Brueckner‐Hartree‐Fock or parquet approximations respect this requirement.

DOI
10.1063/1.1570567

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Effective field theory requires all observables to be independent of the representation used for the quantum field operators. Off‐shell parts of the in‐medium vertex functions depend on the partucular representation so that off‐shell properties of the interactions should not lead to any observable effects. We analyse this issue in the context of many‐body approaches to nuclear matter, where it should be possible to shift into three‐body force the contributions from purely off‐shell two‐body interactions. We show that none of the commonly used truncations of the two‐body scattering amplitude such as the ladder, Brueckner‐Hartree‐Fock or parquet approximations respect this requirement.
Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyze this issue in the context of many-body approaches to nuclear matter, where it should be possible to shift the contributions of lowest order in purely off-shell two-body interactions into three-body forces. We show that none of the commonly used truncations of the two-body scattering amplitude such as the ladder, Brueckner-Hartree-Fock, or parquet approximations respect this requirement.
Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations.
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.
We recently proposed a nonlocal form for the 3-body induced interaction that is consistent with the Fock space representation of interaction operators but leads to a fractional power dependence on the density. Here we examine the implications of the nonlocality for the excitation spectrum. In the two-component weakly interacting Fermi gas, we find that it gives an effective mass that is comparable to the one in many-body perturbation theory. Applying the interaction to nuclear matter, it predicts a huge enhancement to the effective mass. Since the saturation of nuclear matter is partly due to the induced 3-body interaction, fitted functionals should treat the effective mass as a free parameter, unless the 2- and 3-body contributions are determined from basic theory.
This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.