NMR line shape of a one-dimensional system of spins: Continued-fraction approximants

Abstract
Continued-fraction approximants to the NMR line shape of an infinite linear chain of dipolar-coupled spin-1/2 nuclei are computed. Using the values of the first seven even moments recently calculated by Sur and Lowe, an approximant to the transverse spin autocorrelation function is generated that is believed to accurately describe the behavior of an infinite chain for short and long times. This seems to be confirmed by exact calculations of finite chains as well as by experimental results in fluoroapatite.