Multi-pulse methods

11 The WAHUHA pulse cycle, (a) Timing diagram, (b) Time-evolution operators in the rotating coordinate frame, (c) Rotations in the rotating coordinate frame (RCF). 

To gain some insight into the theory of multi-pulse NMR, the WAHUHA sequence (t, -Fx, t, —y, T, T, -Fy, t, —x, t) is applied in the rotating coordinate frame to a pair of spins coupled by the dipole-dipole interaction [Sch9]. The pulses are considered to be infinitely short. Their flip angle is 90°, and they are applied in -Fx, —y, -Fy, and —x directions of the rotating coordinate frame. The density matrix p to- -6x) after completion of a WAHUHA cycle is obtained from the density matrix p(ta) before application of the cycle by transformation with the evolution operator U(i) of the cycle. 

By insertion of the unit operator 1 = pulse operators Pa and free precession 

Application of the pulse operator P to the free precession operator transforms the free 

Multi-pulse sequences are designed in such a way, that the product of pulse operators of a cycle is the unit operator 1. Then, for sufficiently small pulse separations t, the evolution operator in (3.3.33) can be approximated by 

All of this comes with a marked increase in the complexity of the experimental theory. In this book, we have kept the theory to a minimum, so it is impossible to go very far into these methods here. But 

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Section 4 is devoted to multi-pulse methods of removing magneto-acoustic and piezo-electric ringing (MAPER), generated by numerous objects containing metallic, ferrite, ferro- and piezo-electric components, when detecting explosives with NQR landmine detectors and luggage scanners. 

The application of various multi-pulse methods in NQR requires a clear theoretical understanding of physical processes first of all behind the simplest "basic" multi-pulse sequences which include such a popular sequence as multi-pulse spin locking—MW-4, and a sequence of identically spaced coherent radio frequency (RF) pulses with intervals between them less than the time constant of free induction decay (FID) —strong off-resonance comb— SQRC. ... 

The principles behind MAP liquid-phase and gas-phase extractions are fundamentally similar and rely on the use of microwaves to selectively apply energy to a matrix rather than to the environment surrounding it. MAP gas-phase extractions (MAP-HS) give better sensitivity than the conventional static headspace extraction method. MAP-HS may also be applied in dynamic applications. This allows the application of a prolonged, low-power irradiation, or of a multi-pulse irradiation of the sample, thus providing a means to extract all of the volatile analytes from the matrix [477]. 

Until MAS, multi-pulse, and Fourier techniques became available on a commercial basis, wideline NMR was the most frequently used method of solid-state NMR spectroscopy. 

If the functions of the second and the third pulses are interchanged (Fig. 7.2.6(b)), then the third pulse can be repeated for different frequencies to read out stimulated echoes from different slices. The CHESS multi-slice method is comparatively insensitive to spatial variations in flip angles from B inhomogeneities and makes efficient use of the available rf power. 

In NMR, multi-quantum coherences can be excited by just two pulses [Eml, Muni] but for rigid samples multi-pulse sequences are more efficient (cf. Fig. 7.2.26) [Bau2, Muni]. Because the receiver coil in the NMR experiment corresponds to a magnetic dipolar detector, only dipolar single-quantum coherence can be detected directly and not multi-polar multi-quantum coherences. However, the latter can be detected indirectly by methods of 2D NMR spectroscopy [Eml]. 

In the following, some aspects of multi-pulse excitation are reviewed which are relevant for space encoding. The effects of time-invariant and pulsed gradients are addressed as well as methods to increase the line-narrowing efficiency through second averaging and CRAMPS (cf. Section 3.3.4). 

The chapfer consists of four sections, which are devoted to theoretical and practical issues of the detection of nitrogen-containing substances. Section 2 deals with theoretical aspects of the two most popular multi-pulse sequences multipulse spin-locking—MW-4 and "strong off-resonant comb"—SORC. In spite of the fact that the development of these sequences has enabled a dramatic increase in the sensitivity of NQR methods, until recently a number of theoretical and experimental peculiarities of these sequences have not been studied adequately. The primary issue concerns the sequence SORC, and also behaviour of both sequences in case of close times of spin-lattice and dipolar relaxations, which is especially important for the detection of such a popular explosive as hexogen (RDX). There are also demonstrated some experimental techniques for the detection of some other explosives (PETN and trinitrotoluene (TNT)). 

The methods suggested in paper are based on using multi-pulse sequence of the following type ... 

In as much as the problem of reduction of various interactions is not so relevant to NQR as it is to NMR, the multi-pulse sequences with complex cycles, which are so popular in NMR, did not find a wide utility in NQR spectroscopy. Therefore, the issues discussed in this chapter related to theoretical and applied aspects of the elementary multi-pulse sequences MW-4 and SORC are, perhaps, the most important and essential in the direct methods of " N NQR. Further improvement of the direct methods will be conditioned, above all, by introduction of the latest achievements of electronic technology into experiment. 

Multi = multi-elemental method, STEB = sodium tetraethylborate, STPB = sodium tetrapropylborate, SBH = sodium borohydride, PFPD = pulsed flame photometric deteotion,... 

In summary, the multi-pulse scheme is an effective method to average out the dipolar interactions, especially it is indispensable for homonuclear decoupling of abundant spins with high gyromagnetic ratios. 

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