Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals

TL;DR

The paper critically examines the use of projected densities in Skyrme and Gogny functionals, demonstrating that this approach leads to catastrophic energy results in symmetry restoration calculations, especially for spatial symmetries.

Contribution

It provides a detailed analysis showing the inadequacy of the projected density prescription in beyond mean field calculations with Skyrme or Gogny functionals.

Findings

Projected density prescription causes infinite deformation in symmetry restoration.

It leads to catastrophic energy results in calculations.

The approach is unsuitable for symmetry restoration of spatial symmetries.

Abstract

I discuss the inadequacy of the "projected density" prescription to be used in density dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that at least for the restoration of spatial symmetries like rotations, translations or parity the above prescription yields catastrophic results for the energy that drive the intrinsic wave function to configurations with infinite deformation, preventing thereby its use both in projection after and before variation.