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In the framework of the KuboToyabe theory, the effects of field
fluctuations have been taken into account with the `strong collision
model' [36,6]. This model assumes that (1)
fluctuations occur suddenly, and that (2) every time the local field
fluctuates, the muon forgets the previous local field information.
Hereafter, the field fluctuation rate () is defined as the
Markoffian fluctuation rate, namely, the exponential decay rate
of the autocorrelation function of the local fields:
The strong collision model generally calculates the dynamical muon spin
relaxation from the original static relaxation function
G(t) as follows:
The terms of this series account for the muons which experienced field fluctuations in the time interval of .
Fig.18 shows the dynamical Gaussian KuboToyabe
function in zerofield for various fluctuation rates ().
In the slow fluctuation regime (), the
fluctuation induces slow relaxation of the 1/3component. The
asymptotic behavior of this relaxation has been obtained as [6]. In the intermediate
fluctuation regime (), the
relaxation has a Gaussian behavior in the beginning, but loses
the 1/3component. Hence, the existence/absence of the 1/3component
is a clue which distinguishes static/dynamic relaxation.
Figure 18:
The zerofield muon spin relaxation in the fluctuating Gaussian local field
(dynamical Gaussian KuboToyabe function ).

In the fast fluctuation regime (), the relaxation is
approximated by an exponential function [7,37]:
where the relaxation rate is:
In this fast fluctuation regime, the relaxation rate ()decreases with faster fluctuation rates. This phenomenon is known as the
`motional narrowing' of the T_{1} relaxation rate.
The longitudinal field dependence of the relaxation rate ()is consistent with that of the T_{1} relaxation theory
[34], which has been developed for nuclear
magnetic resonance (NMR).
Next: 3.2 Lorentzian theory [#!UemuraPRB85!#]
Up: 3.1 Gaussian KuboToyabe theory
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