Advanced Concepts in Pulsed Magnetic Resonance

Abstract

Hahn’s discovery of spin echoes [8.1] demonstrated that one could defeat the effect of magnet inhomogeneity in obscuring the true width of magnetic resonance lines because the echo amplitude M(2τ) decayed exponentially with 2τ/T ₂, where τ is the time between pulses. However, if the magnet inhomogeneity is large, and if the diffusion rate of the nuclei sufficiently great

$$ M(2\tau ) = M(0)\exp ( - 2\tau /{T_2})\exp [ - {(\gamma \frac{{\partial H}}{{\partial z}})^2}D{\tau ^3} $$

(8.1)

where D is the diffusion constant and ∂H/∂z the gradient in static field. In some instances, then, the τ ³ term might obscure the T ₂. Or, conversely, if ∂H/∂z is known, the τ ³ term gives one a method of measuring D. The derivation of the diffusion term is given in Appendix G.