Superallowed $0^{+}\to 0^{+}$ $\beta$ decay of $T=2$ ${}^{20}$Mg: $Q_{\text{EC}}$ value and $\beta \gamma$ branching

Abstract

\textbf{Background}: Superallowed $0^{+}\to 0^{+}$ $\beta$ decays of isospin $T=2$ nuclides can be used to test theoretical isospin symmetry breaking corrections applied to extract the CKM matrix element $V_{ud}$ from $T=0,1$ decays by measuring precise $ft$ values and also to search for scalar currents using the $\beta -\nu$ angular correlation. Key ingredients include the $Q_{\text{EC}}$ value and branching of the superallowed transition and the half life of the parent. \textbf{Purpose}: To determine a precise experimental $Q_{\text{EC}}$ value for the superallowed $0^{+}\to 0^{+}$ $\beta$ decay of $T=2$ ${}^{20}$Mg and the intensity of ${}^{20}$Mg $\beta$-delayed $\gamma$ rays through the isobaric analog state in ${}^{20}$Na. \textbf{Method}: A beam of ${}^{20}$Mg was produced using the in-flight method and implanted into a plastic scintillator surrounded by an array of high-purity germanium detectors used to detect $\beta$-delayed $\gamma$ rays. The high-resolution $\gamma$-ray spectrum was analyzed to measure the $\gamma$-ray energies and intensities. \textbf{Results}: The intensity of ${}^{20}$Mg $\beta$-delayed $\gamma$ rays through the isobaric analog state in ${}^{20}$Na was measured to be $(1.60\pm 0.04_{\text{stat}}\pm 0.15_{\text{syst}}\pm 0.15_{\text{theo}})\times 10^{-4}$, where the uncertainties are statistical, systematic, and theoretical, respectively. The $Q_{\text{EC}}$ value for the superallowed transition was determined to be $4128.7\pm 2.2$ keV based on the measured excitation energy of $6498.4\pm 0.2_{\text{stat}}\pm 0.4_{\text{syst}}$ keV and literature values for the ground-state masses of ${}^{20}$Na and ${}^{20}$Mg. \textbf{Conclusions}: The $\beta$-delayed $\gamma$-decay branch and $Q_{\text{EC}}$ value are now sufficiently precise to match or exceed the sensitivity required for current low-energy tests of the standard model.