Dynamics of a system of randomly distributed spins with multipolar interactions: Application to dipolar systems

A general first-principles method for the calculation of dynamical spin correlation functions in a system of randomly distributed, strongly interacting spins with multipolar interactions is presented. The method is valid in the high-temperature limit and is applicable at all spin concentrations $c$. As a numerical example, the case of dipolar forces is treated and the magnetic-resonance frequency line shape is calculated for a variety of values of $c$. The general trend of the change in line shape with $c$ obtained agrees with phenomenological theories and with experiment. The theoretical linewidth has the correct $c$ dependence in both the $c\to 1$ and $c\to 0$ limits.