  We introduce a natural and simple to implement renormalization scheme of the
Hartree-Fock-Bogoliubov (HFB) equations for the case of zero range pairing
interaction. This renormalization scheme proves to be equivalent to a simple
energy cut-off with a position or density dependent running coupling constant.
Subsequently, we present self-consistent HFB calculations with a full
consideration of the continuum of long chains of spherical tin and lead nuclei
(essentially from one drip line to another) using the SLy5 interaction. In the
pairing channel we use a zero range interaction, treated by means of this new
regularization scheme.
