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$\beta$-decay rates of neutron-rich nuclei, in particular those located atneutron shell closures, play a central role in simulations of the heavy-elementnucleosynthesis and resulting abundance distributions. We present $\beta$-decayhalf-lives of even-even $N=82$ and $N=126$ $r$-process waiting-point nucleicalculated in the approach based on relativistic quasiparticle random phaseapproximation with quasiparticle-vibration coupling. The calculations includeboth allowed and first-forbidden transitions. In the $N=82$ chain, thequasiparticle-vibration coupling has an important impact close to stability, asit increases the contribution of Gamow-Teller modes and improves the agreementwith the available data. In the $N=126$ chain, we find the decay to proceeddominantly via first-forbidden transitions, even when the coupling tovibrations is included.

Beyond-mean-field calculations of allowed and first-forbidden $\beta^-$ decays of $r$-process waiting-point nuclei