Convergence of ab initio calculated $M1$ observables: The role of symmetry, structure and selection rules

In order to test \textit{ab initio} no core shell model predictions against experiment, we must first obtain well converged calculations of observables. In particular, $M1$ observables converge more rapidly than long range (e.g., $E2$) electromagnetic observables. In order to understand how the $M1$ convergence and predicted strengths relate to underlying structure of the nucleus, we study the contributions of the different components of the $M1$ operator. Each of these components is subject to different selection rules on angular momentum (orbital and spin), isospin and $\mathrm{SU}(3)$ quantum numbers. We use the Lanczos decomposition method to determine the dominant $LS$ and $\mathrm{SU}(3)$ contributions to the calculated wave functions and thus understand the relevant selection rules for each transition. We present analysis of calculated $M1$ moments and low-lying transitions in $p$-shell nuclei, obtained with the Daejeon16 interaction.