Asymmetry parameter definition

Calculated results for the Ar nondipole Is photoelectron angular-asymmetry parameter yis(< ) for free Ar, Ar C60, Ar C60 (-240 and Ar C6o C240 C540 are shown in Figure 15 (the nondipole parameter Sns vanishes, by definition, and the dipole parameter fins = 2, i.e., is constant, nonrelativistically for the photoionization of ns-states). 

From the results shown in Table 1, the following conclusions can be drawn out Ci1 All the spectra correspond to non axially symmetric 31P tensors, (ii) the [dn - 033] difference ranges from 206 to 263 ppm and is definitely larger than the chemical shift difference observed in the liquid phase between a phosphonite and the corresponding thioxo-phosphonate, (iii) a linear relationship appears when the asymmetry parameter n is plotted against the intracyclic O-P-O bond angle a. 

This definition implies that the asymmetry parameter lies in the range 0 < r < 1. 

At first order, it can be shown that only the symmetrized part of the interaction tensor contributes to the frequency shift. The majority of second-order contributions arise from large EFG, the EFG tensor being symmetric by definition. Thus, only symmetric second-rank tensors T can be considered, which can be decomposed into two contributions T = isol3 + AT with D3 the identity matrix. The first term is the isotropic part so = l/3Tr(T) that is invariant by any local symmetry operation. The second term is the anisotropic contribution AT, a symmetric second-rank traceless tensor, which depends then on five parameters the anisotropy 8 and the asymmetry parameter rj that measures the deviation from axial symmetry, and three angles to orient the principal axes system (PAS) in the crystal frame. The most common convention orders the eigenvalues of AT such that IAzzL and defines 8 — Xzz and rj — fzvv i )... 

The nature of the orientational disorder in phases III and II was investigated first by powder experiments to give an overview of the evolution of the anisotropy and asymmetry parameter of the averaged EFG interaction. In all phases, the EFG asymmetry parameter is different from zero, and continuously decreases as temperature increases, with no observed anomaly at the transition temperature. That the asymmetry is definitively nonzero over the whole temperature range shows that the planar reorientational motion consists of jumps over six asymmetric potentials wells, which retain the centrosymmetry on average, and that the population of the different sites continuously evolves with temperature. The authors argued that a precise estimation of the two unknown occupation probabilities cannot be drawn from powder spectra without simplifying assumptions. The reasons come from the model of sixfold jump around the axis normal to the benzene... 

The I spectrum [96] of IFg" contrasts with IFg (Fig. 15.23) in having a large chemical isomer shift of +2-45 mm s and an asymmetry parameter of close to unity. The latter results in a symmetrical spectrum because when j 1 the sign of becomes an arbitrary definition as = —Vyy. 

Definitions the electric field gradient, the asymmetry parameter of the electric field gradient and the deuterium quadrupole coupling constant. 

DEFINITIONS-.THE ELECTRIC FIELD GRADIENT, THE ASYMMETRY PARAMETER OF THE ELECTRIC FIELD GRADIENT AND THE DEUTERIUM QUADRUPOLE COUPLING CONSTANT. 

This definition is analogous to that of the more common spin relaxation generalized order parameter, although the sensitivity to motional timescales is very different. As will be discussed later, a further distinguishing characteristic is that RDC analysis can in principle allow the explicit separation and determination of the direction and extent of the motional asymmetry. 

The traditional definitions of the three principal value components (5i 1, 22, and 533), isotropy 5iso, anisotropy and asymmetry of the chemical shift are equivalent to those of the magnetic shielding. This traditional scheme is indefinite. It leads to a loss of physical and chemical generality which is disadvantageous. Therefore, besides the isotropy two new parameters, span Q and skew k, are often introduced and used instead of the anisotropy A3 and... 

The observed asymmetry of a peak is measured by two parameters, the skewing factor a measured at 10 per cent of its height and the tailing factor TF measured at 5 per cent (for the definition of these terms, see Figure 1.4) ... 

The Haeberlen-Mehring-Spiess convention defines three parameters in terms of the three shielding tensor principal components, Cyy/ and cr z. The three parameters are the isotropic shielding value (ffiso), the shielding anisotropy (Ac), and the shielding asymmetry (77). Their definitions are provided below ... 

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