Structure of the Spectrum

The computation of the matrix elements and the calculation of the transition frequencies and intensities are carried out in a manner analogous to that for the AB system in Section 6.8. The results are summarized in Table B.l in terms of the quantities D+, D, 6+, 0, and vAn, defined by the five equations  

It is easier to use these relations in the analysis of an experimentally obtained ABX spectrum if certain limitations are imposed on these quantities. D+ and D are defined as positive quantities, with D+ D. The nuclei are labeled so that vA — rfe.The values of 26+ varies from 0 to tt/2, while 26- ranges from 0 to it. It can be shown that these limitations do not in any way impose any restrictions on the measurable physical quantities. 

By combining Eq. B.l with B.3 (and B.2 with B.4) and carrying out suitable algebraic operations, we obtain 

The wave functions are mixtures of A and B functions, and the transitions cannot strictly be called A or B transitions. The labeling A and B in the second column of Table B.l is convenient but is strictly applicable only in the limiting case of large (vA — r B).The X transitions are pure, and the combination transitions 14 and 15 also appear in the X region of the spectrum and may have intensities comparable with those of X lines. The combination transition 13 involves simultaneous flipping of all spins and is forbidden. 

An ABX spectrum is completely described by nine quantities the three chemical shifts vA, i B, and nx the magnitudes of the three coupling constants JAB,  

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The intensity of the EPR resonance absorption is a measure of the number of paramagnetic centres present [346], while the type of line observed and the measured g factor are indications of the interactions of the paramagnetic particles and of their distribution within the matrix. Such spectra are much more sensitive to changes in crystal field and atomic orientations than X-ray diffraction and are not dependent upon crystallinity [347]. The nature of the paramagnetic particles may be discerned from the superfine structure of the spectrum. 

The fine structure of the spectrum is the splitting of the resonance into sharp peaks. Note that the methyl resonance in ethanol at 8 = 1 consists of three peaks with intensities in the ratio 1 2 1. The fine structure arises from the presence of other magnetic nuclei close to the protons undergoing resonance. The fine structure of the methyl group in ethanol, for instance, arises from the presence of the protons in the neighboring methylene group. 

R. D. Levine To answer the question of Prof. Lorquet, let me say that the peaks in the ZEKE spectra correspond to the different energy states of the ion. From the beginning one was able to resolve vibrational states, and nowadays individual rotational states of polyatomics have also been resolved. The ZEKE spectrum is obtained by a (weak) electrical-field-induced ionization of a high Rydberg electron moving about the ion. The very structure of the spectrum appears to me to point to the appropriate zero-order description of the states before ionization as definite rovibrational states of the ionic core, each of which has its own Rydberg series. Such a zero-order description is inverse to the one we use at far lower energies where each electronic state has its own set of distinct rovibrational states, known as the Bom-Oppenheimer limit. 

The idea that free radicals occur in many chemical reactions is as old as the study of the mechanisms of these reactions. However, direct physical evidence for the existence of free radicals and for their presence in certain reactions is comparatively recent. Such evidence has been obtained in recent years by the methods of mass spectrometry, optical spectroscopy, and electron spin resonance spectrometry. The optical method of detecting free radicals has the advantage that it simultaneously supplies information about the structure of the radical. Indeed, in many instances the nature of the free radical has been identified by the structure of the spectrum without any assumptions about the mechanism of the reaction in which it appears.1... 

A static NMR spectrum, that representing a non-exchanging spin system, contains full information about the chemical shifts and coupling constants of the system. This is also apparently true for dynamic spectra in the range of slow exchange where the fine structure of the spectrum is still visible. Static spectra are analysed by standard methods which usually consider spectral line positions. (94) Recently methods based on spectral lineshape fitting have been suggested. (95)... 

Whilst the tunneling current is a convolution of the tip and sample density of states, it is the energy spectra of the sample states that we try to determine. For positive biases on the sample, where electrons are injected from the tip into unoccupied sample states, the tunnel current will be dominated by electrons close to the Fermi energy of the tip. Under these conditions the density of states of the tip can be taken to be constant and the structure of the spectrum corresponds largely to the spectrum of... 

As for most of the quadrupolar nuclei, 33S nuclear spin-spin coupling constants have seldom been observed because the signals are very broad and the fine structure of the spectrum is not observed. The evidence of the existence of a 2/... 

Because NL(t) has the same periodicity as A(t) the comb structure of the spectrum, as derived in section 3, is not affected. In an optical fiber self-phase modulation can be quite efficient even though the nonlinear coefficient in fused silica is comparatively small. This is because the fiber core carries a high intensity over an extended length. 

The simplest and most easily recognized crystal field effect is the influence of the symmetry of the crystal on the NQR spectrum. Starting from the molecular field, the NQR spectrum is determined by the isolated molecules. The crystal field then produces a fine structure of the spectrum which can be used to explore the site symmetry of the nuclei considered. 

Oxygen decreases the efficiency of the emission at high oxygen concentrations a limiting yield is attained which is dependent on the acetone pressure but independent of the temperature. Oxygen, like the increase in temperature, eliminates the structure of the spectrum and shifts the intensity maximum towards shorter wavelengths . Nitric oxide exerts a similar influence to Oj. 

Examine each spectrum separately. Is it first or second order Explain. What effect does the higher field have on the structure of the spectrum ... 

Fig. 5. Illustration of the 50 largest eigenvalues of the transition matrix obtained from the global Viterbi path vs. lag time t, e.g. a lag time of 10ps means that transition are considered that occur from time x to time a +10ps. On clearly observes that the structure of the spectrum does not depend on r...

Alteration of the vibrational frequencies and the appearance of new ones in those rare cases when the vibrational structures of the spectrum remains. 

Gaseous pyridine adsorbed on to a sublimed KCl film in vacuo displayed a broad absorption maximum at 255 mp without the vibrational structure of the vapor spectrum (47, 47a). With respect to the onset of the latter, this band was located at higher frequencies and occupied the same range as that of a microcrystalline sublimed layer of pyridine at — 180°C, which, however, exhibited a distinct vibrational structure of the spectrum. A similar behavior has been observed for a-picoline. 

If we know the term scheme for an atom, we can at once read off from it the structure of the spectrum. For the hydrogen atom the term scheme has the form... 

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