$Q$ Values of the Superallowed $\beta$ Emitters ${}^{26}\mathrm{Al}^m$, ${}^{42}\mathrm{Sc}$, and ${}^{46}\mathrm{V}$ and Their Impact on $V_{ud}$ and the Unitarity of the Cabibbo-Kobayashi-Maskawa Matrix

The $\beta$-decay $Q_{\mathrm{EC}}$ values of the superallowed beta emitters ${}^{26}\mathrm{Al}^m$, ${}^{42}\mathrm{Sc}$, and ${}^{46}\mathrm{V}$ have been measured with a Penning trap to a relative precision of better than $8\times {10}^{-9}$. Our result for ${}^{46}\mathrm{V}$, 7052.72(31) keV, confirms a recent measurement that differed from the previously accepted reaction-based $Q_{\mathrm{EC}}$ value. However, our results for ${}^{26}\mathrm{Al}^m$ and ${}^{42}\mathrm{Sc}$, 4232.83(13) keV and 6426.13(21) keV, are consistent with previous reaction-based values. By eliminating the possibility of a systematic difference between the two techniques, this result demonstrates that no significant shift in the deduced value of $V_{ud}$ should be anticipated.

Figure 1

Examples of the time-of-flight (TOF) resonances measured for each of the superallowed beta emitters. The solid curves are fitted functions (see text).

Figure 2

Individual $Q_{\mathrm{EC}}$ values obtained for ${}^{42}\mathrm{Sc}$ in January 2006 by using ${}^{42}\mathrm{Ca}^{+}$ as a reference ion. Each set of measurements corresponds to a different excitation time (see legend). The values given (in keV) for each set contain only statistical uncertainties from fitting and those arising from short-term magnetic field fluctuations. The 400 ms set was shifted earlier by 2 days for plotting convenience.