Linear absorption factor

Linear absorption factor Fourier transform -dimensional Fourier transform -dimensional Fourier back-transform Polarization factor... 

J (s) = Jl (s) dsi is the slit-smeared scattering intensity, P(t is the total primary beam intensity per slit-length element - a quantity determined by the moving slit device. R is the distance between sample and detector slit as measured on the optical axis of the camera. L is the (fixed and known) length of the detector slit in the registration plane. H is the (adjustable) height of the detector slit. exp(—jut) is the linear absorption factor of the sample19. 

Absorption Coefficient, Linear—A factor expressing the fraction of a beam of x- or gamma radiation absorbed in a unit thickness of material. In the expression I=I0e+l x, I0 is the initial intensity, I the intensity of the beam after passage through a thickness of the material x, and p is the linear absorption coefficient. 

The ESA spectra of asymmetrical dyes in toluene are shown in Fig. 25. They show broad structureless bands in the NIR region (750-1,100 nm for G19, 850-1,100 nm for G40, and 950-1,100 nm for G188) and more intense transitions in the visible range (400-550 nm for G19, 400-600 nm for G40, and 450-650 nm for G188). Similarly to symmetrical anionic polymethine dyes (Fig. 20), the increase of conjugation length leads to a small red shift of ESA spectra, and to an enhancement of ESA cross sections and the ratio between the ESA and linear absorption oscillator strengths by approximately a factor of two. More detailed experimental description and quantum-chemical analysis can be found in [86]. 

In order to determine the structural factors maximizing 2PA cross section values, we analyze (8) from Sect. 1.2.1. For all cyanine-like molecules, symmetrical and asymmetrical, several distinct 2PA bands can be measured. First, the less intensive 2PA band is always connected with two-photon excitation into the main absorption band. The character of this 2PA band involves at least two dipole moments, /

symmetry forbidden for centro-symmetrical molecules, such as squaraines with C, symmetry due to A/t = 0, and only slightly allowed for polymethine dyes with C2V symmetry (A/t is small and oriented nearly perpendicular to /t01). It is important to note that a change in the permanent dipole moment under two-photon excitation into the linear absorption peak, even for asymmetrical D-a-A molecules, typically does not lead to the appearance of a 2PA band. 2PA bands under the main absorption peak are typically observed only for strongly asymmetrical molecules, for example, Styryl 1 [83], whose S0 —> Si transitions are considerably different from the corresponding transitions in symmetrical dyes and represent much broader, less intense, and blue-shifted bands. Thus, for typical cyanine-like molecules, both symmetrical and asymmetrical, with strong and relatively narrow, S (I > S) transitions, we observe... 

For a dilute gas, and when the equilibrium curve can be approximated by a linear relationship passing through the origin, Eq. (25) is applicable, and an average absorption factor A can be applied to describe the contactor. Under these conditions, an analytical solution of the material balance equation and the equilibrium relationship is possible, giving the Kremser equation ... 

The formula for the self-absorption factor is exact for gamma rays (see Experiment 3) but approximate for beta particles. That it is applicable at all is due to the near-linear decrease of the logarithm of the count rate with absorber thickness of a beta-particle group (see Figure 2.6 in the Radioanalytical Chemistry textbook). The obvious deviation is that this relation ends at the range of the maximum-energy beta particle, whereas it continues indefinitely for gamma rays. 

The requirements of high-energy resolution are well met by Si and Ge. The photoelectric effect increases with Z to Z, where Z is the atomic number of the substance, and the linear absorption coefficient for lOOkeV y rays in Ge is higher than in Si by a factor of about 40. Therefore, Ge crystals are better suited for measuring y radiation. Semiconductors with still higher atomic numbers, such as CdTe and Hgl2, have been investigated with respect to their suitability as detector materials, but they are not commonly used. 

The material has low linear absorption or the sample is thin so that the incident beam is capable of penetrating all the way through the sample. The absorption correction in this case is a function of Bragg angle as shown in Eq. 2.74. Once again, the constant coefficient l/2peff is usually omitted since it becomes a part of the scale factor ... 

The contribution to the recorded intensity should be corrected for each incident and scattered ray by the factor exp(—/r/), where is the linear absorption coefficient and / is the length of the ray in the sample, which consists of two components the first is the length ly passed by the incident ray in the sample to point A2 from the sample surface, and the second is the distance I2 traversed by the diffracted rays from point 42 to the sample surface. The distance I2 can be considered as a function of dihedral angle ij/ between planes U(Ai, A2, Pci) and H(Ai, A2, P), where P is a point on the conic in the sample plane. Because the scattered rays have different lengths in the sample the corrections, strictly speaking, should be introduced for each scattered ray ... 

One aspect of Eq. (90) deserving comment is its amenability for the identification of resonances. Three-photon resonances are manifest in the first and second terms, through the appearance of the factor (Euo — 3to — zTu) two-photon resonances (Euo — 2to — iTu) are featured in the second and fourth, and single-photon resonances (Euo — to — iTu) are seen in each of the first six. Since exploitation of the latter kind of resonance is in practice usually avoided because of the competing linear absorption with which it is associated, it is the two- and three- photon resonances that are of the most interest. Under suitable conditions, third-harmonic generation in either of those cases is driven largely by just two of the contributions to Eq. (90). Other contributions, signifying... 

Absorption means diminution of coherent x-ray intensity in the crystal through inelastic processes such as atomic absorption and fluorescence, photoelectron emission, and Compton effect extinction means intensity diminution due to loss through diffraction by fortuitously oriented mosaic blocks. The simple extinction expression due to Darwin, given in Eq. (18), is only a rough approximation more accurate treatments will be mentioned in what follows. In Eq. (17) the absorption factor is expressed in terms of the linear absorption coefficient /inn (calculated from tabulated values of the elemental atomic or mass absorption coefficients, updated values of which will appear in Vol. IV of International Tables,2 the path length f, of the incident ray from the crystal surface to the point of diffraction r, and the path length t2 of the diffracted ray from that point to the crystal surface. 

The remainder of the development of the calculational procedure is ordered in the same sequence in which the calculations are carried out. The calculational procedure is initiated by the assumption of a set of temperatures 7 and a set of vapor rates Vj from which the corresponding set of liquid rates L, is found by use of the total material balances presented below. This particular choice of independent variables was first proposed by Thiele and Geddes.14 On the basis of the assumed temperatures and total-flow rates, the absorption factors Aji appearing in Eq. (2-18) may be evaluated for component i on each plate j. Since matrix A, in Eq. (2-18) is of tridiagonal form, this matrix equation may be solved for the calculated values of the vapor rates for component i [denoted by (i )cJ by use of the Thomas algorithm4 which follows. Consider the following set of linear equations in the variables xu x2,. .., xN-u xN whose coefficients form a tridiagonal matrix. 



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