Hyperfine structure of the excited state1s1/2(e)2s1/2(μ)of the muonic helium atom

Abstract

The recoil, vacuum polarization, and electron vertex corrections of first and second orders in the fine structure constant $\ensuremath{\alpha}$ and the ratio of electron to muon and electron to $\ensuremath{\alpha}$-particle masses are calculated for the hyperfine splitting of the $1{s}_{1/2}^{(e)}2{s}_{1/2}^{(\ensuremath{\mu})}$ state of muonic helium atom $(\ensuremath{\mu}{e}_{2}^{4}\text{He})$ on the basis of perturbation theory. We obtain a total result for the muonically excited state hyperfine splitting $\ensuremath{\Delta}{\ensuremath{\nu}}^{\text{hfs}}=4295.66$ MHz, which improves previous calculations, taking additional corrections into account, and a more accurate treatment of the electron vertex contribution.