Title: Detailed study of the decay of $^{21}$Mg

Abstract: Beta-delayed proton and gamma emission in the decay of $^{21}$Mg has been measured at ISOLDE, CERN with the ISOLDE Decay Station (IDS) set-up. The existing decay scheme is updated, in particular what concerns proton transitions to excited states in $^{20}$Ne. Signatures of interference in several parts of the spectrum are used to settle spin and parity assignments to highly excited states in $^{21}$Na. The previously reported $\beta$p$\alpha$ branch is confirmed. A half-life of 120.5(4) ms is extracted for $^{21}$Mg. The revised decay scheme is employed to test mirror symmetry in the decay and to extract the beta strength distribution of $^{21}$Mg that is compared with theory.