$\beta$-delayed fission in $r$-process nucleosynthesis.

We present $\beta$-delayed neutron emission and $\beta$-delayed fission calculations for heavy, neutron-rich nuclei using the coupled Quasi-Particle Random Phase Approximation plus Hauser-Feshbach (QRPA+HF) approach. From the initial population of a compound nucleus after $\beta$-decay, we follow the statistical decay taking into account competition between neutrons, $\gamma$-rays, and fission. We find a region of the chart of nuclides where the probability of $\beta$-delayed fission is $\sim100$%, that likely prevents the production of superheavy elements in nature. For a subset of nuclei near the neutron dripline, neutron multiplicity and the probability of fission are both large, leading to the intriguing possibility of multi-chance $\beta$-delayed fission, a new decay mode for extremely neutron-rich heavy nuclei. In this new decay mode, $\beta$-decay can be followed by multiple neutron emission leading to subsequent daughter generations which each have a probability to fission. We explore the impact of $\beta$-delayed fission in rapid neutron capture process ($r$-process) nucleosynthesis in the tidal ejecta of a neutron star--neutron star merger and show that it is a key fission channel that shapes the final abundances near the second $r$-process peak.