Measurement of the Ra$^+$ $7p$ $^{2}P_{3/2}$ state lifetime

We report a measurement of the radium ion's $7p$ ${}^{2}P_{3/2}$ state lifetime, $\tau=4.78(3)$ ns. The measured lifetime is in good agreement with theoretical calculations, and will enable a determination of the differential scalar polarizability of the narrow linewidth $7s$ ${}^{2}S_{1/2}\rightarrow$ $6d$ ${}^{2}D_{5/2}$ optical clock transition.