Specific gamma constant

The second quick calculation uses the specific gamma ray constant as given in Equation 255. Table 25.3 lists the specific gamma ray constant for some common radionuclides. 

Two of the more direct techniques used in the study of lattice dynamics of crystals have been the scattering of neutrons and of x-rays from crystals. In addition, the phonon vibrational spectrum can be inferred from careful analysis of measurements of specific heat and elastic constants. In studies of Bragg reflection of x-rays (which involves no loss of energy to the lattice), it was found that temperature has a strong influence on the intensity of the reflected lines. The intensity of the scattered x-rays as a function of temperature can be expressed by I (T) = IQ e"2Tr(r) where 2W(T) is called the Debye-Waller factor. Similarly in the Mossbauer effect, gamma rays are emitted or absorbed without loss of energy and without change in the quantum state of the lattice by... 

The conceptual point is as follows. The discrete case X/ = l/N requires the mole fractions of all components to be equal to each other. That does not, however, correspond to a constant X (x) in the continuous description, because ) (x)dx is the mole fraction of species between x and x + dx, and one would need to require (x)dx to be constant. But this can only be done if one has chosen a specific scaling for the label x Any label x that is given by a monotonous function x (x) = X would be legitimate, and of course x)dx could be taken as constant for only one such scale. In other words, in a continuous description one has chosen some label x. The form of the mole fraction distribution must then satisfy certain constraints such as the one discussed earlier for the gamma distribution. The problem is related to the more general problem of the correct generalization to a continuous description of nonlinear formulas. 

The specific Compton mass attenuation coefficient (p) is a material constant. It depends on the energy of the gamma rays and on the ratio (Z/A) of the number of electrons (Z) to the atomic mass (A) of the material (Ellis 1987). For most sediment and rock forming minerals this ratio is about 0.5, and for a Cs source the corresponding mass attenuation coefficient (p ) for sediment grains is 0.0774 cm g. However, for the hydro-... 

The ratio of the resistivity (R ) in sediment to the resistivity (R. ) in pore water defines the formation (resistivity) factor (F). (a) and (m) are constants which characterize the sediment composition. As Archie (1942) assumed that (m) indicates the consolidation of the sediment it is also called cementation exponent (cf. Sect. 3.2.2). Several authors derived different values for (a) and (m). For an overview please refer to Schon (1996). In marine sediments often Boyce s (1968) values (a = 1.3, m = 1.45), determined by studies on diatomaceous, silty to sandy arctic sediments, are applied. Nevertheless, these values can only be rough estimates. For absolutely correct porosities both constants must be calibrated by an additional porosity measurement, either on discrete samples or by gamma ray attenuation. Such calibrations are strictly only valid for that specific data set but, with little loss of accuracy, can be transferred to regional environments with similar sediment compositions. Wet bulk densities can then be calculated using equation 2.3 and assuming a grain density (cf. also section 3.2.2). 

Tn an earlier paper (13) p-nitrosodimethylaniline (RNO) was postu-lated to be an efficient scavenger of the OH radical at pH 9 in cobalt-60 gamma irradiated, air saturated, aqueous solutions. It was also postulated to be specific for the OH radical in these solutions since evidence was presented that neither HOL> nor 02 destroyed the chromophoric group at 440 n.m., the absorption maximum of RNO in the visible region of the spectrum for neutral and basic solutions. Relative rate constants for the reaction of OH with RNO and other molecules were reported to be in good relative agreement with those reported by others who used both the pulse radiolysis method and indirect competition techniques. 

In the early 1970s, Simonits proposed the development of a standardization method using universal fc-factors. In this method, the essential information for a gamma ray emitted by any nuclide produced by neutron activation would be contained in a universal constant, the ko factor, and all factors depending on the specific irradiation and counting conditions would be calculated by models. The inventors of the ko method envisioned that for each sample analyzed at least one neutron flux monitor would be co-irradiated and counted, and all other parameters of the models would be measured once and only remeasmed when irradiation conditions changed. Thus, multielement analysis could be performed with the same amount of work needed for single-element analysis. 

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