Decay ofμ−Mesons Bound in theKShell of Light Nuclei

For ${\mu }^{-}$ mesons bound in the $K$ shell of light nuclei of atomic number $Z$, we calculate the decay electron spectrum accurately up to the first power in $Z$, both for point and extended nuclei. The decay rate is evaluated accurately up to the second power for point nuclei. Our results for the spectrum show the Doppler smearing of its upper end as obtained previously, and demonstrate the small effect of the nuclear extension. The decay rate is obtained as a monotonically decreasing function of $Z$, and we cannot explain recent experiments which show a maximum of the decay rate around $Z\sim 26$. We also find that the decay rate in second order decreases much more slowly with $Z$ than what would be obtained from a phase space consideration alone.