Precise lifetime of the metastable $^{\mathrm{2}}$P$_{\mathrm{1/2}}$ state in Ar$^{\mathrm{9+}}$ ions isolated in a Penning trap*

A measurement with \textless 1{\%} statistical uncertainty is presented for the radiative decay lifetime of the metastable $^{\mathrm{2}}$P$_{\mathrm{1/2}}$ state in the ground-state fine structure of fluorine-like Ar$^{\mathrm{9+}}$ (one hole in the filled 2$p$ subshell). The method involves the extraction of multiply-ionized Ar atoms from an electron beam ion trap (EBIT) and the capture of only Ar$^{\mathrm{9+}}$ ions in a compact Penning trap. The $^{\mathrm{2}}$P$_{\mathrm{1/2}}$ state of the stored Ar$^{\mathrm{9+}}$ ions can spontaneously decay via M1 (spin-flip) radiative transition to the ground state, with the photon emission monitored using a photomultiplier tube and a multichannel scaler. Improvements that reduced measurement uncertainty are discussed. The results are compared with theory and prior measurements.