Fine and hyperfine structure of the muonic ^3He ion

Abstract

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 ${}_2^{3}He$ 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.

Comments: 15 pages, 4 figures, 3 tables