Experimental searches for neutrinoless double-$\beta$ decay offer one of the best opportunities to look for physics beyond the standard model. Detecting this decay would confirm the Majorana nature of the neutrino, and a measurement of its half-life can be used to determine the absolute neutrino mass scale. Important to both tasks is an accurate knowledge of the $Q$ value of the double-$\beta$ decay. The LEBIT Penning trap mass spectrometer was used for the first direct experimental determination of the ${}^{96}\mathrm{Zr}$ double-$\beta$ decay $Q$ value: $Q_{\beta \beta }=3355.85\left(15\right)$ keV. This value is nearly 7 keV larger than the 2012 Atomic Mass Evaluation [M. Wang et al., Chin. Phys. C 36, 1603 (2012)] value and one order of magnitude more precise. The 3-$\sigma$ shift is primarily due to a more accurate measurement of the ${}^{96}\mathrm{Zr}$ atomic mass: $m{(}^{96}\mathrm{Zr})=95.90827735\left(17\right)$ u. Using the new $Q$ value, the $2\nu \beta \beta$-decay matrix element, $|M_{2\nu }|$, is calculated. Improved determinations of the atomic masses of all other zirconium $\left({}^{90-92,94,96}\mathrm{Zr}\right)$ and molybdenum $\left({}^{92,94-98,100}\mathrm{Mo}\right)$ isotopes using both ${}^{12}{\mathrm{C}}_8$ and ${}^{87}\mathrm{Rb}$ as references are also reported.

A nuclear mass survey of rare-earth isotopes has been conducted with the Canadian Penning Trap mass spectrometer using the most neutron-rich nuclei thus far extracted from the CARIBU facility. We present a collection of 12 nuclear masses determined with a precision of $\le 10$ keV/$c{}^2$ for $Z=58–63$ nuclei near $N=100$. Independently, a detailed study exploring the role of nuclear masses in the formation of the $r$-process rare-earth abundance peak has been performed. Employing a Markov chain Monte Carlo (MCMC) technique, mass predictions of lanthanide isotopes have been made which uniquely reproduce the observed solar abundances near $A=164$ under three distinct astrophysical outflow conditions. We demonstrate that the mass surface trends thus far mapped out by our measurements are most consistent with MCMC mass predictions given an $r$ process that forms the rare-earth peak during an extended $(n,\gamma )\rightleftarrows (\gamma ,n)$ equilibrium.

We report the mass measurement of ${}^{56}\mathrm{Cu}$, using the LEBIT 9.4 T Penning trap mass spectrometer at the National Superconducting Cyclotron Laboratory at Michigan State University. The mass of ${}^{56}\mathrm{Cu}$ is critical for constraining the reaction rates of the ${}^{55}\mathrm{Ni}(p,\gamma )$ ${}^{56}\mathrm{Cu}(p,\gamma )$ ${}^{57}\mathrm{Zn}({\beta }^{+})$ ${}^{57}\mathrm{Cu}$ bypass around the ${}^{56}\mathrm{Ni}$ waiting point. Previous recommended mass excess values have disagreed by several hundred keV. Our new value, $\mathrm{ME}=-38626.7(7.1)\mathrm{keV}$, is a factor of 30 more precise than the extrapolated value suggested in the 2012 atomic mass evaluation [ Chin. Phys. C 36, 1603 (2012)], and more than a factor of 12 more precise than values calculated using local mass extrapolations, while agreeing with the newest 2016 atomic mass evaluation value [ Chin. Phys. C 41, 030003 (2017)]. The new experimental average, using our new mass and the value from AME2016, is used to calculate the astrophysical ${}^{55}\mathrm{Ni}(p,\gamma )$ and ${}^{56}\mathrm{Cu}(p,\gamma )$ forward and reverse rates and perform reaction network calculations of the $rp$ process. These show that the $rp$-process flow redirects around the ${}^{56}\mathrm{Ni}$ waiting point through the ${}^{55}\mathrm{Ni}(p,\gamma )$ route, allowing it to proceed to higher masses more quickly and resulting in a reduction in ashes around this waiting point and an enhancement to higher-mass ashes.

Masses of neutron-rich, odd-odd Pm, Eu, and Tb nuclei near $N=98$ were measured using the Canadian Penning Trap mass spectrometer at the Californium Rare Isotope Breeder Upgrade (CARIBU) facility. High-resolution mass measurements yielded the discovery of spin-trap isomers at $N=97$ in ${}^{162}\mathrm{Tb}$, and in the $N=99$ isotones of ${}^{160}\mathrm{Pm}$ and ${}^{164}\mathrm{Tb}$. Furthermore, no evidence of long-lived isomers were observed at $N=95$ in ${}^{158}\mathrm{Eu}$, at $N=97$ in ${}^{158}\mathrm{Pm}$, nor at $N=101$ in ${}^{164}\mathrm{Eu}$ and ${}^{166}\mathrm{Tb}$. These experimental observations are compared to results from multiquasiparticle blocking calculations.