The Shape of Modulation-Broadened, Unsaturated, Lorentzian Magnetic Resonance Transitions

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Abstract
The effect of modulation broadening on the shape of unsaturated, Lorentzian absorption lines is examined. The closed, analytic expressions for the Fourier coefficients anL due to Wahlquist are employed to derive exact formulas relating the location and amplitude of the extrema, the location and amplitude of the slope extrema, the slope extrema ratio, and the location of the zeros of the observed a2L to the true half‐width for arbitrary modulation amplitude [normalized modulation amplitude (1/β)]. Wahlquist's results for a1L are extended to include the location and amplitude of the slope extrema. It is shown that simultaneous measurement of a1L and a2L, when the normalized modulation amplitude is near unity, can be employed to determine if the lineshape is Lorentzian. For a Lorentzian lineshape, these measurements can be used to determine the linewidth and the number of paramagnetic spins under conditions of near‐maximum sensitivity. Graphs and tables of the various results of experimental interest in making these determinations and calculations are included.