Scattering cross section temperature dependence

The temperature dependences of the small-angle neutron scattering (SANS) from solutions and networks of poly(N,N -diethylacrylamide) or from copolymer of DEAAm and MNa (xMNa = 0.05) in deuterated water were measured [41]. Experimental dependences of the effective scattering cross-section... 

The intensity of the Raman lines is proportional to the product of the Raman scattering cross section aR, which depends according to (3.12) on the matrix elements atj) of the polarizability tensor and the density Ni of molecules in the initial state. If the cross sections aR have been determined elsewhere, the intensity of the Raman lines can be used for measurements of the population densities N(v, J). Assuming a Boltzmann distribution (3.11a), the temperature T of the sample can be derived from measured values of N(v, J). This is frequently used for the determination of unknown temperature profiles in flames [325] or of unknown density profiles in liquid or gaseous flows [326] at a known temperature (Sect. 3.5). 

One calculates transport properties by correlating the resistivity with the total scattering cross-section. The electrical resistivity is found to be temperature insensitive at low temperatures, has the ln T/T ) dependence near T , and decreases steadily for T > Tq. The shape of the resistivity curve will be discussed in section 3.3. Clearly the low-temperature resistivity is in disagreement with experiments, which indicate the type Fermi liquid behavior. The discrepancy comes from the implicit assumption that the impurity atoms scatter the conduction electrons Incoherently. How the system achieves coherence at low temperatures is now studied in terms of the spin fluctuation resonance model, but the analysis has not yet reached the level of sophistication of the single-impurity problem. 

The quantity (da/df2)j is called absolute differential Raman scattering cross section. It is often termed absolute Raman intensity as well. From q. (8.45) it is clear that (da/dn)i depends on several factors such as Vq and V and the absolute temperature T. In order to operate with comparable quantities that are independent fi-om the experimental conditions, the so-called "standard intensity" or "scattering coefficient" Sj is commonly used [73,253,260-263]... 

The effects of temperature on the factors of Eq. (1) arise mainly from the neutron-energy dependence of the microscopic absorption (and to a lesser extent scattering) cross sections, and from the variation of the macroscopic cross sections due to variations in core density. Also, the effect of volume changes on the geometrical buckling can be an important effect. With increasing temperature, some factors increase, some decrease, and some hardly change, so that overall coefficient depends on which factors dominate. 

Xab appears here as a universal parameter. However, it was found experimentally to depend on a number of factors [30-33] such as temperature, molecular weight, composition, inter-monomer distance (and therefore on the scattering vector Q), isotopic constitution, tacticity, microstructure, etc. These dependencies are shortcomings of the crude RPA description. The scattered intensity (macroscopic cross section d (Q)/d 2) is given by ... 

Fig. 16a, b. Temperature dependence of the absorption spectrum of 10% Yb + Gs3Lu2Br9 a comparison of the 14 K and 42 K absorption spectra. The intensities of the F5/2(2 ) and 1 5/2(00 features increase markedly, while those of the F5/2(l ) and cold vibronic transitions stay the same or decrease slightly b scatter plot of the normalized 10,591 cm F7/2(0) -> F5/2(2 ) absorption cross section as a function of temperature, compared with the hysteresis data vs pump power for the same sample. The triangles indicate the widths of the power hys-tereses, which get larger as the temperature is lowered. The dashed lines in (b) are both obtained from the same arbitrary polynomial fit to the absorption data, which was inverted and superimposed on the hysteresis data as a guide to the eye. Adapted from [62]... 

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