Scattering form-factor

For anisotropic samples, the space correlation function will depend on the orientation imposed to the vector and P(q) will vary both with the scattering angle 6 and azimuthal angle define scattering form factors along the reference axes as ... 

The general expression for the scattering form factor of randomly oriented particles and vertically polarized light reads ... 

The Debye function is the scattering form factor of a single polymer chain in a melt [88, 92]. Experimentally, this function can be observed using the method of contrast variation in SANS. A calculation similar to the one presented above can be done for soft matter objects of arbitrary shape and a lot of form factors were already derived. A good review for different form factors was given by Pedersen [94]. 

The extent to which charge is transferred back from the anion towards the cation in the alkali metal halides themselves is difficult to determine precisely. Calculations indicate that it is probably only a few percent for some salts such as NaCl, whereas for others (e.g. Lil) it may amount to more than 0.33 e per atom. Direct experimental evidence on these matters is available for some other elements from techniques such as Moss-bauer spectroscopy, electron spin resonance spectroscopy, and neutron scattering form factors. ... 

Neutron scattering studies of setal hydrogen systems The palladium hydrogen system Ab Initio calculations of metal hydrogen systems Experimental measurements of the inelastic neuron scattering form factors for scattering to excited states in PdH... 

EXPERIMENTAL MEASUREMENTS OF THE INELASTIC NEUTRON SCATTERING FORM FACTORS FOR SCATTERING TO EXCITED STATES IN Pd-H... 

We note that the numerical computation of the scattering form factor of a chain with persistence length gives the location of the cross-over between the two laws at q = l/h [17,18]. 

TABLE 1. Values, Corrected for the Experimental Temperature (in p units), of the Determined Stracture Amplitudes and Theoretical Obtained from Electron-Scattering Form Factors of Neutral Na and Br Atoms... 

The present paper is concerned with the problem of the influence of perturbing fields of the or symmetry on the scattering form factor (atomic scattering factor) of x rays and electrons. The results obtained are used to calculate the structure amplitudes of bcc and fee lattices. Possible distortions of the wave functions resulting from the influence of the crystal field are ignored. 

TABLE 1. Scattering Form Factor of X Rays in Fields of Oji and Tj Symmetry... 

The same irreducible representations apply to the group Tj. Thus, we can easily determine the coefficients Cj - and this allows us to find expressions for the scattering form factor of X rays by means of Eqs. (1), (4), and (8)—(11). 

If we measure (s) in p units [3], we find that k 1.58. The components of the scattering form factor of the electrons corresponding to the 2p, 3p, and 3d states are given in Table 2, where the following notation is employed ... 

TABLE 2. Scattering Form Factor of Electrons in Fields of Ojj and T Symmetry... 

Fig. 7 The theoretical scattering form factor, R(<2), from some common objects (7) ideal polymer chain ...

Finally, for hydrogenic systems it has been notedt33] that dominant uncertainty in the nuclear size contribution arises from the normalisation of the electron scattering form factors F(q) which are used to determine the proton and deuteron charge radii. However, if... 

In interacting systems the optical and orientation factors in a are no longer separable quantities. The induced optical effect is determined both by the single particle scattering [form factor P q)] and by the pair distribution function [structure factor 5( )], the latter being direction-dependent [42]. Since in addition to orientation the electric field causes particle translation, even for spherical particles the radial distribution function g q, /) and the "static" structure factor attain time-dependent induced anisotropy. The deformed surface potential also contributes to this effect. 

The discussion of the pleated sheet in /3 keratin and other proteins will be presented in following papers. In this discussion we make use of the x-ray scattering form factor for the sheet. The form factor, calculated for reflections from planes parallel to the median plane of the undistorted sheet, is for convenient later reference given here, in figure 4, as calculated from the equation F = Y,International Tables for the Determination of Crystal Structures. The sum has been taken over the atoms of one residue of the undistorted structure, including also a carbon atom, with y = 2.04. 

The scattering form factor 5(q) from a labeled chain in the network is given by the Fourier transform of the distribution function f2(r,y) of the vector between two scattering centers i and j averaged over all pairs of scattering centers along the chain ... 

Klinskikh (1993) develops a continual model of a macromolecule with excluded volume with the variational principle of the free energy of a molecular chain underlying. As a zeroth approximation, the continual integral of Peynmann s model for polarons in the solid body has been taken. The paper reports calculation of the free energy and the expan.sion coefficient of a molecular chain and the static and dynamic scattering form factors. 

Previously (Peterlin, 1955 Ptitsyn, 1957), the expression for the scattering form factor has been a generalization of Debye s formula and, in the notation accepted lierc, has the form... 

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