Breakdown of the Isobaric Multiplet Mass Equation for the $A=20$ and 21 Multiplets

Using the Penning trap mass spectrometer TITAN, we performed the first direct mass measurements of ${}^{20,21}\mathrm{Mg}$, isotopes that are the most proton-rich members of the $A=20$ and $A=21$ isospin multiplets. These measurements were possible through the use of a unique ion-guide laser ion source, a development that suppressed isobaric contamination by 6 orders of magnitude. Compared to the latest atomic mass evaluation, we find that the mass of ${}^{21}\mathrm{Mg}$ is in good agreement but that the mass of ${}^{20}\mathrm{Mg}$ deviates by $3\sigma$. These measurements reduce the uncertainties in the masses of ${}^{20,21}\mathrm{Mg}$ by 15 and 22 times, respectively, resulting in a significant departure from the expected behavior of the isobaric multiplet mass equation in both the $A=20$ and $A=21$ multiplets. This presents a challenge to shell model calculations using either the isospin nonconserving universal $sd$ USDA and USDB Hamiltonians or isospin nonconserving interactions based on chiral two- and three-nucleon forces.

Figure 1

A schematic drawing of the ISAC target with the IG-LIS. See the text for a detailed description.

Figure 2

Time-of-flight ion cyclotron resonance of ${}^{21}\mathrm{Mg}$ with 97 ms excitation time. The line is a fit of the theoretical shape [27].