  The Hartree-Fock-Bogolyubov (HFB) problem for the cutoff local energy-density
functional is solved numerically by using the Gor'kov formalism with an exact
treatment of the particle continuum. The contributions from the resonant and
"gas" continuum to the spectral density of the HFB eigenstates as well as the
shifting and broadening of the discrete HF hole orbitals are clearly
demonstrated with the illustrative example of the drip-line nucleus ^{70}Ca.
The structure of the neutron density distribution in the localized ground state
is analyzed, and the formation of its extended tail ("halo") is shown to be a
collective pairing effect.
