Form factor definition

In addition to electric charge between particles other factors are in some cases operative in preventing actual contact, thus the medium may be strongly adsorbed by the surface, and the thin film may not readily be displaced on collision of the two neutral particles, in other cases a tough elastic film may be formed, possessing definite mechanical strength and necessitating a violent impact to ensure rupture. 

The general result for the nuclear charge radius and the Darwin-Foldy contribution for a nucleus with arbitrary spin was obtained in [9]. It was shown there that one may write a universal formula for the sum of these contributions irrespective of the spin of the nucleus if the nuclear charge radius is defined with the help of the same form factor for any spin. However, for historic reasons, the definitions of the nuclear charge radius are not universal, and respective formulae have different appearances for different spins. We will discuss here only the most interesting cases of the spin zero and spin one nuclei. 

In all considerations above we have assumed the most natural theoretical definition of nuclear form factors, namely, the form factor was assumed to be an intrinsic property of the nucleus. Therefore, the form factor is defined via the effective nuclear-photon vertex in the absence of electromagnetic interaction. Such a form factor can in principle be calculated with the help of QCD. The electromagnetic corrections to the form factor defined in this way may be calculated in the framework of QED perturbation theory. Strictly speaking all formula above are valid with this definition of the form factor. 

What is the definition of the form factor (or intraparticle structure factor) ... 

The disadvantages of the cogredient form of definition are connected with the presence of the factor (—1) in the normalizing coefficient 2Nk (D.32), which is a result of defining the reduced matrix element of the tensor operator (D.ll) into which this factor is introduced, in our opinion, without particular necessity. 

This corresponds to (f + d" ) lv(0), except that for the present pourposes we took into account the dispersionof f by an additional factor 1.4. N is the number of resonant atoms which form a definite structure, e.g. as metal binding sites a macromolecule. The ratio of resonant zero angle scattering to fluorescence Op in forward direction is... 

It has not yet been found possible to work the atom form factor into the dynamic theory. To a first approximation it would probably have an effect similar to that of temperature, for in both cases we have to take account of the fact that the centres of diffraction are not points but have definite dimensions in space. 

In the formation of valuable oxygen-containing compounds by the controlled or partial oxidation of hydrocarbons, such as benzene, two factors are of great importance, i.e., temperature and type of catahst. Other factors such as composition of hydrocarbon-air mixture and time of contact are also important. All of these factors are intimately related to each other and the successful operation of the process depends upon the control of each of them. It was early found that if mixtures of benzene apor and air in excess of tliat necessary for complete combustion were passed through heated tubes of such non-catalytic materials as iron, silica, aluminum, etc., and the temperature allowed to rise at will, only complete combustion products could be obtained, and no intermediate oxidation products could be isolated. On the other hand, if such mixtures of benzene vapor and air were passed over a catalyst such as platinum black, complete combustion also occurred but at a temperature far below that necessary in the empty tube made of non-catalytic material. However, only very small amounts of intermediate products could be obtained with such an active catalyst even when the temperatures were carefully controlled or the time of contact made very short. It is difficult to form any definite idea as to the temperatures which were actually attained by the reacting gases in most of the early experiments reported in the literature. Lack of uniformity in construction of reaction chambers, in displacement of cata-... 

In all of the applications of the 2N Newton-Raphson method which follow, both the functions and the variables were normalized for the purpose of reducing roundoff error. The functions Fj and Gj are stated in a normalized form. The definition of the 0/s contains a normalizing factor, namely, (Lj/Vj)a. Temperatures were normalized by dividing each temperature by some base temperature. Although other more precise methods of normalization may be used such as the... 

Here the structure factor signifies the vectorial sum of the waves scattered by the single atoms which show amplitude f and phase y. Every atom contributes a scattered wave to the whole diffraction effect, the amplitude of which is proportional to the so-called form factor. The phase is thus defined by the position of the atom in the elementary cell, whilst the form factor is a characteristic constant for every sort of atom which represents a measure of its scattering power. Hence no special differences exist in the positions of the diffracted beams, which in both X-ray and electron diffraction cases satisfy the geometric relations between lattice constant and X-ray or material wavelengths, according to the Bragg equation. However, there are definitely differences in their intensities. 

In the European community, the occupational exposure level is defined as the limit of the time-weighted average of a chemical agent in the air within the breathing zone of a worker in relation to a specified reference period, usually 8 h or a work shift. In addition, to avoid adverse health effects, there is a need to set limits for short-term exposure peaks. In the occupational safety legislation of most countries within the European Community the lists of occupational exposure levels include limits for short-term exposure for many substances, either in the form of definite concentration values or so-called short-term exposure factors. In case of factors, the allowed maximum short-term concentration is calculated by multipHca-tion of the OEL by the short-term exposure factor. Typically, many hazardous substances have factors within the range of 1-4. 

The definition of a form factor is somewhat arbitrary. In this article the term is restricted to those cases where (r) contains no phase factor that is Q(r) is a positive definite quantity. 

Each of the theoretical charge distributions will give rise to a definite dependence of the atomic form factor F upon its argument s according to equation (5 2). For the Thomas-Fermi distribution, again, an especially simple expression results for F, One finds... 

In case a the permeate concentration of the organic vapour (Xp) is determined form the definition of the selectivity factor a. 

Statements 2, 3, and 4 are all based on the mole definition, and are very useful in solving numerical problems involving balanced reaction equations and the factor-unit method described earlier in Section 1.9. Any two quantities from statements 2, 3, and 4 can be used to form factors that can be used to solve problems. For example, the following factors are just four of the many that can be obtained from stat ents 2, 3, and 4 by combining various quantities from the statements ... 

Due to the fact that non-Fickean diffusion is influenced by a change in the free volume of the adhesive, the viscoelastic bulk and shear compliances in the form of two separate Prony series are used. Poisson s ratio is allowed to vary with time for the adhesive. A shift factor definition based on the free-volume concept is used in the analysis. The adhesive is assumed to be initially moisture-free. A moisture concentration value of unity is specified on the adhesive boundary. 

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