Kinetic-Theory Calculation of the Nuclear-Magnetic-Resonance Line Shape in Dipolar and Exchange-Coupled Systems

Abstract

A set of kinetic equations for the anisotropic Heisenberg paramagnet is presented. These are an extension of equations derived previously for the isotropic system and used to predict the spectral densities in RbMn${\mathrm{F}}_3$. The equations conserve the total spin and energy and have for their stationary solution the anisotropic-spherical-model correlation functions. An approximate solution of these equations using a constant-relaxation-time approximation yields results for the free-induction decay of the transverse magnetization in a dipolar lattice in a strong magnetic field that is in good agreement with the experiments on Ca${\mathrm{F}}_2$.