High-precision measurements of superallowed $0^{+}\to 0^{+}$ $\beta$ decays of $T=2$ nuclides such as ${}^{20}\mathrm{Mg}$, ${}^{24}\mathrm{Si}$, ${}^{28}\mathrm{S}$, and ${}^{32}\mathrm{Ar}$ can contribute to searches for physics beyond the standard model of particle physics if the $Q_{\mathrm{EC}}$ values are accurate to a few keV or better. As a step toward providing precise $Q_{\mathrm{EC}}$ values for these decays, the ground-state masses of the respective daughter nuclei ${}^{20}\mathrm{Na}$, ${}^{24}\mathrm{Al}$, ${}^{28}\mathrm{P}$, and ${}^{32}\mathrm{Cl}$ have been determined by measuring the (${}^3\mathrm{He},t$) reactions leading to them with the ${}^{36}\mathrm{Ar}$(${}^3\mathrm{He},t$)${}^{36}\mathrm{K}$ reaction as a calibration. A quadrupole-dipole-dipole-dipole (Q3D) magnetic spectrograph was used together with thin ion-implanted carbon-foil targets of ${}^{20}\mathrm{Ne}$, ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, ${}^{32}\mathrm{S}$, and ${}^{36}\mathrm{Ar}$. The masses of ${}^{20}\mathrm{Na}$ and ${}^{32}\mathrm{Cl}$ are found to be in good agreement with the values from the 2003 Atomic Mass Evaluation (AME03) [G. Audi, A. H. Wapstra, and C. Thibault, Nucl. Phys. A 729, 337 (2003)], and the precision has been improved by a factor of 6 in both cases. The masses of ${}^{24}\mathrm{Al}$ and ${}^{28}\mathrm{P}$ are found to be higher than the values from AME03 by 9.5 keV ($3.2\sigma$) and 11.5 keV ($3.6\sigma$), respectively, and the precision has been improved by a factor of 2.5 in both cases. The new ${}^{32}\mathrm{Cl}$ mass is used together with the excitation energy of its lowest $T=2$ level and the mass of ${}^{32}\mathrm{Ar}$ to derive an improved superallowed $Q_{\mathrm{EC}}$ value of 6087.3(22) keV for this case. The effects on quantities related to standard-model tests including the $\beta$-$\nu$ correlation coefficient $a$ and the isospin-symmetry-breaking correction ${\delta }_C$ are examined for the $A=32$ case.

• Received 5 March 2010

DOI:https://doi.org/10.1103/PhysRevC.81.055503