Periodic two-pulse NMR echo-signal excitation

Abstract

If a magnetic system in resonance is influenced by two radio-frequency pulses separated by a time t it is sometimes possible to observe not only the single echo signal at time 2~ but also secondary or repeated echo signals at times t = nT, where n = 3, 4, 5 .... A distinction is drawn between these secondary echoes due to Hahn and other mechanisms (quadrupole-interaction inhomogeneity [i, 2], multipole nuclear-moment excitation [3], and frequency echo [4]). In the first case, the secondary signals arise because of residual disequilibrium in the magnetic system because the condition T >> T I is violated, where T is the period between the pair of exciting pulses and TI is the longitudinal-relaxation time. In what follows, we consider only the Hahn mechanism. These signals were identified at an early stage in spin echo research [5, 6], but nevertheless, the theoretical description has so far been restricted to calculating only one secondary signal (n = 3), and that does not reflect the phase features [7]. Also, no phase-feature studies have been made on the secondary signals by experiment. As that mechanism may occur in various systems, a detailed knowledge is required to exclude the contribution when one is establishing the causes for secondary signals when other mechanisms are decisive. Also, if a suitable theoretical model is available, the phenomenon can be used to determine relaxation times when it is impossible to meet the condition T >> T I because of apparatus constraints (for example, at low or ultralow temperatures). If the specimen has a long T1, the condition T >> T I means a very lengthy experiment. For example, the proton T I in chloroform is 86 sec, and several hours would be needed to record the relaxation dependence for the echo amplitude. In such prolonged measurements, there may be additional difficulties related to magnetic-field drift and temperature fluctuation, which can affect the accuracy in measuring T I substantially [8]. Existing methods of determining relaxation times for T < T I [8, 9] are difficult to apply to any system where the nuclear magnetic moment is small because the induction and echo signals are weak. Signal accumulation and coherent detection enable one to examine not only weak NMR signals but also to use secondary echo signals to determine relaxation parameters.