Ultra-low $Q_β$ 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 $β$ spectral shape near the $β$ endpoint of a $β^-$ 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 ($Q^{\ast}_{β,m}=-0.12(131)$ 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 $Q^{\ast}_{β,m}=405(135)$ eV, for the $^{110}\text{Ag}(6^+_\text{m}) \rightarrow {^{110}\text{Cd}}(5^+_2)$ transition. This represents the lowest $Q_β$ value for any allowed transition observed to date. In order to estimate the partial half-life ($t_{1/2}$) 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 $t_{1/2} = 2.23^{+5.24}_{-1.28} \times 10^7$ years and $\textrm{Br} = 3.07^{+4.16}_{-2.15} \times 10^{-8}$, along with the thermal-neutron capture on stable $^{109}$Ag as a viable production method, make $^{110}\textrm{Ag}^m$ a promising candidate for future antineutrino-mass measurements.