Ultra-low $Q_{\beta }$ value for the allowed decay of ${}^{110}$Ag${}^m$ confirmed via mass measurements

The mass of the electron-antineutrino can be determined in dedicated measurements of the $\beta$ spectral shape near the $\beta$ endpoint of a ${\beta }^{-}$ transition, with a low $Q$ value enhancing the sensitivity of the measurement. One such low-$Q$-value candidate is the transition between the $6^{+}$ isomer of ${}^{110}$Ag and the $5_2^{+}$ state in ${}^{110}$Cd ($Q_{\beta ,m}^{\ast }=-0.12(131)$ keV). To reduce the uncertainty of the $Q$ value, we have used the phase-imaging ion-cyclotron-resonance technique with the JYFLTRAP double Penning trap and performed a high-precision atomic-mass measurement of ${}^{109}$Ag with ${}^{110}$Cd as a reference. Combined with the known spectroscopic data, we obtain a re-evaluated value $Q_{\beta ,m}^{\ast }=405(135)$ eV, for the ${}^{110}\text{Ag}(6_{\text{m}}^{+})\to {}^{110}\text{Cd}(5_2^{+})$ transition. This represents the lowest $Q_{\beta }$ value for any allowed transition observed to date. In order to estimate the partial half-life ($t_{1\mathrm{/}2}$) and branching ratio (Br) of the transition, nuclear shell-model calculations were performed using the $jj45pnb$ Hamiltonian in combination with state-of-the-art atomic calculations. The computed values $t_{1\mathrm{/}2}=2.23_{-1.28}^{+5.24}\times {10}^7$ years and $\text{Br}=3.07_{-2.15}^{+4.16}\times {10}^{-8}$, along with the thermal-neutron capture on stable ${}^{109}$Ag as a viable production method, make ${}^{110}{\text{Ag}}^m$ a promising candidate for future antineutrino-mass measurements.