Linear-absorption coefficient

Other absorption coefficients are also used, the most important of which is the linear absorption coefficient, ni, used in thickness measurements. In accordance with its definition, ni is given by the equation... 

D, is the dose rate emerging from a shield of thickness t u is the linear absorption coefficient of shield material. 

Absorption Coefficient—Fractional absorption of the energy of an unscattered beam of x- or gamma-radiation per unit thickness (linear absorption coefficient), per unit mass (mass absorption coefficient), or per atom (atomic absorption coefficient) of absorber, due to transfer of energy to the absorber. The total absorption coefficient is the sum of individual energy absorption processes (see Compton Effect, Photoelectric Effect, and Pair Production). 

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. 

Absorption Coefficient, Mass—The linear absorption coefficient per cm divided by the density of the absorber in grams per cubic centimeter. It is frequently expressed as p/p, where p is the linear absorption coefficient and p the absorber density. 

Example PET. Let us consider polyethylene terephthalate) (PET, C oHK(h n, Ppet=1-35 g/cm3) of tpET =2 mm thickness and an X-radiation wavelength X= 0.15418 nm (CuKa). We set up a table with one row for each chemical element and sum both the masses and the mass absorption coefficients multiplied by the masses. After normalization to the molecular mass of the PET monomer, 192.17 amu, we find (p/p)pet = 1291.97/192.17 cm2/g a value 6.72 cm2/g. Considering the density ppet we find for the linear absorption coefficient Ppet =... 

Since ft and /" represent an absorption of the propagating beam, they are related to the linear absorption coefficient p oS). This relation is called the optical theorem... 

Recall from Eq. (6.71) that the fractional change in light intensity, dl/I, over a distance x within the absorbing medinm is directly proportional to the linear absorption coefficient,... 

XAS refers to the measurement of the variation of the linear absorption coefficient, p, as a function of the energy E of the incident photons. In a transmission experiment, the absorption coefficient of a sample of thickness x is related to the intensities of the incident (I0) and transmitted (I) beams through the Beer-Lambert s law I = Io exp(-px). The X-ray absorption spectrum is typically plotted as px vs E as shown in Figure 1. 

In concentrated systems obtained in a thin uniform shape, the simplest way to record X-ray absorption data is the transmission mode in which the incident and transmitted photons are directly measured by means of ionisation chambers. However, in dilute systems or for surface characterisations, data are usually recorded using secondary effects resulting from the creation of the core hole during the absorption process and from its subsequent relaxation by radiative or non-radiative decays. These processes are the X-ray fluorescence emission and the total electron yield (TEY) emission, respectively. In these detection modes, the linear absorption coefficient is proportional to the ratio of the fluorescence or TEY intensity to... 

The mathematical reconstruction of a property field, F(x,y), from its projection in the 0 direction is the basis of "Computerized Tomography" (1,2). An identical technique can be used to reconstruct a field of linear absorption coefficient functions in a combusting flow field from multiangular path integrated absorption measurements. The linear absorption coefficient is the familiar N.Q. product, where is the concentration of species i and Q. is the absorption cross section of species i at the frequency v. The Bouguer-Lambert-Beer law states that... 

The linear absorption coefficient functions can thus be reconstructed using only projection data. 

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