  We employ the Gamow shell model (GSM) to describe low-lying states of the
oxygen isotopes 24O and 25O. The many-body Schrodinger equation is solved
starting from a two-body Hamiltonian defined by a renormalized low-momentum
nucleon-nucleon (NN) interaction, and a spherical Berggren basis. The Berggren
basis treats bound, resonant, and continuum states on an equal footing, and is
therefore an appropriate representation of loosely bound and unbound nuclear
states near threshold. We show that such a basis is necessary in order to
obtain a detailed and correct description of the low-lying 1+ and 2+ excited
states in 24O. On the other hand, we find that a correct description of binding
energy systematics of the ground states is driven by proper treatment and
inclusion of many-body correlation effects. This is supported by the fact that
we get 25O unstable with respect to 24O in both oscillator and Berggren
representations starting from a 22O core. Furthermore, we show that the
structure of these loosely bound or unbound isotopes are strongly influenced by
the 1S0 component of the NN interaction. This has important consequences for
our understanding of nuclear stability.
