Dirac-Brueckner Hartree-Fock Approach: from Infinite Matter to Effective Lagrangians for Finite Systems

TL;DR

This paper explores deriving effective Lagrangians from Dirac-Brueckner-Hartree-Fock calculations to predict properties of finite nuclei, aiming to bridge complex nuclear matter models with practical finite system applications.

Contribution

It proposes a method to create density-dependent effective Lagrangians based on DBHF results for use in finite nuclei calculations, advancing nuclear structure modeling.

Findings

DBHF reproduces symmetric nuclear matter properties without 3-body forces

Effective Lagrangians can be constructed from DBHF results

Current schemes vary, and fully consistent calculations are yet to be performed

Abstract

One of the open problems in nuclear structure is how to predict properties of finite nuclei from the knowledge of a bare nucleon-nucleon interaction of the meson-exchange type. We point out that a promising starting point consists in Dirac-Brueckner-Hartree-Fock (DBHF) calculations us- ing realistic nucleon-nucleon interactions like the Bonn potentials, which are able to reproduce satisfactorily the properties of symmetric nuclear matter without the need for 3-body forces, as is necessary in non-relativistic BHF calculations. However, the DBHF formalism is still too com- plicated to be used directly for finite nuclei. We argue that a possible route is to define effective Lagrangians with density-dependent nucleon-meson coupling vertices, which can be used in the Relativistic Hartree (or Relativistic Mean Field (RMF)) or preferrably in the Relativistic Hartree- Fock (RHF) approach. The density-dependence is matched to the nuclear matter DBHF results. We review the present status of nuclear matter DBHF calculations and discuss the various schemes to construct the self-energy, which lead to differences in the predictions. We also discuss how effective Lagrangians have been constructed and are used in actual calculations. We point out that completely consistent calculations in this scheme still have to be performed.