Multiphoton NMR spectroscopy on a spin system with I=1/2

Abstract

Multiple quantum effects in double frequency (df) pulsed NMR experiments on multilevel spin systems are studied. In these experiments, the spin systems are irradiated by two rf fields, applied simultaneously. A general theoretical description of these experiments is presented using the theory of Shirley for time dependent Hamiltonians. Multiphoton resonance conditions are given and time independent fictitious spin-1/2 Hamiltonians are derived using his perturbation theory treatment. With these Hamiltonians, the evolution of the spin systems during df irradiation is approximated. The example of df NMR experiments on an I=1/2 spin system is discussed. High order perturbation theory is developed to describe the time evolution of this spin system at a three photon resonance. Accurate computer calculations are performed to examine this time evolution. Df NMR experiments are performed on the single 31P(I=1/2) transition of phosphoric acid to check the theoretical results. The three photon resonance condition for these measurements is studied as a function of the rf irradiation intensities and of the resonance offsets of the two frequency components of df irradiation fields. Special NMR pulse cycles are used to study the dependence of the phase of the coherence created by df pulses on the initial rf phases of the two frequency components. Spin-echo type of experiments are developed to detect the spiral motion of the magnetization vector of the I=1/2 spin system at the three-photon resonance.