High-precision $Q_{\mathrm{EC}}$-value measurement of the superallowed ${\beta }^{+}$ emitter ${}^{22}\mathrm{Mg}$ and an ab initio evaluation of the $A=22$ isobaric triplet

A direct $Q_{\mathrm{EC}}$-value measurement of the superallowed ${\beta }^{+}$ emitter ${}^{22}\mathrm{Mg}$ was performed using TRIUMF's Ion Trap for Atomic and Nuclear Science. The direct ground-state to ground-state atomic mass difference between ${}^{22}\mathrm{Mg}$ and ${}^{22}\mathrm{Na}$ was determined to be $Q_{\mathrm{EC}}=4781.40\left(22\right)$ keV, representing the most precise single measurement of this quantity to date. In a continued push toward calculating superallowed isospin-symmetry-breaking corrections from first principles, ab initio shell-model calculations of the $A=22$ isobaric multiplet mass equation are also presented for the first time using the valence-space in-medium similarity renormalization group formalism. With particular starting two- and three-nucleon forces, this approach demonstrates good agreement with the experimental data.

Figure 1

Typical time-of-flight (top) quadrupole-excitation and (bottom) Ramsey-excitation resonance spectra for ${}^{22}\mathrm{Mg}^{+}$ ions. The solid lines are known analytic fits to the experimental data.

Figure 2

Predictions from both the (red) NN+3N(400) and (blue) 1.8/2.0(EM) VS-IMSRG calculations compared to the experimental data (black). Panel (a) shows the $0^{+}$ IAS energies (solid lines) for the $A=22,T=1$ isobaric triplet. In ${}^{22}\mathrm{Na}$, the $0^{+}$ IAS has an experimentally measured excitation energy of 657.00(14) keV, while the ground state (dashed line) has $J^{\pi }=3^{+}$. Panel (b) highlights the remarkable agreement of the $T=1$, $0^{+}$ IAS excitation energy predicted by the 1.8/2.0(EM) VS-IMSRG calculation relative to the evaluated experimental data from Ref. [40], discussed further in the text.