Resonance line center

At the beginning of the hydrothermal transformation, the spectrum consists of a single, broad low-field-shifted resonance line centered at 100 ppm (chemical shifts were measured from natrolite). As the hydrothermal treatment proceeds, the spectra show five well-resolved lines at -85.2, -89.3, -94,0, -98.9, and -103.5ppm, corresponding to Si surrounded by 4, 3, 2,1, and 0 Al, respectively [81]. 

Experimental methods of measuring the Lamb shift can be broadly classified into two basic types. The first is the microwave resonance technique originally used by Lamb and Retherford, in which the 2s - 2p transition is observed directly in a microwave cavity. The prime factor limiting the accuracy is the precision with which the resonance line center can be located. Since the width r of the 2pi state is about one tenth of the Lamb shift, the line center must-be located to a precision of lOx ppm relative to F for a precision of x ppm n the Lamb shift. Line narrowing can be achieved by use of Ramsey s separated oscillatory fields technique, but at the expense of a lower signaj-to-noise ratio. Since the Lamb shift increases in proportion to Z, the f quency lies outside the micro-wave region for ions heavier than Li. A tunable laser can then be used in conjunction ith a fast ion beam as further discussed below. 

In a rigid polycrystalline system, a nucleus does not experience an isolated dipole interaction but many such interactions arising from neighboring nuclei having (in most instances) different R and 0 relationships with the nucleus. The result is a Gaussian shaped resonance line centered at 0)q and characterized by a second moment given by7... 

In a conventional Fe Mossbauer experiment with a powder sample, one would observe a so-called quadrupole doublet with two resonance lines of equal intensities. The separation of the lines, as given by (4.36), represents the quadrupole splitting The parameter Afg is of immense importance for chemical applications of the Mossbauer effect. It provides information about bond properties and local symmetry of the iron site. Since the quadrupole interaction does not alter the mean energy of the nuclear ground and excited states, the isomer shift S can also be derived from the spectrum it is given by the shift of the center of the quadrupole spectrum from zero velocity. 

Fig. 10. The ESR signal produced at various points on the resonant line in a magnetic field modulated spectrometer. The vertical magnetic field modulation interacts with the bell-shaped adsorption curve [F(H)1 to produce the horizontal ESR signal. Here AH is the half amplitude line width and Hu is the center of resonance (S3).

The anion structure of the Mott insulator k-(ET)2Cu2(CN)3 34 in Fig. 21 revealed the disorder in the position of C and N atoms of the C=N groups (L2 part Table 6, Fig. 21a) [205-207, 370], due to the existence of an inversion center. However, NMR experiments observed very sharp resonance lines due to the homogeneous local field in the metallic state [371], which suggests that the C/N disorder, if any, does not work as the disorder potential in the conduction layer. 

From the preceding discussion it may be concluded that the main resonance line at g — 2.0006 in irradiated frozen alkali hydroxide solutions is attributable to the radiation-produced electron trapped around a hydrated O- radical ion. Insofar as the latter is an electron vacancy created by the reaction of the radiation produced holes with the OH ions, the trapped electron may be considered to be analogous to an F center formed in alkali halide crystals, where, however, the electron vacancies exist even prior to irradiation. The term trapped electron (symbolized T ) has been used throughout the present paper. This model will be... 

Fig. 9.6 Resonance line shapes in model He 1I, complex. The Q space composed of the He H, complex in which the H2 fragment is confined to the / — 2 rotational state is coupled by potential anisotropy to the P space composed of the He-H2 (j — 0) manifold. Shown are four (l> = 0, 1,2, 3) vibrational resonances, with v = 0 marked as O, i = 1 marked as A, v = 2 marked as +, and v — 3 marked as X, in the vicinity of the center of the v — 2 resonance. Left-hand scale pertains to o = 2 and right-hand scale to all other resonances. We see that although the resonances do not overlap appreciably (note difference between the v = 2 scale on left-hand side and right-hand scale pertaining to the tails of the other resonances), each of the o — 0, 1, 3 resonance exhibits a hole at the exact position of v = 2 maximum.

In Figure 10.2a we show the hE n(t) continuum coefficients [Eq. (10.44)] function of time, at different intensities. The onset of off-resonance processes- typified by a nonmonotonic behavior At off-pul se-center energies, the continuii coefficients rise and fall with the pulse, with the effect becoming more pronouns the further away from the line center the continuum energy levels are. In the wings of the pulse the continuum coefficients are zero at the end of the pulse, giv rise to a pure transient, otherwise known as a virtual state. These results should compared to the weak-field transients discussed in Section 2.1 and shown inFi ... 

Fig. 1. On the left is a simplified energy-level diagram for l Hg+. The 281.5 nm quadrupole "clock" transition can be observed by monitoring the 194 nm fluorescence. If the ion has made a transition from the Si to the 5/2 level the 194 nm flourescence disappears. For the figure on the right, on the horizontal axis is plotted the relative detuning from line center in frequency units at 281.5 nm. On the vertical axis is plotted the probability that the fluorescence from the 6s Si - 6p pi first resonance transition, excited by laser radiation at 194 nm, is on immediately after the 281.5 nm pulse. The electric-quadrupole-allowed S-D transition and the first-resonance S-P transition are probed sequentially in order to avoid light shifts and broadening of the narrow S-D transition. The recoilless absorption resonance or carrier (central feature) can provide a reference for an optical frequency standard. (From ref. 11)...

Here r,(co) shows the effect of the surface reflectivity, which appears as a lorentzian line, centered at the surface resonance, if we neglect the variation of rv(co) with co around the surface resonance ( lOcnU1). The surface excitations are renormalized relative to the bulk-free surface, leading for coupled surface excitons to a frequency shift ds and to a new radiative width rs, both quantities simply related to the complex amplitude of the bulk reflectivity ... 

Another contribution to variations of intrinsic activity is the different number of defects and amount of disorder in the metallic Cu phase. This disorder can manifest itself in the form of lattice strain detectable, for example, by line profile analysis of X-ray diffraction (XRD) peaks [73], 63Cu nuclear magnetic resonance lines [74], or as an increased disorder parameter (Debye-Waller factor) derived from extended X-ray absorption fine structure spectroscopy [75], Strained copper has been shown theoretically [76] and experimentally [77] to have different adsorptive properties compared to unstrained surfaces. Strain (i.e. local variation in the lattice parameter) is known to shift the center of the d-band and alter the interactions of metal surface and absorbate [78]. The origin of strain and defects in Cu/ZnO is probably related to the crystallization of kinetically trapped nonideal Cu in close interfacial contact to the oxide during catalyst activation at mild conditions. A correlation of the concentration of planar defects in the Cu particles with the catalytic activity in methanol synthesis was observed in a series of industrial Cu/Zn0/Al203 catalysts by Kasatkin et al. [57]. Planar defects like stacking faults and twin boundaries can also be observed by HRTEM and are marked with arrows in Figure 5.3.8C [58],... 

For 20 years center stage has been occupied by two-dimensional (and now three-and four-dimensional) NMR techniques. 2D NMR and its offshoots offer two distinct advantages (1) relief from overcrowding of resonance lines, as the spectral information is spread out in a plane or a cube rather than along a single frequency dimension, and (2) opportunity to correlate pairs of resonances. In the latter respect 2D NMR has features in common with various double resonance methods, but as we shall see, 2D NMR is far more efficient and versatile. Hundreds of different 2D NMR techniques have been proposed in the literature, but most of these experiments can be considered as variations on a rather small number of basic approaches. Once we develop familiarity with the basic principles, it will be relatively easy to understand most variations of the standard 2D experiments. 

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