Zero-field spin relaxation of positive muons

The spin dynamics of a muon interacting with neighboring nuclear spins in the presence of a strong quadrupolar coupling is investigated. An approximation for calculating the time-dependent muon polarization is presented which works equally well for integer and half-odd-integer spins $J$. In the particular case of equivalent nuclei with $J=\frac{3}{2}$, an analytic solution is given. The influence of nuclei in more-distant shells is discussed, and the change of the polarization with muon diffusion is calculated.