Jason A. Clark

An ultra-low Q value $β$-decay can occur from a parent nuclide to an excited state in the daughter with $Q_{UL}$ <1 keV. These decays are of interest for nuclear $β$-decay theory and as potential candidates in neutrino mass determination experiments. To date, only one ultra-low Q value $β$-decay has been observed -- that of $^{115}$In with $Q_β$ = 147(10) eV. A number of other potential candidates exist, but improved mass measurements are necessary to determine if the decays are energetically allowed and, in fact, ultra-low. We performed precise $β$-decay Q value measurements of $^{112,113}$Ag and $^{115}$Cd and combined them with nuclear energy level data for the daughter isotopes to determine if the potential UL Q value $β$-decay branches of $^{112,113}$Ag and $^{115}$Cd are energetically allowed and <1 keV. The Canadian Penning Trap at ANL was used to measure the cyclotron frequency ratios of singly-charged $^{112,113}$Ag and $^{115}$Cd ions with respect to their daughters. From these measurements, the ground-state $β$-decay Q values were obtained. The $^{112}$Ag, $^{113}$Ag, and $^{115}$Cd $β$-decay Q values were measured to be 3990.16(22) keV, 2085.7(4.6) keV, and 1451.36(34) keV, respectively. These results were compared to energies of excited states in $^{112}$Cd at 3997.75(14) keV, $^{113}$Cd at 2015.6(2.5) and 2080(10) keV, and $^{115}$In at 1448.787(9) keV, resulting in $Q_{\textrm{UL}}$ values of --7.59(26) keV, 6(11) keV, and 2.57(34) keV, respectively. The potential UL Q value decays of $^{112}$Ag and $^{115}$Cd have been ruled out. $^{113}$Ag is still a possible candidate until a more precise measurement of the 2080(10) keV, 1/2$^{+}$ state of $^{113}$Cd is available. In the course of this work we have found the ground state mass of $^{113}$Ag reported in the 2020AME to be lower than our measurement by 69(17) keV (a 4$σ$ discrepancy).

The development of the phase-imaging ion-cyclotron resonance (PI-ICR) technique for use in Penning trap mass spectrometry (PTMS) increased the speed and precision with which PTMS experiments can be carried out. In PI-ICR, data sets of the locations of individual ion hits on a detector are created showing how ions cluster together into spots according to their cyclotron frequency. Ideal data sets would consist of a single, 2D-spherical spot with no other noise, but in practice data sets typically contain multiple spots, non-spherical spots, or significant noise, all of which can make determining the locations of spot centers non-trivial. A method for assigning groups of ions to their respective spots and determining the spot centers is therefore essential for further improving precision and confidence in PI-ICR experiments. We present the class of Gaussian mixture model (GMM) clustering algorithms as an optimal solution. We show that on simulated PI-ICR data, several types of GMM clustering algorithms perform better than other clustering algorithms over a variety of typical scenarios encountered in PI-ICR. The mass spectra of $^{163}\text{Gd}$, $^{163m}\text{Gd}$, $^{162}\text{Tb}$, and $^{162m}\text{Tb}$ measured using PI-ICR at the Canadian Penning trap mass spectrometer were checked using GMMs, producing results that were in close agreement with the previously published values.