  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.
