Dynamics of negative muonium inn-type silicon

Temperature-dependent diamagnetic amplitudes from radio-frequency muon spin-resonance data on two moderately to heavily doped n-type silicon samples require the presence of ${\mathrm{Mu}}_T^{-}.$ We determine the ${\mathrm{Mu}}_T^{-}$ to ${\mathrm{Mu}}_T^0$ ionization energy to be $0.56\pm 0.03\hspace{0.5em}\mathrm{eV}$ for silicon, considerably higher than the ${\mathrm{Mu}}_{\mathrm{BC}}^0$ to ${\mathrm{Mu}}_{\mathrm{BC}}^{+}$ ionization energy of $0.21\pm 0.01\hspace{0.5em}\mathrm{eV}.$ Thus muonium will be a negative-$U$ impurity only if the energy difference between the ${\mathrm{Mu}}_T^0$ and ${\mathrm{Mu}}_{\mathrm{BC}}^0$ configurations is less than 0.35 eV. The $\mathrm{Mu}\mathrm{}(0/+)\mathrm{}$ thermodynamic level correlates well with results for monatomic hydrogen, but the $\mathrm{Mu}(-/0)$ level is estimated to be shallower than that claimed for $\mathrm{H}(-/0).\mathrm{}$ The muonium data show a complicated set of transitions active during the muon lifetime, and involving four separate muonium states. Similar rapid transitions should be considered when interpreting data on isolated hydrogen centers.