Three-Body Interactions in Many-Body Effective Field Theory

This contribution is an advertisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful.Comment: 5 pp, 9 figs, invited parallel talk at 17th International IUPAP Conference on Few-Body Problems in Physics, June 5-10, 2003, Durham, North Carolina, US

Pionic contribution to relativistic Fermi Liquid parameters

We calculate pionic contribution to the relativistic Fermi Liquid parameters (RFLPs) using Chiral Effective Lagrangian. The RFLPs so determined are then used to calculate chemical potential, exchange and nuclear symmetry energies due to $\pi$$N$ interaction. We also evaluate two loop ring diagrams involving $\sigma$, $\omega$ and $\pi$ meson exchanges and compare results with what one obtains from the relativistic Fermi Liquid theory (RFLT).Comment: 6 pages, 2 figures, Published in Canadian Journal of Physics, vol. 88, issue 8, pp. 585-59

Relativistic Point-Coupling Models as Effective Theories of Nuclei

Recent studies have shown that concepts of effective field theory such as naturalness can be profitably applied to relativistic mean-field models of nuclei. Here the analysis by Friar, Madland, and Lynn of naturalness in a relativistic point-coupling model is extended. Fits to experimental nuclear data support naive dimensional analysis as a useful principle and imply a mean-field expansion analogous to that found for mean-field meson models.Comment: 26 pages, REVTeX 3.0 with epsf.sty, plus 5 figure

Three-Body Forces Produced by a Similarity Renormalization Group Transformation in a Simple Model

A simple class of unitary renormalization group transformations that force hamiltonians towards a band-diagonal form produce few-body interactions in which low- and high-energy states are decoupled, which can greatly simplify many-body calculations. One such transformation has been applied to phenomenological and effective field theory nucleon-nucleon interactions with success, but further progress requires consistent treatment of at least the three-nucleon interaction. In this paper we demonstrate in an extremely simple model how these renormalization group transformations consistently evolve two- and three-body interactions towards band-diagonal form, and introduce a diagrammatic approach that generalizes to the realistic nuclear problem.Comment: 25 pages, 18 figures, minor typos corrected and references update

Density Functional Theory for a Confined Fermi System with Short-Range Interaction

Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Representative results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates.Comment: 36 pages, 20 figures, RevTeX

Are Occupation Numbers Observable?

The question of whether occupation numbers and momentum distributions of nucleons in nuclei are observables is considered from an effective field theory perspective. Field redefinitions lead to variations that imply the answer is negative, as illustrated in the interacting Fermi gas at low density. Implications for the interpretation of (e,e'p) experiments with nuclei are discussed.Comment: 8 pages, revtex4, 4 ps figure

Collective modes of asymmetric nuclear matter in Quantum HadroDynamics

We discuss a fully relativistic Landau Fermi liquid theory based on the Quantum Hadro-Dynamics ($QHD$) effective field picture of Nuclear Matter ({\it NM}). From the linearized kinetic equations we get the dispersion relations of the propagating collective modes. We focus our attention on the dynamical effects of the interplay between scalar and vector channel contributions. A beautiful ``mirror'' structure in the form of the dynamical response in the isoscalar/isovector degree of freedom is revealed, with a complete parallelism in the role respectively played by the compressibility and the symmetry energy. All that strongly supports the introduction of an explicit coupling to the scalar-isovector channel of the nucleon-nucleon interaction. In particular we study the influence of this coupling (to a $\delta$-meson-like effective field) on the collective response of asymmetric nuclear matter ($ANM$). Interesting contributions are found on the propagation of isovector-like modes at normal density and on an expected smooth transition to isoscalar-like oscillations at high baryon density. Important ``chemical'' effects on the neutron-proton structure of the mode are shown. For dilute $ANM$ we have the isospin distillation mechanism of the unstable isoscalar-like oscillations, while at high baryon density we predict an almost pure neutron wave structure of the propagating sounds.Comment: 18 pages (LATEX), 8 Postscript figures, uses "epsfig

Perturbative Effective Field Theory at Finite Density

An accurate description of nuclear matter starting from free-space nuclear forces has been an elusive goal. The complexity of the system makes approximations inevitable, so the challenge is to find a consistent truncation scheme with controlled errors. Nonperturbative effective field theories could be well suited for the task. Perturbative matching in a model calculation is used to explore some of the issues encountered in extending effective field theory techniques to many-body calculations.Comment: 21 pages, 5 figure