The Mass of ${}^{22}\mathrm{M}\mathrm{g}$

Mass measurements with a relative precision of better than $1.5\times {10}^{-8}$ were performed on ${}^{22}\mathrm{M}\mathrm{g}$ and its reaction partners ${}^{21}\mathrm{N}\mathrm{a}$ and ${}^{22}\mathrm{N}\mathrm{a}$ with the ISOLTRAP Penning trap mass spectrometer at CERN, yielding the mass excesses $D({}^{22}\mathrm{M}\mathrm{g})=-399.92(27)\mathrm{k}\mathrm{e}\mathrm{V}$, $D({}^{21}\mathrm{N}\mathrm{a})=-2184.71(21)\mathrm{k}\mathrm{e}\mathrm{V}$, and $D({}^{22}\mathrm{N}\mathrm{a})=-5181.56(16)\mathrm{k}\mathrm{e}\mathrm{V}$. The importance of these results is twofold. First, a comparative half-life ($Ft$ value) has been obtained for the superallowed $\beta$ decay of ${}^{22}\mathrm{M}\mathrm{g}$ to further test the conserved-vector-current hypothesis. Second, the resonance energy for the ${}^{21}\mathrm{N}\mathrm{a}$ proton capture reaction has been independently determined, allowing direct comparisons of observable $\gamma$ radiation in nova explosions with the yield expected from models.

Figure 1

(a) “Hot” and “cold” reaction paths of the NeNa cycle. The bottom row (black boxes) are stable nuclides; (b) level scheme of ${}^{22}\mathrm{M}\mathrm{g}$, showing the levels with astrophysical relevance [31]. The level energies $E_x$ (center) are shown along with the center-of-mass energies $E_x-Q_p$ (left; both in keV) and the spin parity (right).

Figure 2

(a) Typical time-of-flight (TOF) cyclotron resonance of ${}^{22}\mathrm{M}\mathrm{g}^{+}$. The solid line is a fit of the theoretically expected line shape [21] to the data; (b) comparison of the mass excess value from the measurement reported here with previous results and the AME 2003 [3]. For Ref. 29, both the original (open circle) and the recalibrated (solid circle) [1] values are shown. The dashed line is the central value of our result.

Figure 3

Comparative half-life for the decay ${}^{22}\mathrm{M}\mathrm{g}({\beta }^{+}){}^{22}\mathrm{N}\mathrm{a}$ (square) compared with the high-precision data for the other nine nuclides ${}^{10}\mathrm{C}\mathrm{\text{−}}{}^{54}\mathrm{C}\mathrm{o}$ (circles) [5]. The dashed lines indicate the confidence interval of the weighted mean $\overline{Ft}=3072.2(9)\mathrm{s}$ of the other data.