Theory of the hyperfine structure of the S states of muonic tritium

Abstract

The hyperfine structure of the energy spectrum of the S levels of muonic tritium has been calculated using the quasi-potential method in quantum electrodynamics (QED). The α⁵- and α⁶-order effects on the polarization of vacuum, the structure and recoil of the nucleus, and relativistic corrections have been taken into account. The obtained numerical values of hyperfine splittings of 239.819 meV (1S state) and 29.965 meV (2S state) can be treated as reliable estimates for comparing with future experimental data of the CREMA collaboration, and hyperfine structure interval Δ₁₂ = 8ΔE^hfs (2S)–ΔE^hfs (1S) =–0.100 meV can be used for verifying the QED predictions. The resultant precision values of hyperfine splitting are also important for calculating the rates of formation of (μ dt) mesomolecules in muonic catalysis reactions.