Spin dynamics under magic angle spinning by Floquet formalism

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Abstract
A new analytical method is presented for studying in a uniform way the spin dynamics in NMR experiments performed under the conditions of magic angle spinning. It was derived on the basis of the formalized Floquet theory and consists in transforming the Fourier-state representation of the NMR signal into an integral one. The integral representation proves to be well suited in combination with Rayleigh-Schrodinger perturbation theory for both the fast and the slow spinning regimes. The corresponding perturbation expansions can be readily extended to higher-order correction terms, which also allows the inclusion of more moderate spinning speeds. Explicit expressions of the perturbation series were derived for both spinning regimes and applied to the case of isolated dipolar-coupled spin-1/2 pairs for which the results can be compared with those obtained by the exact evaluation of the equation of motion.