Abstract
Numerical calculations have been performed to obtain exact results for the high-temperature space- and time-dependent transverse spin pair correlation functions , where is the spatial separation of the spins, and the free-induction-decay function , for a linear chain of dipolar coupled spins () for with periodic boundary conditions. The range of the dipolar interaction was allowed to take separately the values 1, 2, and 3. The moments of the NMR line shape ( through ) were obtained for the infinite chain with and and were found to be in excellent agreement with previous reliable moment calculations ( through ). By an evaluation of the contribution of the four-particle terms to , it is shown that the Bersohn-Das theorem fails in one dimension. We find that for even (odd) values of are predominantly positive (negative). This gives rise to a damped beat structure for . A study of for shows that our 11-spin solution reproduces that of the infinite chain at least up through the fifth node, and is also in good agreement with recent free-induction-decay measurement in fluoroapatite. The nodes of were found to shift towards shorter values of time as was allowed to increase. Further, for , a comparison of our exact results for for , with a Gaussian broadening of for , shows that the effect of the weak interactions is not well approximated by a simple Gaussian broadening for this case.
- Received 30 June 1975
DOI:https://doi.org/10.1103/PhysRevB.12.4597
©1975 American Physical Society