Interplay of quasiparticle-vibration coupling and pairing correlations on β-decay half-lives

The nuclear β-decay half-lives of Ni and Sn isotopes, around the closed shell nuclei ⁷⁸Ni and ¹³²Sn, are investigated by computing the distribution of the Gamow–Teller strength using the Quasiparticle Random Phase Approximation (QRPA) with quasiparticle-vibration coupling (QPVC), based on ground-state properties obtained by Hartree–Fock–Bogoliubov (HFB) calculations. We employ the effective interaction SkM^⁎ and a zero-range effective pairing force. The half-lives are strongly reduced by including the QPVC. We study in detail the effects of isovector (IV) and isoscalar (IS) pairing. Increasing the IV strength tends to increase the lifetime for nuclei in the proximity of, but lighter than, the closed-shell ones in QRPA calculations, while the effect is significantly reduced by taking into account the QPVC. On the contrary, the IS pairing mainly plays a role for nuclei after the shell closure. Increasing its strength decreases the half-lives, and the effect at QRPA and QRPA+QPVC level is comparable. The effect of IS pairing is particularly pronounced in the case of the Sn isotopes, where it turns out to be instrumental to obtain good agreement with experimental data.