In the framework of the Density Functional Theory for superconductors,
we study the restoration of the particle number symmetry by means of
the projection technique. Conceptual problems are outlined
and numerical difficulties
are discussed. Both are related to the fact that neither the many-body
Hamiltonian nor the wave function of the system appear explicitly in the
Density Functional Theory. Similar obstacles are encountered in
self-consistent theories utilizing density-dependent effective interactions.

**J. Dobaczewski,
M.V. Stoitsov,
W. Nazarewicz,
P.-G. Reinhard**

**August 8, 2007**

- Introduction
- Particle-Number-Projected HFB
- Shifted HFB states
- Projected HFB states
- HFB sum rules
- Transition matrix elements and transition densities
- Poles of transition densities

- Particle-Number-Projected DFT
- Transition energy density
- Projected DFT energy
- Analytic properties
- Residues
- The DFT sum rules
- Density-dependent terms with fractional powers

- Numerical examples
- Numerical accuracy
- Dependence of projected energy on integration contours in spherical nuclei
- Calculations for deformed nuclei
- Distribution of poles as a function of deformation
- Deformation energy within the HFB+PNP method

- Conclusions
- Bibliography
- About this document ...

Jacek Dobaczewski 2007-08-08