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We report the first detection of the second-forbidden, non-unique,$2^+\rightarrow 0^+$, ground-state transition in the $\beta$ decay of $^{20}$F.A low-energy, mass-separated $^{20}\rm{F}^+$ beam produced at the IGISOLfacility in Jyv\"askyl\"a, Finland, was implanted in a thin carbon foil and the$\beta$ spectrum measured using a magnetic transporter and aplastic-scintillator detector. The $\beta$-decay branching ratio inferred fromthe measurement is $b_{\beta} = [ 0.41\pm 0.08\textrm{(stat)}\pm0.07\textrm{(sys)}] \times 10^{-5}$ corresponding to $\log ft = 10.89(11)$,making this one of the strongest second-forbidden, non-unique $\beta$transitions ever measured. The experimental result is supported by shell-modelcalculations and has significant implications for the final evolution of starsthat develop degenerate oxygen-neon cores. Using the new experimental data, weargue that the astrophysical electron-capture rate on $^{20}$Ne is now known towithin better than 25% at the relevant temperatures and densities.

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