**E. Perlinska, S.G. Rohozinski, J. Dobaczewski, and W. Nazarewicz**

**60th draft: October 1, 2003, today: 3 January 2004**

In the present study we generalize the self-consistent
Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate
space to the case which incorporates an arbitrary mixing between protons and
neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing)
channels. We define the HFB density matrices, discuss their
spin-isospin structure, and construct the most general energy density functional
that is
quadratic in local densities.
The consequences of the local gauge invariance are discussed and
the particular case of the Skyrme energy density functional is studied.
By varying the total
energy with respect to the density matrices the self-consistent
one-body HFB Hamiltonian is
obtained and the structure of the resulting mean fields is shown. The
consequences of
the time-reversal symmetry, charge invariance, and proton-neutron
symmetry are summarized.
The complete list of expressions required to calculate total
energy is presented.

- Introduction
- Proton-neutron pairing, a concise overview
- Density matrices in the isospin space

- The Energy Density Functional

- The P-H and P-P Mean Fields
- The HFB equations
- Conserved symmetries

- Conclusions
- Acknowledgments
- Bibliography
- About this document ...

Jacek Dobaczewski 2004-01-03