Theory of multiple pulse NMR at low and zero fields

Abstract

Coherent averaging with time-dependent magnetic fields at low and zero static magnetic fields encounters several features which are unfamiliar in high-field magnetic resonance. The principal differences are that magnetic field pulses act generally on all spin species in the sample and that the Hamiltonian contains additional terms that are normally discarded in a high static magnetic field. We illustrate how the full Hamiltonian or different terms of the Hamiltonian may be averaged to zero by sequences of 90° rotations around the x, y, and z axes. The two limiting cases of ideal delta-function pulses and windowless sequences are treated. We also show that the duality between rotations of space coordinates and spin coordinates allows one to replace spatial reorientations of the sample, such as magic-angle spinning, by time-dependent magnetic fields. Sequences of delta-function pulses at zero field are analogous to recursive expansion schemes of multiple-pulse sequences at high field. The terms of the full Hamiltonian appear also in the average Hamiltonian of high-field pulse sequences and can be manipulated by the same sequence of configurations as in zero-field multiple-pulse NMR.