Measurement of the $2^{+}\to 0^{+}$ ground-state transition in the $\beta$ decay of ${}^{20}$F

We report the first detection of the second-forbidden, non-unique, $2^{+}\to 0^{+}$, ground-state transition in the $\beta$ decay of ${}^{20}$F. A low-energy, mass-separated ${}^{20}{\mathrm{F}}^{+}$ beam produced at the IGISOL facility in Jyv"askyl"a, Finland, was implanted in a thin carbon foil and the $\beta$ spectrum measured using a magnetic transporter and a plastic-scintillator detector. The $\beta$-decay branching ratio inferred from the measurement is $b_{\beta} = [ 0.41\pm 0.08$\text{(stat)}$\pm 0.07$\text{(sys)}$] \times 10^{-5}$correspondingto$\log ft = 10.89(11)$, making this one of the strongest second-forbidden, non-unique $\beta$ transitions ever measured. The experimental result is supported by shell-model calculations and has significant implications for the final evolution of stars that develop degenerate oxygen-neon cores. Using the new experimental data, we argue that the astrophysical electron-capture rate on ${}^{20}$Ne is now known to within better than 25% at the relevant temperatures and densities.