  Single-particle resonant states, also called Gamow states, as well as bound
and scattering states of complex energy form a complete set, the Berggren
completeness relation. It is the building block of the recently introduced
Gamow Shell Model, where weakly bound and resonant nuclear wave functions are
expanded with a many-body basis of Slater Determinants generated by this set of
single-particle states. However, Gamow states have never been studied in the
context of Hartree-Fock-Bogoliubov theory, except in the
Bardeen-Cooper-Schriefer (BCS) approximation, where both the upper and lower
components of a quasiparticle wave function are assumed to possess the same
radial dependence with that of a Gamow state associated with the Hartree-Fock
potential. Hence, an extension of the notion of Gamow state has to be effected
in the domain of quasiparticles. It is shown theoretically and numerically that
bound, resonant and scattering quasiparticles are well defined and form a
complete set, by which bound Hartree-Fock-Bogoliubov ground states can be
constructed. It is also shown that the Gamow-Hartree-Fock single-particle basis
can be used to solve the Gamow-Hartree-Fock-Bogoliubov problem. As an
illustration, the proposed method is applied to neutron-rich Nickel isotopes
close to the neutron drip-line.
