Calculation of the muonicHe3hyperfine structure

A calculation of the ground-state hyperfine splitting in muonic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is given. It is based on a perturbative approach that was applied to the analogous calculation in muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The result for the hyperfine splitting is $\Delta \nu =4164.9\mathrm{}\pm 3.0$ MHz. A semiempirical value for this splitting, based on the measured splitting in muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, is $\Delta \nu =4166.5\mathrm{}\pm 0.4$ MHz.