Shape of Modulation-Broadened Unsaturated Lorentzian Magnetic Resonance Transitions. III. Absorption, aIIIL (Third Harmonic)

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Abstract
The effect of modulation broadening on the shape of unsaturated Lorentzian absorption lines is examined. The closed analytic expression for the Fourier coefficients anL due to Wahlquist [H. Wahlquist, J. Chem. Phys. 35, 1708 (1961)] is employed to derive exact formulas relating the location and amplitude of the extrema, the amplitude extrema ratio, the location and amplitude of the slope extrema, the slope extrema ratios and the location of the zeros of the observed aIIIL to the true half‐width for arbitrary modulation amplitude [normalized modulation amplitude (1/β)]. This Fourier coefficient is recorded when synchronous demodulation is employed at the third harmonic of the magnetic‐field modulation frequency. It is of considerable experimental interest since it has two zeros symmetrically located with respect to a central zero and the total amplitude of the pairs of antisymmetric peaks is approximately the same as for the two antisymmetric peaks of aIL when the modulation amplitude is near optimum. It is shown that linewidth measurements can be made more precisely and easily under conditions of near‐maximum sensitivity using aIIIL than either aIL or aIIL since zero crossings can be located more accurately than the amplitude extrema. Graphs of the various results of experimental interest are included.