proceeding˙lacroix˙2 International Journal of Modern Physics E c ○ World Scientific Publishing Company

Configuration mixing within the energy density functional formalism: pathologies and cures. Received (received date) Revised (revised date) 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 1 and applied with success to particle number restoration 2. 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 3 is also discussed. The nuclear Energy Density Functional (EDF) method is a unique tool to study static and dynamical properties of nuclei in a unified framework 4. Although the nuclear EDF shares several features with Density Functional Theory 5 (DFT), the strategy used is different as it embraces two successive levels of description. On the first level, traditionally called " self-consistent mean-field theory " , Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB), a single product state Φ 0 provides the normal ρ 00 and anomalous κ 00 density matrices the many-body energy is a functional of. We call this method a single-reference (SR) EDF approach and denote by E SR [Φ 0 ] = E SR [ρ 00 , κ 00 , κ 00 * ] the actual EDF. Although such a restriction is not necessary, one usually builds the EDF from an effective vertex (of the Skyrme or Gogny type), whose parameters are adjusted to reproduce a selected set of experimental observations. Independently of the starting point, the EDF can be