Counting Spins with a New Spin Echo Double Resonance

In traditional spin echo double resonance (SEDOR), the echo amplitude M is decreased when the observed spins S are flipped by π together with the π refocusing pulse on the observed spins I; the dependence on τ is then determined. In the new version of SEDOR, the echo amplitude is measured as a function of the S spin flip angle θ at a constant pulse spacing τ. The analysis is simple and powerful for long τ, where the strong collision limit applies. There, the variation of M with θ can be fit, yielding the number n of spins S to which each spin I is coupled. Data from amorphous silicon with ¹H and ²D show the described effect. A MAS version of the new method is used on multiply labeled alanine and urea, with results in good agreement with the predictions for n = 2, as expected. By Fourier transforming M with respect to the flip angle θ, a stick spectrum results; the largest numbered non-vanishing stick yields the number n of spins S coupled to each spin I. Simulations are presented for an n = 2 system. The present technique is compared to the multiple-quantum spin-counting method.