Hyperfine structure of the ground state muonic 3He atom

On the basis of the perturbation theory in the fine structure constant a and the ratio of the electron to muon masses we calculate one-loop vacuum polarisation and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom (mu e (3)(2) He). We obtain total results for the ground state hyperfine splittings Delta nu(hfs) = 4166.648 MHz which improves the previous calculation of Lakdawala and Mohr due to new corrections of orders alpha(5) and alpha(6). The remaining differences between our theoretical result and experimental value of the hyperfine splitting lie in the range of theoretical and experimental errors and require the subsequent investigation of higher order corrections.