Asymmetric line shape

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

Fig. 9. This Larmor spectrum was measured in the analysis trap by resonant excitation (at 104 GHz) of the transition between the two spin states (spin up and down) of the bound electron. The asymmetric line shape of the resonance curve is due to the strong magnetic inhomogeneity in the analysis trap in combination with the thermal Boltzmann distribution of the ion s axial oscillation amplitude...

Figure 2 shows the reconstructed spectrum. The symbols correspond to the intensities of the fluorescence at the measured wavelength at a given time r. The lines are the least-square-fits to the points using a log-normal function. The log-normal function describes an asymmetric line shape and is often used to fit broad featureless absorption or fluorescence spectra. 

Fig. 9 shows the experimental visibility curves for p ow = 3.10 8 mbar (full circles) and Phigh = 5.10 7 mbar (hollow circles) and compares them to the quantum calculation (solid and dashed line, respectively) with the same model parameters as already used for Fig. 7. The remarks of the discussion of Fig. 7 apply also here. This holds for the reduction of the visibility at long wavelengths due to vibrations, the shift of the maxima with respect to the Talbot length and the asymmetric line shapes - caused by the molecule-...

Thus, it is concluded that (1) the quadrupolar N nuclei are responsible for NH signal broadening and the asymmetric line shape (2) the asymmetric line shape is different for a-helix and /3-sheet conformations and (3) the true NH proton chemical shift of a-helical [Ala ]n-2 can be determined (8.0 ppm) but that of [Ala ] - (/3-sheet) is difficult to determine because of the low S/N ratio using BR-24 pulse sequences at 2.0 kHz MAS speed. 

The efficient relaxation of quadrupolar nuclei in solution generally results in self-decoupling, such that quadrupolar effects are generally not observed in NMR spectra of spin-1/2 nuclei. Self-decoupling may also be a factor in NMR spectra of solid samples this often manifests itself as an asymmetric line shape. By decreasing the temperature, the Ti relaxation time of the quadrupolar nucleus may increase sufficiently to allow acquisition of NMR spectra where the effects of residual dipolar coupling are sufficiently resolved. ... 

It was pointed out independently by Williams (1967) and Culvahouse et al. (1967) that for a non-Kramers ion at a site lacking in full inversion symmetry, terms linear in an electric held may exist for a doublet state. Thus for Cj, symmetry (but not for C y) the system may have a permanent electric dipole moment, and its interaction with an electric held may be represented by additional terms of the form -I- SyEy). Transitions then occur with an RF electric held normal to the z-axis, even in the absence of a distortion from axial symmetry. As before, random distortions again produce an asymmetrical line shape, but with a maximum corresponding to the point for zero distortion, unlike the magnetic transitions referred to above. The asymmetry is present because in each case the distortions move the transitions to higher frequency at constant applied held, or to lower held at constant frequency. Such electric dipole moments also give rise to electric interactions between the ions (see section 5.6). 

The effects of interaction between closely packed microcrystals of a-FeOOH have been reported by M<Mossbauer spectra obtained with increasing temperature show firstly pronounced asymmetric line shapes and then the collapse of the hyperfine field, without any coexistence of magnetic and collapsed components that characterises the spectra of isolated particles. 

From the ESCA spectra, the binding energies of Al-2p and -2s orbital electrons of both silicates have been obtained. The asymmetric line shape of the Al-2p signal, as shown in Fig. 1, was observed because of the octahedral and tetrahedral coordinations of aluminium in the lattice and it was separated into two peaks with the help of a curve fitting program. One of the separated peaks at 73.2 eV is attributable to Al-2p of a tetrahedrally coordinated aluminium atom, because it corresponds exactly to the Al-2p line of synthetic saponite, where all the aluminium atoms occupy the tetrahedral sites. The major peak at 74.3 eV is consequently assigned to the Al-2p of octahedrally coordinated atoms. The peak shift of about 1.0 0.1 eV... 

Further characteristics of the interface modes are their broad and asymmetric line shape due to their allowed frequency range, the dependence of their frequency on the energy of the incident light and their resonance behavior [132,172]. For the investigation of interfaces, effects arising from the lattice mismatch also have to be considered [120]. 

In order to estimate the oxidation state, a few considerations are given in the following. A possible oxidation state of +IV can be excluded, based on the observed chemical shift of 3eV compared to the pure metallic platinum as mentioned above. Unfortunately, the oxidation states +II and 0 cannot be distinguished based on their chemical shift, as the difference between those states is too small. For the results of Watanabe et al. [9, 10] for Pt clusters containing up to 15 atoms measured under UHV conditions, an oxidation state of 0 can be assumed and shows considerably lower BE than the ones from Eberhardt et al. The question arises, whether this difference of 0.6eV is solely caused by the different supports or also by the conditions to which the samples were exposed and later treated. An oxidation state of 0 could be present considering the contamination of the clusters (physisorbed species) and the observed asymmetric line shape. To achieve an ultimate insight, further experiments for the same type of samples under constant UHV conditions are necessary, however it seems likely that an oxidation state of +II (e.g. Pt OH)x ) is present. 

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