In anticipation of results from current and future double-$\beta$ decay studies, we report a measurement resulting in a ${}^{82}\mathrm{Se}$ double-$\beta$ decay $Q$ value of 2997.9(3) keV, an order of magnitude more precise than the currently accepted value. We also present preliminary results of a calculation of the ${}^{82}\mathrm{Se}$ neutrinoless double-$\beta$ decay nuclear matrix element that corrects in part for the small size of the shell model single-particle space. The results of this work are important for designing next generation double-$\beta$ decay experiments and for the theoretical interpretations of their observations.

The JYFLTRAP double Penning trap at the Ion Guide Isotope Separator On-Line facility has been used to measure the atomic masses of 13 neutron-rich rare-earth isotopes. Eight of the nuclides, ${}^{161}\mathrm{Pm}, {}^{163}\mathrm{Sm}, {}^{164,165}\mathrm{Eu}, {}^{167}\mathrm{Gd}$, and ${}^{165,167,168}\mathrm{Tb}$, were measured for the first time. The systematics of the mass surface has been studied via one- and two-neutron separation energies as well as neutron pairing-gap and shell-gap energies. The proton-neutron pairing strength has also been investigated. The impact of the new mass values on the astrophysical rapid neutron capture process has been studied. The calculated abundance distribution results in a better agreement with the solar abundance pattern near the top of the rare-earth abundance peak at around $A\approx 165$.

Background: The precise determination of $ft$ values for superallowed mixed transitions between mirror nuclide are gaining attention as they could provide an avenue to test the theoretical corrections used to extract the $V_{ud}$ matrix element from superallowed pure Fermi transitions. The ${}^{17}\mathrm{F}$ decay is particularly interesting as it proceeds completely to the ground state of ${}^{17}\mathrm{O}$, removing the need for branching ratio measurements. The dominant uncertainty on the $ft$ value of the ${}^{17}\mathrm{F}$ mirror transition stems from a number of conflicting half-life measurements.

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.

A new precision half-life measurement of ${}^{13}\mathrm{N}$ has been conducted using the TwinSol $\beta$-counting station at the University of Notre Dame. The measured value of $t_{1/2}^{\mathrm{new}}=597.05\left(19\right)\mathrm{s}$ differs from the previous world value by about $2.8\sigma$. An evaluation of the ${}^{13}\mathrm{N}$ half-life results in a $t_{1/2}^{\mathrm{world}}=597.19\left(22\right)\mathrm{s}$. Updated standard model predictions for the Fermi to Gamow-Teller mixing ratio $\rho$ and its associated correlation parameters have been calculated using the new ${}^{13}\mathrm{N}$ world half-life in preparation for a future measurement of the mixing ratio. Finally, an ab initio no-core configuration interaction (NCCI) calculation for the $B\left(\mathrm{GT}\right)$ of this decay, carried out using the Daejeon16 interaction, has been performed, revealing the need for higher-order chiral corrections.

We report a new direct measurement of the transition energy $Q_{EC}$ of the ${}^{23}\mathrm{Mg}$ ${\beta }^{+}$ decay, using the TITAN Penning-trap mass spectrometer. This value is found to agree with the latest atomic mass evaluation while being four times more precise. The increase in precision changes the uncertainty contribution of the $Q_{EC}$ value on the statistical rate function $f_v$ from $11\%$ to $0.6\%$, an improvement by a factor of 18. This enables a more robust determination of the corrected $\mathcal{F}t$ value of this mirror transition to the required precision, making possible further test of the Cabibbo-Kobayashi-Maskawa matrix unitarity.