Measurement of the (1s)(2${\mathrm{p}}_{1/2}$) $2^3$${\mathrm{P}}_0$-(1s)(2${\mathrm{p}}_{1/2}$) $2^3$${\mathrm{P}}_1$ fine-structure splitting in heliumlike ${\mathrm{Ag}}^{45+}$

A new method is described which is capable of determining ‖Δ${\mathrm{E}}_{0\mathrm{-}1}$‖, the absolute value of the fine-structure splitting of the interval $2^3$ ${\mathrm{P}}_0$-$2^3$ ${\mathrm{P}}_1$ from the hyperfine quenched lifetime of the $2^3$ ${\mathrm{P}}_0$ state of heliumlike ions with nuclear spin. Based on this method a measurement is reported of ‖Δ${\mathrm{E}}_{0\mathrm{-}1}$‖ in the heliumlike ion ${}_{}{}^{107}{}_{}{}^{}$ ${\mathrm{Ag}}^{45+}$ with the result ‖Δ${\mathit{E}}_{0\mathrm{-}1}$‖=0.${74}_{\mathrm{-}0.19}^{+0.16\mathrm{}}$ eV. The error in the measurement is substantially smaller than the natural linewidth of 1.1 eV.