(a) |$E_n^{\mathrm {pair}}$| and (b) |$E_{\mathrm {HF}}-E_{{\mathrm { HFB}}}$| in the |$Z=8$| nuclei. The blue and red lines represent the results with the D1M and M3Y-P6 interactions, respectively. In (b), the |$\lambda _{\mathrm {sub}}$| values (⁠|$0.5\,{\mathrm {MeV}}$| and |$0.8\,{\mathrm {MeV}}$|⁠) are shown by the thin dotted and dot-dashed lines.