Hyperfine structure of the2sstate ofHe+3

Using an electrostatic ion-storage device and a microwave state-selection technique, we have measured the hyperfine structure $\Delta {\nu }_2$ of the $2s$ state of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$. Our result is $\Delta {\nu }_2=1083.354\mathrm{}9807\left(88\right)\mathrm{}$ MHz (the equivalent uncertainty is 0.009 ppm). When combined with the $1s$-state hyperfine structure $\Delta {\nu }_1$ to make the quantity $D_{21}\equiv 8\Delta {\nu }_2-\Delta {\nu }_1$, we obtain $D_{21}\left(\mathrm{experiment}\right)=1.189\mathrm{}979\left(71\right)\mathrm{}$ MHz. Current theory produces $D_{21}\left(\mathrm{theory}\right)=1.189\mathrm{}801\left(1\right)\mathrm{}$ MHz. The 178(71) Hz difference may arise from a combination of quantum-electrodynamic and nuclear structure effects which remain to be treated theoretically.