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

We report on high-precision $Q_{\mathrm{EC}}$ values of the ${}^{21}\mathrm{Na}\to {}^{21}\mathrm{Ne}$ and ${}^{23}\mathrm{Mg}\to {}^{23}\mathrm{Na}$ mirror $\beta$ transitions from mass measurements with ISOLTRAP at the CERN ISOLDE facility. A precision of $\delta m/m=9\times {10}^{-10}$ and $\delta m/m=1.5\times {10}^{-9}$ was reached for the masses of ${}^{21}\mathrm{Na}$ and ${}^{23}\mathrm{Mg}$, respectively. We reduce the uncertainty of the $Q_{\mathrm{EC}}$ values by a factor of 5, making them the most precise experimental input data for the calculation of the corrected $\mathcal{F}t$ value of these mixed Fermi and Gamow-Teller transitions. For the ${}^{21}\mathrm{Na}\to {}^{21}\mathrm{Ne}{Q}_{\mathrm{EC}}$ value, a $2.3\sigma$ deviation from the literature $Q_{\mathrm{EC}}$ value was found.

Figure 1

Schematic overview of the ISOLTRAP setup. On-line beam from the CERN ISOLDE facility or off-line beam from ISOLTRAP's offline source enters to the left to go through a sequence of four ion traps: a linear radio-frequency Paul trap (RFQ, pink), a multi-reflection time-of-flight (MR-ToF, yellow) device, and two Penning traps (green, red). For particle detection and time-of-flight measurements, a secondary electron multiplier (EMP) ion detector and a micro-channel plate (MCP) ion detector are used.

Figure 2

Typical time-of-flight spectrum using laser ionization (for details, see text), here shown for 80 summed spectra of $A=21$ after 2000 revolutions in ISOLTRAP's MR-ToF MS.

Figure 3

Typical Ramsey-type ion-cyclotron resonances, here shown for ${}^{21}\mathrm{Ne}^{+}$ and for ${}^{23}\mathrm{Mg}^{+}$ after a total of $600\mathrm{ms}$ measurement time (Ramsey pattern: 50-500-$50\mathrm{ms}$) in ISOLTRAP's precision Penning trap. For each frequency bin, the mean of the recorded, unbinned time-of-flight distribution (black) and its associated standard deviation is depicted in green. The red line represents a least squares fit to the expected line shape [37].

Figure 4

Cyclotron-frequency-ratio determination using a simultaneous polynomial fit for a subset of measured cyclotron frequencies (including error bars) of ${}^{21}\mathrm{Ne}^{+}$ and ${}^{21}\mathrm{Na}^{+}$.

Figure 5

Comparison between different mirror-nuclei $V_{\mathrm{ud}}$ values: ${}^{19}\mathrm{Ne}$ [49], ${}^{29}\mathrm{P}$ [16], ${}^{35}\mathrm{Ar}$ [9], ${}^{37}\mathrm{K}$ [13] (blue), our new value for ${}^{21}\mathrm{Na}$ (green), the weighted mean $V_{\mathrm{ud}}$ value of all values (red = two $\sigma$ band), and the mean $V_{\mathrm{ud}}$ value for the superallowed transitions [48] (gray = two $\sigma$ band).

Figure 6

Comparison of the relative uncertainty contributions to the $\mathcal{F}{t}^{\mathrm{mirror}}$ value: the nucleus-dependent radiative corrections, ${\delta }_R^{{}^{\prime }}$, and ${\delta }_{\mathrm{NS}}^V$, the isospin-symmetry-breaking corrections ${\delta }_{\mathrm{C}}^V$, the half-lives, the branching ratios $\mathrm{BR}$, and the $Q_{\mathrm{EC}}$ values from Ref. [16] for ${}^{21}\mathrm{Na}$ (blue), from Ref. [15] for ${}^{23}\mathrm{Mg}$ (red), as well as from this work. For details, see text.