Cross section intensity

FRAP data were analysed by a non-linear least squares fit to an expression [8,23,29], defining the time dependence of the fluorescence recovery (F(t)). The apparatus as described above delivered a laser spot of uniform circular cross sectional intensity to the sample and the recovery curves obtained could be analysed with the expression ... 

Figure 19. Photon energy dependence of the photoionization cross section intensity of photoelectron peak varies depending upon input photon energy, due to the variation in the deBroglie wavelength of outgoing electron. These wavelengths are compared to the radial wavefunctions of Cu 3d and Cl 3p orbitals. Reproduced from Ref. 28. Copyright 1985, American Chemical Society.

Plate heat exchangers are intensively used in the food and pharmaceutical industries, but less so in chemical industries. Because of the small cross section, intensive heat transfer can be realized, as for example from 400 W/m2 K with viscous fluids up to 6000W/m2 K for water. Gasket plate devices are the most common. The effective area per plate can be larger than lm2. Up to 400 plates can be... 

Energies, polarizations, photoionization cross sections (intensity dependence on photon energy)... 

Figure 6. Beam profiles and diffraction patterns for the experiment shown in Figure 3. Intensity vs. x for Electrode + Beam represents the cross-sectional intensity of the laser beam, truncated by the electrode its diffraction pattern was calculated using a Fourier transform algorithm. The lower pair of plots shows the same case with a chromophore near the electrode. The sharpness of the electrode edge is decreased, and the wings of the diffraction pattern are affected the most. The dashed line shows the diffraction from a bare electrode for comparison.

The experimental results are given in Fig. 12. Plotted is the total reaction cross section (intensity of product fluorescence) versus the angle B between E and V. The signal is significantly dependent on B with a maximum at B=9(P and a minimum at B=0. That is, the difference of cross sections for j roughly perpendicular and parallel to v (a(9(P) - a((P)) is larger than zero as it is also for K + HF. 

Figure 6.3. PS-OCT measurements of injection-molded polystyrene part (A) OCT cross-section (intensity image) (B) polarization-sensitive retardation image exhibiting a homogenous core and anisotropic surface regions. (From Stifter et al. [42] reproduced with permission.)...

SAXS cross-sectional intensity (Ql/C) versus Q for organogels of 5 in 1-octanol (1 ( ),... 

The algorithm contains five minimisation procedures which are performed the same way as in the method " i.e. by minimisation of the RMS between the measured unidirectional distribution and the corresponding theoretical distribution of die z-component of the intensity of the leakage field. The aim of the first minimisation is to find initial approximations of the depth d, of the crack in the left half of its cross-section, die depth d in its right half, its half-width a, and the parameter c. The second minimisation gives approximations of d, and d and better approximations of a and c based on estimation of d,= d, and d,= d,j. Improved approximations of d] and d4 are determined by the third minimisation while fixing new estimations of d dj, dj, and dj. Computed final values dj , d/, a and c , whieh are designated by a subscript c , are provided by the fourth minimisation, based on improved estimations of d, dj, dj, and d . The fifth minimisation computes final values d, , d, dj, d while the already computed dj , d/, a and c are fixed. 

Experimentally, it is these invariants (equation (B 1.3.17), equation (B 1.3.18) and equation (B 1.3.19)) that can be obtained by scattering intensity measurements, though clearly not by measuring the total cross-section only. 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

It should be noted that this technique is not without some disadvantages. The blackbody emission background in the near IR limits the upper temperature of the sample to about 200°C [43]. Then there is the dependence of the Raman cross-section ( equation (B 1.3.16) and equation ( B1.3.20)-equation ( B 1.3.21)) which calls for an order of magnitude greater excitation intensity when exciting in the near-IR rather than in the visible to produce the same signal intensity [39]. 

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

The detection technique can also have an effect upon the angle- and velocity-dependent intensities. Cross sections refer to fluxes of molecules into a given range of velocities and angles. The connnonly employed teclmique of mass spectrometric detection provides a measure of the density in the ionization region. Since density and flux are related by the velocity, we must include a factor of 1/v hr making the transfonnation indicated in equation (B2.3.10) from the CM cross sections to tire measured laboratory intensities. 

Figure B2.3.6. CM angle-velocity contour plot for the F + D2 reaction at an incident relative translational energy of 1.82 kcal mol [26], Contours are given at equally spaced intensity intervals. This CM differential cross section was used to generate the calculated laboratory angular distributions given in figure B2.3.4. (By pennission from AIP.)...

Equations (C3.4.5) and (C3.4.6) cover the common case when all molecules are initially in their ground electronic state and able to accept excitation. The system is also assumed to be impinged upon by sources F. The latter are usually expressible as tlie product crfjo, where cr is an absorjition cross section, is tlie photon flux and ftois tlie population in tlie ground state. The common assumption is tliat Jo= q, i.e. practically all molecules are in tlie ground state because n n. This is tlie assumption of linear excitation, where tlie system exhibits a linear response to tlie excitation intensity. This assumption does not hold when tlie extent of excitation is significant, i.e. 

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