Fourier transform NMR in the rotating frame

Abstract

A density matrix description of the Fourier transform (FT) NMR experiment on a coupled spin system interacting with a strong rf field (maintained throughout the experiment) is presented. The strong irradiation causes a mixing of the nuclear spin states giving rise to additional transitions, as well as polulation redistribution among the various energy levels. Both these features manifest themselves in the FT NMR spectrum in the form of intensity and linewidth changes that are dependent upon the details of the nuclear spin relaxation as well as the parameters of the irradiating rf field. Thus this experiment provides an interesting alternative to the study of the details of nuclear spin relaxation in coupled spin systems using the FT NMR technique. The problem is solved in a frame rotating at the frequency of irradiation. The resulting expressions indicate that the FT NMR spectrum is dependent upon the flip angle as well as the relative phase angle ψ (at the time of pulse) between the irradiating rf field and the pulse rf field. The conditions under which this experiment can be analyzed by the much simpler theory of the slow passage continuous wave (cw) Nuclear Magnetic Double Resonance (NMDR) experiment are discussed. General expressions for the FT NMR line shapes are derived for the case of a single nucleus of spin 1/2 and the theory is tested on the single spin 1/2 system in a sample of neat undegassed CHCl3. The experiment is in good agreement with theory.