Nuclear pairing correlations within and beyond HFB-BCS models

Abstract : Pairing correlations in nuclear systems play a crucial role in several aspects, i.e. binding energies and odd-even effects, superfluid phenomena and pair transfer mechanisms, just to quote few of them. On the theoretical side, the standard description of these features is done by using BCS or HFB models which allow to describe in a simple way pairing effects. However, due to the explicit breaking of the particle number, these theories present some limitations which can be cured by using particle number projection techniques. In this paper, we will show the merits of these techniques and their accuracy in treating pairing correlations. First, a beyond BCS-HFB method is introduced where the effect of four quasi-particle states is included perturbatively and subsequently the particle number is restored. We will then show the need of restoring the good particle number also for excited states that are essential in the pair transfer process between superfluid systems. Applications to the Richardson model are shown and discussed.