Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory ?

TL;DR

This paper introduces the Symmetry-Conserving EDF (SC-EDF), a novel method for treating pairing and restoring broken symmetries in finite systems within Energy Density Functional theory, addressing issues in existing approaches.

Contribution

It proposes the SC-EDF approach that unifies symmetry breaking and restoration, avoiding pathologies of previous methods and allowing flexible density dependence.

Findings

SC-EDF is free from pathologies observed in MR-EDF

It can be used with flexible density dependence

Provides a consistent framework for symmetry restoration

Abstract

The Multi-Reference Energy Density Functional (MR-EDF) approach (also called configuration mixing or Generator Coordinate Method), that is commonly used to treat pairing in finite nuclei and project onto particle number, is re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can be interpreted as a functional of the one-body density matrix of the projected state with good particle number. Based on this observation, we propose a new approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and restoration of symmetry are accounted for simultaneously. We show, that such an approach is free from pathologies recently observed in MR-EDF and can be used with a large flexibility on the density dependence of the functional.