β -delayed one-neutron emission probabilities within a neural network model

Abstract

$\ensuremath{\beta}$-delayed neutron emission is one of the key ingredients for astrophysical $r$-process nucleosynthesis, and theoretical model predictions have still large uncertainties. In this work, we apply a novel feed-forward neural network model to calculate accurately $\ensuremath{\beta}$-delayed one-neutron emission probabilities. A model is trained with a set of input data of known physical quantities; one-neutron emission $Q$ value, the $Q$-value difference between the one- and two-neutron emissions, $\ensuremath{\beta}$-decay half-life, the distance from the least neutron-rich nucleus with ${Q}_{\ensuremath{\beta}1n}>0$ in each isotope, and the exponential form of the ratio of $Q$-value $\mathrm{exp}(\ensuremath{-}{Q}_{\ensuremath{\beta}2n}/{Q}_{\ensuremath{\beta}1n})$. The results give improvements for predictions of medium heavy isotopes and provide reasonable results in $r$-process nuclei, especially in the waiting point nuclei for neutron magic numbers $N=50$ and 82, in comparison with other microscopic models.