  The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei
(RHFBz) is introduced. The model is based on an effective Lagrangian with
density-dependent meson-nucleon couplings in the particle-hole channel, and the
pairing part of the Gogny force is used in the pairing channel. The RHFBz
quasiparticle equations are solved by expansion in the basis of a deformed
harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon,
Neon and Magnesium isotopes. The effect of the explicitly including the pion
field is investigated for binding energies, deformation parameters, and charge
radii.
