Asymmetry parameter defined

This case is shown schematically in Fig. 5c. In Eq. (50), qj. are generalized y-photon asymmetry parameters, defined, by analogy to the single-photon q parameter of Fano s formalism [68], in terms of the ratio of the resonance-mediated and direct transition matrix elements [31], j. is a reduced energy variable, and <7/ y, is proportional to the line strength of the spectroscopic transition. The structure predicted by Eq. (50) was observed in studies of HI and DI ionization in the vicinity of the 5<78 resonance [30, 33], In the case of a... 

The mismatch can be characterized by a conformational asymmetry parameter defined as [35]... 

Consequently, there remain only two independent components, usually chosen as Vj-j. and rj which is the asymmetry parameter defined by... 

In another study, Yamakazi and Elliott [73] measured the interference within a single angular momentum state arising from coupling to different continua. They defined an asymmetry parameter,... 

In the general case, when the shielding tensor is not of axial symmetry, in place of its diagonal elements axx, ayy and kyyl > axx i the following parameters are generally used asymmetry parameter V = <3xx — ayy)/Gzz = (3/2)(cTj.j. — oyy)/h.o. The second form of rj arises from the fact that, as far as relaxation is concerned, the shielding tensor can be defined with respect to any time-independent reference (which therefore will not act as a relaxation mechanism). [Pg.96]

It is well known that at lower densities the properties of the EoS are primarily determined by the SE [2], The latter is defined in terms of a Taylor series expansion of the energy per particle for nuclear matter in terms of the asymmetry parameter a = (N — Z)/A (or equivalently the proton fraction x = Z/A),... 

In addition, the asymmetry parameter of the quadrupolar coupling, r], is defined in equation 9... 

A function closely related to QCC is the Li quadrupolar splitting constant (QSC), defined as QSC = (1 -h/7 /3) x( Li), where r is the asymmetry parameter. The Li QSC values can be estimated from the Li and C(para) spin-lattice relaxation times. The QSC values are correlated with the effects of structure, solvent and temperature on association in solution for aryllithium compounds (155, 171, 172). Conclusions can be drawn about the structure of the associated species in cases where no supporting XRD evidence is available. ... 

For atoms in sites of low symmetry, the EFG tensor must be diagonalized to obtain its principal components V y. Since the tensor as defined by Eq. (8.9) is traceless, two values will define all three principal elements. They are commonly chosen as V 33, the principal component with the largest magnitude, and the asymmetry parameter t] = V 22 — V n / V 33, which has the range 0 < q < 1. 

Some typical CT-only spectra simulated for static samples considering solely the quadrupole interaction are shown in Figure lA, for sites with different values of the asymmetry parameter r/q. The widths of these lineshapes depend on the rjq value and are proportional to the parameter A, defined for a nucleus with 1=5/2 as ° ... 

Figure 1 Simulations of CT lineshapes corresponding to (A) static and (B) MAS experiments, for different values of the asymmetry parameter rjq.The positions of the isotropic chemical shift (c5iso) and some well-defined singularities are shown, in terms of the parameter A, defined in Equation 8. All simulations were done with the DMFIT software. ...

The asymmetry parameter, which was defined in Section 3.4 as the average cosine of the scattering angle, depends, in general, on the polarization state of the incident light. However, the asymmetry parameter for a spherical particle is clearly independent of polarization and is given by... 

Fig. 5.4 Correlation diagram for asymmetric-top levels. Ray s asymmetry parameter k is defined as k = (2B — A — C)/(A - C). The symmetric-top levels have been taken from Fig. 5.3 thus it is assumed that A =4.5C. Note that the 1], energy is independent of B and hence gives a horizontal line.

Two parameters describe the quadrupole interaction there are the quadrupole splitting and the asymmetry parameter, rj, which is defined as,... 

One factor which may contribute to the longer MeM bond length in the carbonyl complexes is the presence of semi-bridging carbonyls which interact with orbitals involved in MeM multiple bonding. An "asymmetry parameter", a, may be defined as a = (d2-dj)/ dx (see Table I) where d2 = long M -C0 distance and d short M-C distance. For symmetrically bridged carbonyls, d2 = d and a = 0. For terminal carbonyls, a > ca. 0.6, and the semi-bridging appellation is appropriate if 0.1 < a < 0.5. 

TABLE 6.3 The fitted parameters of the O3 Hartley Band. Two fits are compared in the left column the 3 parameters of a fitted Gaussian are given with the resulting Chi /DoF. This fit corresponds to s = 0 in Formula (29). In the right column, the four fitted parameters of Formula (29) are given. The ChiV oF decreases by almost two orders of magnitude compared with the Gaussian fit. The uncertainties are 2 S.D (Standard Deviation). Note that s, the dimensionless asymmetry parameter, is defined to within 0.3%... 

Here 7 is the nuclear spin, is the quadrupolar coupling constant, tj is an asymmetry parameter, is the Gd- O distance, and r j is defined by Eq. 12. The difficulty of this technique is that both the quadrupolar coupling constant and the Gd - O distance can only be estimated. However, rotational correlation times obtained from longitudinal 2Q relaxation rates can provide a good comparison for similar Gd(III) complexes. One advantage is that the rotational correlation time is measured directly on the Gd(III) complex. Furthermore, the determined in this way corresponds to the rotation of the Gd(III) - coordinated water oxygen vector which is probably analogous to the rotation of the Gd(III) - coordinated water proton, which, itself determines proton relaxivity. 

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