Solid angle, generalized

The quantity N(6, cp, i//) sin ddddcpdi// represents the fraction of structural units oriented in the generalized solid angle sinOdOdtfidij/, with the following... 

From Fock s projection, one can show that the generalized solid angle on Fock s hypersphere is related to the volume element in momentum space by... 

We now introduce a generalized solid angle element, dO, defined by... 

For a general, isotropic and condensed multiphase material with short-range order, the CLD offers the best possible model-free visualization of the nanostructure. Nevertheless, the image does not show many details because of the inherent solid-angle average. 

The equilibrium constants can be approximated by ratios of ion currents in some instances otherwise, the currents are converted to partial pressures by comparison with the evaporation of known amounts of a standard material. Various geometric corrections (K) such as the solid angle subtended by the sample at the orifice, the Clausing factor for orifice geometry, molecular cross-section (o-), which control ionization efficiency, and detector efficiency are included in the general relationship... 

We now need to convert dco into terms involving the spherical coordinates 9 and cf>. As shown in Fig. 3.19a, a given solid angle co traces an area a on the surface of a sphere of radius r. When a = r2, the solid angle co is by definition 1 sr (sr = steradian). For the more general case of a surface area a subtended by the solid angle co,... 

The quantitative treatment of solid-angle effects is rather cumbersome. A concise formulation can be derived only if the theoretical angular correlation is known, for example, by the general parametrization of equ. (4.68) with known A-coefficients, and if a point source can be assumed. (The condition for simulating a point source is not so much an infinitely small dimension, but an equal angular... 

The flux of the radiation scattered, 7(0, X), into a solid angle element AT2 may be expressed in general terms in the following way ... 

The amplitude of the signal, A, is also determined. It depends on spins, multipolarities, and eventually on mixing ratios of the transitions involved, that is, entirely on nuclear parameters, and thus is a well-known quantity in practice, it is further reduced by solid angle correction factors. If more than one structure at the site of the PAC probe is present in the sample, the relative amplitudes will, in general, directly reflect the relative population of the different sites. 

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