LOCAL-FIELD MUON TRANSVERSE DEPOLARIZATION AND NUCLEAR FREE INDUCTION DECAY AT LOW-TEMPERATURES

The form of the transverse depolarization function of an I spin due to dipolar interaction with a system of S spins is analysed for local field interactions without using the high-temperature approximation. This analysis is valid in the absence of diffusion and in the presence of a large, static external magnetic field. It is relevant to muons implanted in metals and to the free induction decay of dilute I nuclei in a system of S nuclei, for which the local field model is valid for short times. An analytic expression for the transverse depolarization function is obtained using the Boltzmann distribution for the occupation of Zeeman states of the S spins at a temperature T. The behaviour of the depolarization function depends on the ratio of the external magnetic field B to the temperature T and three regimes are identified. For small B/T the familiar high-temperature result is independent of B/T and sample shape. For intermediate values of B/T the depolarization function depends on B/T and has an envelope that is independent of sample shape and a time-dependent phase that is dependent on sample shape. For larger values of B/T the depolarization function is again independent of B/T with the phase remaining dependent on sample shape. The results indicate the effects that could be observed at values of B/T larger than those corresponding to the high-temperature approximation and provide the values of B/T at which these would be apparent.