Modulation-Effect Corrections for Moments of Magnetic Resonance Line Shapes

Corrections are derived for the calculation of the second and fourth moments of magnetic resonance lines from experimental data, obtained by using the low-frequency modulation method. The results for 0° phase shift between field modulation and the lock-in reference are ${〈\Delta {{\omega }_{\exp }}^2〉}_{\mathrm{Av}}={〈\Delta {\omega }^2〉}_{\mathrm{Av}}+\frac{1}{3}{{\omega }_M}^2+\frac{1}{4}{\left(\gamma H_M\right)}^2,$ ${〈\Delta {{\omega }_{\exp }}^4〉}_{\mathrm{Av}}={〈\Delta {\omega }^4〉}_{\mathrm{Av}}+{〈\Delta {\omega }^2〉}_{\mathrm{Av}}[2\mathrm{}{{\omega }_M}^2+\frac{3}{2}{\left(\gamma H_M\right)}^2]+\frac{1}{5}{{\omega }_M}^4+\frac{3}{4}{{\omega }_M}^2{\left(\gamma H_M\right)}^2+\frac{1}{8}{\left(\gamma H_M\right)}^4.$