β+-Delayed-Proton Decay ofMg21

Identified protons with energies from 900 keV to 6.3 MeV have been observed following the positron decay of ${}_{}{}^{21}{}_{}{}^{}\mathrm{Mg}$. The half-life of ${}_{}{}^{21}{}_{}{}^{}\mathrm{Mg}$ was measured to be 123.1 ± 3.3 msec, which, combined with previous results, gives a best value of 122.5 ± 2.8 msec. The energies and intensities of the proton groups have been used to determine precise excited state energies in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$ above 5 MeV and the strength of the preceding ${\beta }^{+}$ transition feeding each level. These data, and the assumption of isospin purity for the lowest $T=\frac{3}{2}$ level in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$, then yield absolute $\mathrm{ft}$ values for the beta decay. The ${}_{}{}^{21}{}_{}{}^{}\mathrm{Mg}$ transition rates compared with the negatron decay rates in its mirror, ${}_{}{}^{21}{}_{}{}^{}\mathrm{F}$, give $\frac{{\mathrm{}\left(\mathrm{ft}\right)\mathrm{}}^{+}}{{\mathrm{}\left(\mathrm{ft}\right)\mathrm{}}^{-}}=1.10\mathrm{}\pm 0.08$. All significant particle decays of the lowest $T=\frac{3}{2}$ level have been observed, including an upper limit on energetically possible, but unobserved, $\alpha$ decay. The measured transition strengths were compared to recent shell model calculations for $\beta$ decay in the $s-d$ shell.