Fine and hyperfine structure of the muonic ^3He ion

On the basis of quasipotential approach to the bound state problem in QED we calculate the vacuum polarization, relativistic, recoil, structure corrections of orders $\alpha^5$ and $\alpha^6$ to the fine structure interval $\Delta E^{fs}=E(2P_{3/2})-E(2P_{1/2})$ and to the hyperfine structure of the energy levels $2P_{1/2}$ and $2P_{3/2}$ in muonic $^3_2He$ ion. The resulting values $\Delta E^{fs}= 144803.15 \mu eV$, $\Delta \tilde E^{hfs}(2P_{1/2})=-58712.90 \mu eV$, $\Delta \tilde E^{hfs}(2P_{3/2})=-24290.69 \mu eV$ provide reliable guidelines in performing a comparison with the relevant experimental data.