Abstract
The theory we will outline in the following is based on the Bloch/Wangsness/Redfield (BWR) density-operator perturbation-theoretical approach of the weak-collision case [1, 41, 42, 397, 503]. This formalism is superior to theories based on the standard time-dependent perturbation theory [5, 43, 461] because of its universality.1 Versions of the BWR theory suitable for more complex spin systems, as they usually are the subject of NOESY experiments (see Sect. 23.2), for instance, have been published in Refs. [478, 500, 514].
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Notes
Recently it was shown that the same master equation as for the BWR theory can be derived without any perturbation-theoretical approach [143]. However, this exact formalism is more demanding and somewhat unwieldy.
This is not to be confused with the ensemble average inherent in the density operator which concerns the distribution of state vectors in the ensemble (i.e., different compositions of eigenstates and different phases). Here we are dealing with an ensemble average over “different time dependences” of the ensemble average over “different state vectors,” so to speak.
By contrast, the corresponding average of the Liouville/von Neumann equation (Eq. 11.7) does not vanish because the density operator and the Hamiltonian refer to the same time in that case.
In a sense, we insert the zeroth approximation in the reverse direction.
This also includes “observables” such as longitudinal order or multiple-quantum coherences that can only be indirectly detected by RF signals (see Sect. 9.1.1).
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© 1997 Springer-Verlag Berlin Heidelberg
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Kimmich, R. (1997). Perturbation Theory of Spin Relaxation. In: NMR. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60582-6_11
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DOI: https://doi.org/10.1007/978-3-642-60582-6_11
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