Second moment Lorentzian line

However, the Lorentzian form of the dipolar broadening function, which has the advantage of mathematical simplicity, is not suitable for an interpretation in terms of second moments it is replaced with a Gaussian dipolar function S(oa, AG), where the parameters AG correspond to the appropriate fractions of the square root of the intra-group rigid lattice second moments. With appropriate values for AG, calculated and experimental line shapes I(oo) are found to be in a good agreement for cross-linked polyethylene oxide) swollen in chloroform 1U). 

Results of calculation of second moment line for analyzed systems were obtained by summation over 106 cells in lattice, they are presented in Table 2. The Lorentzian linewidth calculated from these M2 values... 

In general, if the NMR line has any Lorentzian character to it, the second moment is not an ideal parameter for study because so much of the crucial information is lost in the wings of the spectrum. A line can be considered to be a Gaussian when S /CSg) =3. When such difficulties exist, it may be easier to get the true second and fourth moments from the FID as will be described shortly. For discussions of moments of Lorentzian-like lines, the relationship between the true moment and the measurable moment, and which component of the second moment is affected by molecular motion, see Abragam (Appendix A), Sections IV.II.B, IV.IV.A, X.V.A. 

This is a Lorentzian line profile (Fig. 2.26) with a full halfwidth yah = ya + Yb-After taking the second-time derivative of (2.94b) and using (2.108a-2.108c), the equation of motion for the dipole moment D of the atom under the influence of a radiation field, becomes... 

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