Direct measurement of muonium hyperfine frequencies in Si and Ge

The hyperfine frequency ${\nu }_0$ of normal muonium Mu has been measured as a function of temperature in zero magnetic field with an apparatus of high time resolution. Compared with the usual two-frequency method, the direct measurement of ${\nu }_0$ typically gives more accurate results by a factor of 10. For Mu in Ge, ${\nu }_0$ shows a monotonic decrease with increasing temperature which is well described by a Debye model. For Mu in Si, ${\nu }_0$ exhibits a nonmonotonic temperature variation with a maximum at 80 K. By a measurement with external pressure up to 1.5 kbar it is shown that the nonmonotonic lattice expansion of Si cannot cause the observed effect. Rapid relaxation of the direct transition was observed in Si below 20 K. A similar anomaly of the triplet transition signals in a magnetic field could not be found. A model is presented which assumes diffusion of Mu over slightly different sites and which explains all observed effects consistently.