Electroweak transitions in nuclei from first principles

We present beta decay rates and recoil matrix elements calculated using the \textit{ab initio} symmetry-adapted no-core shell model (SA-NCSM). The SA-NCSM utilizes emergent symmetries in nuclei in order to reduce the dimensionality of the model space. This, in turn, allows one to reproduce the low-energy nuclear dynamics with only a small fraction of the model space, and hence making solutions to heavier nuclei feasible. The symmetry-adapted basis of the SA-NCSM is well suited for describing electromagnetic and beta-decay transitions enabling us to use the full capability of the model and perform calculations for up to pf-shell nuclei. This work discusses calculations of beta recoil matrix elements from first principles that help to probe fundamental interactions. It also focuses on a study of the $g_A$ quenching problem for bare interactions (no renormalization involved) and with collective correlations that are well described within the model, as well as on a study of $^{48}$Ca and $^{48}$Ti of interest to neutrinoless double beta decays.