$\mathrm{ft}$ Value of ${\mathrm{O}}^{14}$ and the Universality of the Fermi Interaction

The conserved-vector-current theory of the strangeness-conserving weak decays predicts that $G_V$, the vector coupling constant in nuclear beta decay, should be equal to $G_{\mu }$, the coupling constant in the muon decay. To make possible a more precise comparison of $G_V$ and $G_{\mu }$, the $\mathrm{ft}$ value of ${\mathrm{O}}^{14}$ has been remeasured. The endpoint energy of the positron decay has been determined by measuring the $Q$ values of the reactions ${\mathrm{C}}^{12}({\mathrm{He}}^3, n){\mathrm{O}}^{14}$ and ${\mathrm{C}}^{12}({\mathrm{He}}^3, p){\mathrm{N}}^{14*}$ (2.311-MeV state), using the same techniques and equipment where possible in order to minimize the uncertainty in the difference of the $Q$ values. The results of these measurements are $Q_n=-1148.8\mathrm{}\pm 0.6$ keV and $Q_p=2468.4\mathrm{}\pm 1.0$ keV, which yield $E_{max}\left({\beta }^{+}\right)=1812.6\mathrm{}\pm 1.4$ keV, all energies relative to the ${\mathrm{Li}}^7(p, n){\mathrm{Be}}^7$ threshold assumed as 1880.7±0.4 keV. The half-life of ${\mathrm{O}}^{14}$ has also been remeasured as 71.00±0.13 sec, which implies a partial half-life of 71.43±0.15 sec for the transition to the 2.311-MeV state of ${\mathrm{N}}^{14}$. Averaged with the recent half-life measurement of Hendrie and Gerhart, we obtain an $\mathrm{ft}$ value of 3075±10 sec for the ${\mathrm{O}}^{14}$ decay, after correcting for nuclear form factors, electron screening, and $K$-capture competition. With the radiative corrections of Kinoshita and Sirlin, the value obtained for $G_V$ is (1.4025±0.0022)×${10}^{-49\mathrm{}}$ erg-${\mathrm{cm}}^3$, where the quoted error is experimental in origin. This is to be compared with the value computed from recent muon decay measurements, $G_{\mu }=(1.4312\mathrm{}\pm 0.0011)\times {10}^{-49\mathrm{}}$ erg-${\mathrm{cm}}^3$, which is (2.0±0.2)% larger. As there appear to be several possible theoretical explanations for this small discrepancy, the present results are consistent with the conserved-vector-current hypothesis.