Continued-fraction approximants to spin correlation functions. Application to NMR line shapes

A simple decoupling procedure for the equations of motion of the Green's function relevant to the NMR-line-shape problem is proposed. Explicit formulas are presented for approximants to the line shape incorporating the exact values of several moments. In Ca${\mathrm{F}}_2$ the approximants containing the second through eighth moments are found to be in very good agreement with the experimental ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ free-induction-decay signals. Excellent agreement is also found between the approximants containing the second through sixth moments and the exchange-narrowed ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ line shapes in paramagnetic Mn${\mathrm{F}}_2$, RbMn${\mathrm{F}}_3$, and KMn${\mathrm{F}}_3$.