Nuclear pairing correlations within and beyond HFB-BCS models

International audiencePairing 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, justto quote few of them. On the theoretical side, the standard description of these features is doneby 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 limitationswhich can be cured by using particle number projection techniques. In this paper, we willshow the merits of these techniques and their accuracy in treating pairing correlations. First, abeyond BCS-HFB method is introduced where the effect of four quasi-particle states is includedperturbatively and subsequently the particle number is restored. We will then show the need ofrestoring the good particle number also for excited states that are essential in the pair transferprocess between superfluid systems. Applications to the Richardson model are shown anddiscussed