Quasiparticle Resonances in the BCS Approach

We present a simple method for calculating the energies and the widths of quasiparticle resonant states. The method is based on BCS equations solved in the Berggren representation. In this representation the quasiparticle resonances are associated to the Gamow states of the mean field. The method is illustrated for the case of neutron-rich nuclei $^{20-22}$O and $^{84}$Ni. It is shown that the contribution of the continuum coupling to the pairing correlations is small and largely dominated by a few resonant states close to the continuum threshold.