An ensemble of paired spin-12 nuclei in a rotating solid: Polarization evolution and NMR spectrum in a wobbling frame

The evolution of the magnetic polarization of an ensemble of paired spin-12 nuclei in an MAS NMR (nuclear magnetic resonance) experiment and the induced spectrum are described theoretically by means of a Liouville-von Neumann equation representation in a wobbling rotating frame in combination with the averaged Hamiltonian theory. In this method, the effect of a high-intensity external static magnetic field and the effects of the leftover interaction components of the Hamiltonian that commute with the approximate Hamiltonian are taken into account simultaneously and equivalently. This method reproduces details that really exist in the recorded spectra, caused by secular terms in the Hamiltonian, which might otherwise be smoothed out owing to the approximate treatment of the effects of the secular terms. Complete analytical expressions, which describe the whole NMR spectrum including the rotational sideband sets, and which consider all the relevant intermolecular interactions, are obtained.