Two-pulse echo experiments in the spectral diffusion regime

Abstract

The two-pulse echo sequence is examined for the case in which the frequency modulation time τm of the transition is intermediate between the well known limiting cases of very fast modulation (motional narrowing) and very slow or static modulation (inhomogeneous broadening). Within this spectral diffusion regime, the interpretation of the echo decay differs markedly from standard treatments. If the frequency-frequency correlation function initially decays as 1−tβ, the echo decay time TE is proportional to τmβ/(β+2). These results reduce to those of Yan and Mukamel [J. Chem. Phys. 94, 179 (1991)] for β=1. Drawing on a viscoelastic model, the theoretical results are compared to viscosity and temperature dependent vibrational echo experiments on myoglobin–CO. A τm1/3 dependence is observed, as is predicted for an exponential decay of the frequency–frequency correlation function.