Electron capture decay of116Inand nuclear structure of doubleβdecays

Quasiparticle-random-phase-approximation (QRPA) calculations of double $\beta$ decays have not been able to reproduce data in the $A=100\mathrm{}$ system. We propose the $A=116\mathrm{}$ system—because of its smaller deformation—as a simpler system to test QRPA calculations. We present results of two experiments we performed, which determine the electron-capture-decay branch of ${}^{116}\mathrm{In}$ to be $(2.27\mathrm{}\pm 0.63)\times {10}^{-2}\%$, from which we deduce $\log {ft=4.39\mathrm{}}_{-0.15}^{+0.10\mathrm{}}$. We present QRPA calculations and compare their predictions to experimental data. Finally we use these calculations to predict the $2\nu$ double-$\beta$-decay rate of ${}^{116}\mathrm{Cd}$ to the ground and excited states of ${}^{116}\mathrm{Sn}$.