On the formulation of functional theory for pairing with particle number restoration

TL;DR

This paper proposes a new formulation for particle number restoration in energy density functional theory, using density matrices directly, avoiding recent pathologies and enabling broader functional applications.

Contribution

It introduces an alternative approach to particle number restoration that directly uses density matrices, bypassing issues with transition density matrix methods.

Findings

The proposed method avoids pathologies seen in previous approaches.

It can be applied with functionals of arbitrary density dependencies.

The approach is potentially advantageous for nuclear mass models and thermodynamics.

Abstract

The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an alternative that might be advantageous for mass models, nuclear dynamics and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an Energy Density Functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.