Timescales in relaxation phenomena

The nucleus in a Mossbauer experiment is part of a many-body system consisting of the surrounding electrons and the quasiparticles corresponding to the various other degrees of freedom of the solid. Relaxation effects result from the various time-dependent processes in the vicinity of the nucleus. The nucleus thus acts as a local microscopic probe, which does not participate directly in the relaxation processes in its environment, but which senses these processes via the hyperfine interactions. Now, in interpreting the relaxation behaviour it is necessary to consider the nature and interrelationship of the important timescales of the problem. Some of these timescales are determined by the nature of the Mossbauer isotope and the interaction being studied, i.e., the mean lifetime of the Mossbauer excited state and the Larmor precession time t,. The other timescales relate to, and are characterised by, the nature of the fluctuations in the nuclear environment. These latter timescales are the inverse of the various relaxation rates and, as mentioned earlier, these can be controlled in the laboratory in various ways. The character of the relaxation spectra obtained obviously depends crucially on the interplay of the various timescales as discussed below. 

It has already been noted that in order for resolved magnetic splitting to be observed there must be sufficient time for the nucleus to sense the effects of the magnetic field acting on it. This means that at least one complete Larmor precession must take place before the nucleus decays, i.e. Tl Tn. Given this restriction it is possible to distinguish between two cases  

Finally it is necessary to consider one other point which illustrates a certain limitation of Mossbauer spectroscopy in the investigation of time-dependent hyperfine interactions. Suppose T Tr, which in conjunction with the restriction implies that a static spectrum should be 

The classification of the relaxation times becomes somewhat more subtle when a laiger set of degrees of freedom have to be taken into account in interpreting the spectra. For instance, consider the magnetic case in which there is an axially symmetric hyperfine coupling between the nuclear and electronic spins, while the effect of the other degrees of freedom of the system on the electronic spins can be described by an effective random field Bjlt). Thus an appropriate spin Hamiltonian for the magnetic hyperfine 

In order to use the Hamiltonian of Equation (5.27) in lineshape calculations it is necessary to specify its spectral properties, which depend, amongst other things, on the correlation function of B,(f). A simple form of this correlation function is given by 

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