Theory of Nuclear-Magnetic-Resonance Saturation in Solids

Abstract

By using the method of projection operators introduced by Zwanzig, steady-state solutions of the master equation of the density matrix of the spin system in the rotating reference frame have been obtained in the limit of weak spin-lattice interaction and high temperature. With the aid of these solutions, the saturation behaviors of the spin system in solids have been investigated in the two limiting cases, weak-H₁ and strong-H₁, where the spin system is not uniform and some sorts of cross relaxation take place. Furthermore, the remaining terms of the steady-state solution obtained under Redfield’s assumption of a single spin temperature have been derived directly starting from the master equation.