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) exchange) on NMR spectra is presented. This theory is based on a reexamination of the transition probability. The classic expression for this is as the square of the transition moment, but we feel it is useful to separate the square into two separate terms. In the generalization presented here, we show that one of these terms corresponds to the share of the initial magnetization that each spin coherence receives at the start of the experiment. The second term is how much that coherence contributes to the total detected signal. The final intensity is the product of these two factors. For a static spectrum, these two terms are complex conjugates, so the product is real and we recover the standard transition probability. When there is dynamics, the product becomes complex, so the time evolution includes oscillatory and dispersive terms. This means that a dynamic spectrum is still a sum of individual transitions, but the lineshapes are distorted in phase, intensity, position, and linewidth by the dynamic process. In this paper we develop the general theory, and illustrate it with a calculation of the classic problem of mutual exchange in an AB spin system.