The Width of Nuclear Magnetic Resonance Rotary Saturation Lines

The first rotary saturation experiments of Redfield in 1955 gave line-widths considerably narrower than the theory predicted. The anomaly is explained as a consequence of the truncation of the Hamiltonian after transformation into the rotating frame. It is shown that this truncation leads to the loss of a cross term between the part discarded and the part retained, in the expression for the second moment of the line. This term can be negative and leads in the case of Redfield's experiments to a smaller second moment for the total Hamiltonian than for the truncated version. The effect of these considerations is to displace the line to a higher frequency, while causing it to become asymmetric with the lower frequencies intense and the higher frequencies weak. This distortion appears as a narrowing, since only a part of the line is observed. This behaviour is illustrated for a pair of nuclei with I = ½.