Precision mass measurements of magnesium isotopes and implications for the validity of the isobaric mass multiplet equation

If the mass excess of neutron-deficient nuclei and their neutron-rich mirror partners are both known, it can be shown that deviations of the isobaric mass multiplet equation (IMME) in the form of a cubic term can be probed. Such a cubic term was probed by using the atomic mass of neutron-rich magnesium isotopes measured using the TITAN Penning trap and the recently measured proton-separation energies of ${}^{29}\mathrm{Cl}$ and ${}^{30}\mathrm{Ar}$. The atomic mass of ${}^{27}\mathrm{Mg}$ was found to be within $1.6\sigma$ of the value stated in the Atomic Mass Evaluation. The atomic masses of ${}^{28,29}\mathrm{Mg}$ were measured to be both within $1\sigma$, while being 7 and 33 times more precise, respectively. Using the ${}^{29}\mathrm{Mg}$ mass excess and previous measurements of ${}^{29}\mathrm{Cl}$, we uncovered a cubic coefficient of $d=28\left(7\right)\mathrm{keV}$, which is the largest known cubic coefficient of the IMME. This departure, however, could also be caused by experimental data with unknown systematic errors. Hence there is a need to confirm the mass excess of ${}^{28}\mathrm{S}$ and the one-neutron separation energy of ${}^{29}\mathrm{Cl}$, which have both come from a single measurement. Finally, our results were compared with ab initio calculations from the valence-space in-medium similarity renormalization group, resulting in a good agreement.

Figure 1

Typical quadrupole resonance of ${}^{29}\mathrm{Mg}^{+}$ with the fitted theoretical lineshape [32]. The quadrupole excitation time was $T_{\text{rf}}=997\mathrm{ms}$.

Figure 2

Difference between individual frequency ratios $R$ and the averaged frequency ratios $\overline{R}$ for ${}^{27–29}\mathrm{Mg}^{+}$ (${}^{23}\mathrm{Na}^{+}$ was the calibrant). The double red lines indicates the $1\sigma$ statistical uncertainty on $\overline{R}$. The Birge ratio ${\chi }_{\nu }$ for each weighted average is also given. An excitation time of 997 ms was used for all frequency ratio measurements except for the last $10{}^{29}\mathrm{Mg}^{+}$ measurements, which were done using a 97 ms excitation.

Figure 3

Residuals of the $b$ coefficient parametrization $\mathrm{\Delta }b$ as a function of the atomic mass number $A$ for all fully determined multiplets, as described in the text. The solid line represents a spline interpolation of a five-point moving average of the residual. The standard deviation of the difference between the interpolation and the residual is represented by the doted lines.