  We present a new and efficient method to obtain a Gamow shell-model basis and
matrix elements generated by realistic nucleon-nucleon interactions. We derive
a self-consistent Hartree-Fock potential from the renormalized N3LO interaction
model. The corresponding Gamow one-body eigenstates are generated in a plane
wave basis in order to build a Gamow shell-model set of basis states for the
closed shell nuclei 4He and 16O. We address also the problem of representing a
realistic nucleon-nucleon interaction in a two-particle Berggren basis in the
laboratory frame. To achieve this, an expansion of matrix elements of the
residual nucleon-nucleon interaction in a finite set of harmonic oscillator
wave functions is used. We show that all loosely bound and narrow resonant
states converge surprisingly fast. Even broad resonances in these two-particle
valence systems converge within a reasonable number of harmonic oscillator
functions. Examples of 6He and 18O Gamow shell-model calculations using 4He and
16}O as closed shell cores are presented. This procedure allows Gamow
shell-model calculations to be performed with all realistic nucleon-nucleon
interactions and with either momentum or position space representations for the
Gamow basis. The possibility to remove the center of mass spuriosity of Gamow
shell-model nuclear states with this method is also discussed. Perspectives for
nuclear structure calculations of dripline nuclei are outlined.
