Calculation of NMR Line Shapes Using the Memory-Function Approach

The formal solution of the line-shape problem in terms of a memory function has been used to illustrate the calculation of line shapes characteristic of both liquids and solids. A memory function is associated with a corresponding free-induction-decay (fid) curve and it is related to the behavior of a local-field correlation function. Its relaxation time T₂** varies from a relatively large value in solids T₂**≈M₂^-1/2, to a very short value in liquids T₂**M₂^-1/2, where M₂=〈Δω²〉 is the second moment of the absorption line. In spite of this wide range of decay times the functional form of a memory function remains insensitive to the form of a line shape. This insensitivity may be exploited in the calculation of line shapes. The method requires a knowledge of the qualitative form of a line shape and the first few of its moments and is a compromise between a qualitative approach and a full miscroscopic calculation of the relevant spin autocorrelaton function. Examples discussed include pair line shapes in solids, line shapes during motional narrowing, exchange-narrowed line shapes in paramagnetic MnF₂, and fid curves in CaF₂.