Cross Section frequency dependence

With infrared-radiation pump lasers, where the frequency of the exciting photons approaches the energy of the direct band gap of several semi-conductos (e.g., InSb, PbTe), the effective mass m becomes very small and the light scattering cross section can approach one million times that of the free electron. The SFR cross section furthermore depends on the magnetic field strength. 

Both microwave and millimetre wave radiation can be channelled in any direction by a waveguide made from metal tubing of rectangular cross-section, the dimensions depending on the frequency range. The absorption cell is also made from waveguide tubing. 

The strength of a photon—molecule interaction is deterrnined by the frequency-dependent cross section 0 (v), expressed in cm for absorption and related to a(y) in equation 1 or by the differential cross section (k5(y) jin units of cm /sr for scattering (14). The latter specifies the likelihood that active species scatter some portion of the incident laser fluence (photons /cm ) into a viewing soHd angle, AQ, measured in steradians (Fig. 1). The cross sections can be expressed as in equation 5 ... 

The first term in Eq. (7.7) is the in-phasc signal, which has the same phase as that of the pump, and the second term is a quadrature or out-of-phase signal, which has a 90° phase relative to that of the pump. Their respective frequency dependencies are shown in Figure 7-2. The normalized change in transmission can be related to the excitation cross-section and quantum yield of generation ... 

Fig, 3.16. The density-dependence of the frequency shift of the Q-branch maximum. The y values for the curves are in the notation of Fig. 3.15. When plotting the experimental data, the cross-section found in the fitting of the density dependence of the width was employed (Fig. 3.15). 

The influence of bilinear cross terms of this type in force field caculations has been studied systematically only once so far (79). They are standard for vibrational-spectroscopic force field expressions (20), and accordingly vibrational frequencies depend considerably more sensitively on cross terms than e.g. conformational parameters. An example for the significant influence of cross terms also with respect to the latter is described in Section 6.1.3. 

The frequency-dependent absorption cross section of a metallic ellipsoid with dielectric function (9.26) is... 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

The arrangement used is shown in Fig. 12(a). The horizontal plates are pierced with holes of small diameter (approximately J -in. diameter), whose total cross section may be 20 to 25% that of the column. No downspouts are provided, as for ordinary perforated-plate extractors, and both liquids must pass through the same holes. The plate spacing is usually small, 2 in. in large-diameter columns, for example. Columns of this sort may be pulsed at amplitudes of 1 in. and frequencies up to 150 cycles/min., depending upon the circumstances. 

The concept of supermolecules allows a rather rigorous treatment of the aspects of collision-induced light scattering in the binary regime. The frequency dependence of the scattered light is described by the differential photon scattering cross section per unit angular frequency and per pair,... 

In section Section 10.1.2.3 we derived formulas for the collision frequency between two unlike molecules 1 and 2. Each molecule was characterized by a radius r,-, and any time the distance between the centers of the molecules was less than or equal to the sum of the radii, a collision was said to occur. The exact nature of a collision and what the radii (or the collision cross section) depend on were not specified. For example, whether a collision happened to be head-on or just grazing did not matter in deriving Eq. 10.52 or 10.59. All types of collisions counted. 

This section considers the cross section for reactive collisions ar. Bimolecular reactions will be treated explicitly. The rate (frequency) of collisions depends on the collision cross section. The larger the cross section, the more often molecules run into one another. In a similar way the reactive cross section determines how often molecules run into one another and react. This section introduces the simple line-of-centers model for scaling of the reactive cross section with energy. 

Cross sections of the a and fi Fermi surfaces and the y and 6 Fermi surfaces in the plane which includes the axis of rotation are shown in Figure 6.8. Each of the experimental Fermi surfaces has the axis of rotation about the [0001] axis. The dFIvA frequency values used to construct the Fermi surfaces are shown in Table 6.2. The values in parentheses in Table 6.2 are estimated frequencies that take into account the angular dependencies and the frequency ratios between the flux-grown crystal and the hole-doped crystal. The obtained Fermi surface dimensions are summarized in Table 6.3. 

The skin effect resistance of a rectangular-cross-section line also depends on its aspect ratio. For a given cross-sectional area, as the ratio tlw approaches 1, the skin depth perimeter decreases and the resistance increases, as shown in Figure 10, in which the measured resistance is plotted as a function of frequency for lines of fixed cross-sectional area with different aspect ratios (52, 53). Unfortunately, the lines with high aspect ratios that are desirable for high wiring density and low dc resistance have a higher skin effect resistance compared with thin, wide lines. 

Rubber Particle Size and Shape. If rubber particles act as crack or craze branch points along an advancing crack in matrix polymer, impact strength should depend on the frequency with which branch points are encountered. If C = rubber phase volume fraction, N = number of dispersed particles, and d = average particle diameter, N C -r (P, N is maximized as C increases or d decreases. The probability of an advancing crack hitting a particle as it advances an incremental distance is proportional to cross sectional area Nd2, which equals C/d. Again, C... 

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