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Physical Review Letters

Relativistic Theory of the Effective Interaction in Nuclei

Louis S. Celenza, W. S. Pong, Carl M. Shakin

Published Jul 20, 1981• 10 citations
Publisher

Abstract

We show that the relativistic many-body theory that has recently been used to explain the saturation properties of nuclear matter also explains the remarkable density dependence (found in phenomenological studies) of the Landau-Migdal parameter, ${F}_{0}$. This result provides further evidence that the nucleus is a relativistic system.

DOI
10.1103/physrevlett.47.156

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We show that the relativistic many-body theory that has recently been used to explain the saturation properties of nuclear matter also explains the remarkable density dependence (found in phenomenological studies) of the Landau-Migdal parameter, F0{F}_{0}F0​. This result provides further evidence that the nucleus is a relativistic system.
In this paper we present the theory of nuclear matter in the framework of relativistic nuclear field theory utilizing the technique of relativistic many-body Green's functions. The analytic properties of the Green's functions and related quantities are given and used to obtain the final set of equations for the nuclear matter problem. In detail, we have investigated theoretically and numerically the so-called ${\ensuremath{\Lambda}}^{00}$ and ${\ensuremath{\Lambda}}^{10}$ approximations. For comparison we also calculated the relativistic Hartree-Fock and the Brueckner-Hartree-Fock approximation, respectively. For masses and coupling strengths we used (phenomenological) parameter sets given by the Bonn and Groningen group. The results of the \ensuremath{\Lambda} approximations are similar to the relativistic Brueckner treatment.
We discuss the description of a many-body nuclear system using Hamiltonians that contain the nucleon relativistic kinetic energy and potentials with relativistic corrections. Through the Foldy-Wouthuysen transformation, the field theoretical problem of interacting nucleons and mesons is mapped to an equivalent one in terms of relativistic potentials, which are then expanded at some order in 1mN\frac{1}{{m}_{N}}mN​1​. The formalism is applied to the Hartree problem in nuclear matter, showing how the results of the relativistic mean field theory can be recovered over a wide range of densities.
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
The methods of quantum statistics previously developed by the author are applied to the determination of properties of the ground state of nuclear matter. An expansion in powers of the pair-function of quantum statistics is made and expressions are derived for the momentum distribution, pair-correlation function, binding energy, and effective single-particle energies. The leading terms of these expressions can be interpreted in terms of an effective two-body interaction, and a model of nuclear matter which consists of interacting quasi-particles whose energies are the effective single-particle energies is thereby suggested. The theory is compared with Brueckner's theory and also with Landau's phenomenological theory of the Fermi liquid.