A UNIFIED APPROACH TO DYNAMIC NMR BASED ON A PHYSICAL INTERPRETATION OF THE TRANSITION-PROBABILITY

A general theory of the effect of dynamics (relaxation and (or) exchan ge) on NMR spectra is presented. This theory is based on a reexaminati on of the transition probability. The classic expression for this is a s the square of the transition moment, but we feel it is useful to sep arate the square into two separate terms. In the generalization presen ted here, we show that one of these terms corresponds to the share of the initial magnetization that each spin coherence receives at the sta rt of the experiment. The second term is how much that coherence contr ibutes to the total detected signal. The final intensity is the produc t of these two factors. For a static spectrum, these two terms are com plex conjugates, so the product is real and we recover the standard tr ansition probability. When there is dynamics, the product becomes comp lex, so the time evolution includes oscillatory and dispersive terms. This means that a dynamic spectrum is still a sum of individual transi tions, but the lineshapes are distorted in phase, intensity, position, and linewidth by the dynamic process. In this paper we develop the ge neral theory, and illustrate it with a calculation of the classic prob lem of mutual exchange in an AB spin system.