Examining the justification for the introduction of a fermion localization function

TL;DR

This paper critically examines the justification for using a fermion localization function, originally proposed for electrons, in nuclear systems, highlighting limitations and the need for correlation effects beyond mean-field approximations.

Contribution

It challenges the applicability of the fermion localization function in interacting nuclear systems and discusses the role of two-body density matrices in energy functional derivation.

Findings

The localization function's assumptions are questionable for interacting systems.

Correlations beyond mean-field are essential for accurate localization descriptions.

Insights into exchange and two-body density matrices inform energy functional development.

Abstract

Becke and Edgecombe suggested in 1990 a theoretical tool to describe electron localization in atoms and molecules, an idea which was borrowed by a large number of nuclear theorists since 2011 to describe nucleon localization in nuclear systems. I argue here that these arguments are highly questionable and cannot be used in interacting systems, where effects beyond the naive mean field or the simple Hartree-Fock framework are important and the inclusion of correlations induced by particle interactions is necessary in order to introduce such a localization function. I also describe several aspects of the exchange and irreducible 2-body density matrices, which depend on the character and strength of the 2-particle interaction and, which can be useful in justifying the derivation of an appropriate energy density functional.