Configuration mixing within the energy density functional formalism: pathologies and cures

TL;DR

This paper discusses the issues of divergences in configuration mixing calculations within the energy density functional framework and presents a regularization method to address these pathologies, especially for EDFs with integer density powers.

Contribution

It introduces a minimal regularization approach to fix divergences in multi-reference EDF calculations, applicable to functionals with integer density powers.

Findings

Regularization successfully removes pathologies in EDF calculations

Method applied to particle number restoration with positive results

Addresses issues with fractional density powers

Abstract

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.