Theoretical hyperfine structure of muonic helium

Abstract

The study of the hyperfine structure of the muonic helium atom (${\ensuremath{\alpha}}^{++}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$) can provide a test of quantum electrodynamics and yield precise values for the magnetic moment and mass of the negative muon. In the lowest-order approximation the hyperfine structure interval $\ensuremath{\Delta}\ensuremath{\nu}$ is given by the Fermi formula. The principal corrections, which contribute about 10 MHz to the splitting, arise from the relativistic, radiative, and recoil effects. The theoretical hyperfine structure of the ground state of muonic helium is given as $\ensuremath{\Delta}\ensuremath{\nu}=4465.1\ifmmode\pm\else\textpm\fi{}1.0$ MHz.