Hyperfine structure and $(e^{-},e^{+})$-pair annihilation in the muonium-positronium MuPs and positronium hydrides

The hyperfine structure of the ground states in a number of positronium hydrides (TPs, DPs, ${}^{1}$HPs) and MuPs ($μ^{+} e^{-}_2 e^{+}$) is determined with the use of highly accurate variational wave functions. We also evaluate the probabilities of various processes in the MuPs system, including the $(e^{-}, e^{+})$-pair annihilation and its conversion into the charge conjugate system $μ^{+} e^{-}_2 e^{+} \to μ^{-} e^{-} e^{+}_2$.

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