Breakdown of linear response theory under low-power excitation in NMR. I. The case of long-lived signals in inhomogeneously broadened spin systems

In this work, we examine the application of linear response theory to the problem of low-power excitation in inhomogeneously broadened spin systems when the strength of the radiofrequency (RF) pulse, nu(RF), is smaller than the inhomogeneous linewidth. Even for small overall excitations [Theta = 2 pi nu T-RF(p) << 1 where T-p is the RF pulse length], linear response theory is shown to break down for spins with resonance frequencies that are on the order of nu(RF), which is due to the fact that the RF interaction cannot be treated as a small perturbation in this case. This breakdown in linear response theory can be partially corrected for by enforcing unitarity in the linear response. Furthermore, the nature of the spin echo generated by a pi(X)-pulse applied immediately after a low-power pulse is investigated. Numerical calculations and experiments performed in an inhomogeneously broadened H2O/D2O solution confirm the theoretical predictions presented in this work. Published by AIP Publishing.