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Summary In summary it is clear that µSR in the presence of traps has led to a significant generalization of prior NMR theories of spin relaxation to include the effects of a non-stationary distribution of diffusing particles. In both the high field transverse geometry and in zero field it is possible to extract significant information regarding the concentrations and binding energies of traps, and, in the latter case, to unambiguously measure the temperature dependence of the relaxation rate to traps.

We consider the zero field depolarization of stationary muons at various sites in fcc and bcc crystals. Significant derivations from the classic Kubo-Toyabe treatment are explained as due to violations of some fundamental assumptions underlying this theory.

Positron annihilation lifetime spectroscopy, which is applied to measure distributions of hole volume sizes in polymers, uses a model to relate the positronium (Ps) lifetime to hole volume dimensions. It is assumed in this model that the Ps remains in one site until annihilation. Recently, the validity of this last assumption has been questioned by Yu et al. (Yu, Z.; McGervey, J. D.; Jamieson, A. M.; Simha, R. Macromolecules 1995, 28, 6268.), who calculated the tunneling rate between sites and concluded that the rate was rapid enough that a Ps would typically sample many hole volumes before annihilating. To investigate this question we calculated the rate for Ps in one potential well to transfer to a second. We found for appropriate, equal wells, that the rate is comparable with that of Yu et al., while for only slightly unequal wells the transfer is cut off. This cutoff is a consequence of the removal of the degeneracy of the single well energies. For multiple wells it is found that Anderson localization applies so that quite generally a Ps is trapped at only a single hole volume until it decays. Thus Ps-lifetime hole-size-distribution measurements should be unaffected by tunneling.

A systematic procedure which enables the study of complicated internal field distributions is discussed. It is proposed that this may be useful for studying the fields due to the flux line lattice (FLL) of the high temperature superconductors. Moment distributions of the Fourier transform of the internal field components can be obtained. We have used the London theory as developed by Kogan and others to calculate the internal field distributions, explicitly including those field components which are transverse to the average internal field. We have used this to make estimates of the expected frequency dependence of these moment distributions.