Depolarization of a Muon by Hyperfine Interaction

The further depolarization of a muon captured in the $1s$ Bohr orbit by hyperfine interaction with a nucleus of spin $j$ is calculated. The main result is that the asymmetry parameters of the decay electrons from the $J=j\pm \frac{1}{2}$ states are multiplied by respective asymmetry reduction factors $\frac{1}{3}\left[\frac{1\pm 2}{\mathrm{}(2j+1)\mathrm{}}\right]$.