Positron Emission in the Decay of ${\mathrm{K}}^{40}$

Positron emission has been detected in the decay of ${\mathrm{K}}^{40}$ in a triple coincidence experiment using a liquid-scintillation positron detector and two NaI(Tl) annihilation gamma detectors. A ratio of $\frac{{\beta }^{+}}{{\beta }^{-}}=(1.12\mathrm{}\pm 0.14)\times {10}^{-5\mathrm{}}$ was found. This corresponds to a ratio of the squared matrix elements of $\frac{{M_{+}}^2}{{M_{-}}^2}=0.18\mathrm{}\pm 0.03$ which is in substantial agreement with a theoretical estimate of $\frac{1}{8}$. The effect of this result on the decay constants of ${\mathrm{K}}^{40}$ is discussed.