A GENERALIZED KUBO-TOYABE FORMULA FOR MUON SPIN RELAXATION IN CRYSTALS WITH UNIAXIAL SYMMETRY

The Kubo-Toyabe semiclassical formula, describing the time development of the polarization of a particle in zero external field at a lattice site with cubic local environment, is generalized for uniaxial site s ymmetry. The relaxation function and, in particular, its first moments and long time asymptotics obtained in a closed form, depend on the an gle Theta between polarization and the crystal c-axis and are shown to vary sensitively with the asymmetry epsilon of the field distribution at the particular muon site. Besides the exact ''uniaxial'' variant o f the Kubo-Toyabe relaxation function, an approximate simple interpola tion formula is also derived, which is correct for both short times an d in its long time asymptotics. The two parameters (epsilon, Delta(1)) in the ''uniaxial'' formulae can be determined by using the observed values of the second moment M(2) for two different crystal orientation s.