Ground state hyperfine structure in muonic lithium ions

Abstract

On the basis of perturbation theory in fine structure constant alpha and the ratio of electron to muon masses we calculate one-loop vacuum polarization, electron vertex corrections, nuclear structure and recoil corrections to hyperfine splitting of the ground state in muonic lithium ions $(\mu\ e\ ^6_3Li)^+$ and $(\mu\ e\ ^7_3Li)^+$. We obtain total results for the ground state small hyperfine splittings in $(\mu\ e\ ^6_3Li)^+$ $\Delta\nu_1=21572.16$ MHz and $\Delta\nu_2=14152.56$ MHz and in $(\mu\ e\ ^7_3Li)^+$ $\Delta\nu_1=21733.06$ MHz and $\Delta\nu_2=13994.35$ MHz which can be considered as a reliable estimate for a comparison with future experimental data.