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HowToDetectMuonium< Muonium detailed calculation | Index | Precession in the radical state > The intention of this page is eminently practical and it is related to nearly free muonium, as it may be observed in e.g.
A direct, difficult way to observe this species is by means of a very high resolution spectrometer, in zero external field, looking for the direct hyperfine transition at {$\nu_0$}. Another way to detect a spectroscopic signature of muonium is in weak transverse fields, with moderate time resolution. Whereas the triplet-singlet transitions {$\nu_{13},\nu_{34}$} (Eq. 3, previous page) are always larger than {$\nu_0$}, the triplet precession frequencies {$\nu_{12},\nu_{24}$} in moderate fields are much smaller: {$ \begin{eqnarray}\nu_{12} &=& \frac {\nu_0} 4 +\nu_-\,+\frac {\nu_0} 4 \left(1-2\sqrt{1+\frac {\nu_+^2} {\nu_0^2}}\right) \,\approx\, \nu_-\, -\, \frac {\nu_+^2}{4\nu_0}\\ \nu_{24} &=& -\frac {\nu_0} 4 +\nu_-\,-\frac {\nu_0} 4 \left(1-2\sqrt{1+\frac {\nu_+^2} {\nu_0^2}}\right) \,\approx\, \nu_-\, +\, \frac {\nu_+^2}{4\nu_0} \end{eqnarray}$} and of comparable amplitudes {$\approx 1/4$} for very low fields, below 10-15mT (the exact amplitudes are the factors {$c,s$} respectively from the (previous page). In practice weak transverse field muonium appears as a doublet centered at {$ \frac {\gamma_e-\gamma_\mu} 2 B$}, i.e. shifting with field at a rate of 1.4 MHz/G. < Muonium detailed calculation | Index | Precession in the radical state > |