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We report on high-precision $Q_{\textrm{EC}}$ values of the$^{21}$Na$\rightarrow^{21}$Ne and $^{23}$Mg$\rightarrow^{23}$Na mirror$\beta$-transitions from mass measurements with ISOLTRAP at ISOLDE/CERN. Aprecision of $\delta m/m = 9 \cdot 10^{-10}$ and $\delta m/m = 1.5 \cdot10^{-9}$ was reached for the masses of $^{21}$Na and $^{23}$Mg, respectively.We reduce the uncertainty of the $Q_{\textrm{EC}}$ values by a factor five,making them the most precise experimental input data for the calculation of thecorrected $\mathcal{F} t$-value of these mixed Fermi/Gamow-Teller transitions.For the $^{21}$Na$\rightarrow^{21}$Ne $Q_{\textrm{EC}}$ value, a $2.3 \sigma$deviation from the literature $Q_{\textrm{EC}}$-value was found.

physical review. c

$Q_{\textrm{EC}}$-value determination for $^{21}$Na$\rightarrow^{21}$Ne  and $^{23}$Mg$\rightarrow^{23}$Na mirror-nuclei decays using high-precision  mass spectrometry with ISOLTRAP at ISOLDE/CERN