  The Bardeen-Cooper-Schrieffer (BCS) formalism is extended by including the
single-particle continuum in order to analyse the evolution of pairing in an
isotopic chain from stability up to the drip line. We propose a continuum
discretized generalized BCS based on single-particle pseudostates (PS). These
PS are generated from the diagonalization of the single-particle Hamiltonian
within a Transformed Harmonic Oscillator (THO) basis. The consistency of the
results versus the size of the basis is studied. The method is applied to
neutron rich Oxygen and Carbon isotopes and compared with similar previous
works and available experimental data. We make use of the flexibility of the
proposed model in order to study the evolution of the occupation of the
low-energy continuum when the system becomes weakly bound. We find a larger
influence of the non-resonant continuum as long as the Fermi level approaches
zero.
