Spin Echoes and Chemical Exchange

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Abstract
The amplitude of the nuclear induction signal is calculated for pulsed nuclear magnetic resonance experiments for systems in which chemical exchange takes place between two sites of different Larmor frequency. General expressions are given, within the scope of first order rate theory for one and two pulse experiments as well as multiple pulse (Carr—Purcell) sequences. It is proven that for a Carr—Purcell sequence the decay is always expressible as a sum of two exponentials. The two time constants are derived for the general case and some special cases are discussed in detail. The theory makes possible the measurement of exchange rate constants using spin-echo techniques without the use of computers and seems relatively easy to generalize to more complicated systems.