  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.
