Spin Diffusion in Inhomogeneously Broadened Systems

The theory of cross-relaxation within inhomogeneous spin systems (spin diffusion) is discussed. The qualitative theory of Bloembergen, Shapiro, Pershan, and Artman is generalized. For the special case where the exchange- and concentration-independent contribution to the cross-relaxation linewidth are zero, the diffusion time is given by τ=T₁₂〈νc²〉^-3/2(T₂*)^-3. An exact theory of cross-relaxation in the limit T₂T₂* is also developed and spin-diffusion is shown to be governed by an integro-differential equation. The conditions under which an ordinary diffusion equation describes spin diffusion is examined and the diffusion constant derived. The expression for τ given above is verified by this theory.