  The shell model in the complex k-plane (the so-called Gamow Shell Model) has
recently been formulated and applied to structure of weakly bound, neutron-rich
nuclei. The completeness relations of Newton and Berggren, which apply to the
neutron case, are strictly valid for finite-range potentials. However, for
long-range potentials, such as the Coulomb potential for protons, for which the
arguments based on the Mittag-Leffler theory do not hold, the completeness
still needs to be demonstrated. This has been done in this paper, both
analytically and numerically. The generalized Berggren relations are then used
in the first Gamow Shell Model study of nuclei having both valence neutrons and
protons, namely the lithium chain. The single-particle basis used is that of
the Hartree-Fock-inspired potential generated by a finite-range residual
interaction. The effect of isospin mixing in excited unbound states is
discussed.
