Importance of the single-particle continuum in BCS pairing with a pseudo-state basis

In a recent work [arXiv:1510.03185] the use of the Transformed Harmonic Oscillator (THO) basis for the discretization of the single-particle continuum into a Generalized Bardeen-Cooper-Schrieffer (BCS) formalism was proposed for the description of weakly bound nuclei. We make use of the flexibility of this formalism to study the evolution of the pairing when the nucleus becomes more and more weakly bound. Specifically we focus on the evolution of the occupation of the different partial waves in ²²O when the Fermi level approaches zero. The importance of the resonant configuration decreases consistently when the system becomes more and more weakly bound until a situation is reached where the resonant configuration is no longer the dominant part of the single-particle continuum. However, we also show that for not so extreme situations, it is the resonant part that carries almost all the importance of the continuum