Spectral lines absorption coefficient

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

In addition to measuring total recombination coefficients, experimentalists seek to determine absolute or relative yields of specific recombination products by emission spectroscopy, laser induced fluorescence, and optical absorption. In most such measurements, the products suffer many collisions between their creation and detection and nothing can be deduced about their initial translational energies. Limited, but important, information on the kinetic energies of the nascent products can be obtained by examination of the widths of emitted spectral lines and by... 

Fig. 14. The 1-H line at 6 K in n+ GaAsiSi implanted with a 500 nA current of 190 keV protons. The spectral resolution is 0.4 cm 1, (a) as implanted, (b) after 20 min. annealing at 200°C. (c) after additional 20 min. annealing at 400°C. The apparent increase of the absorption coefficient in (c) is due to the diffusion of hydrogen throughout the Si-doped layer. B. Pajot et al., Mat. Res. Soc. Symp. Proc, 104, 345 (1988). Materials Research Society.

Monochromatic detection. A schematic of a monochromatic absorbance detector is given in Fig. 3.12. It is composed of a mercury or deuterium light source, a monochromator used to isolate a narrow bandwidth (10 nm) or spectral line (i.e. 254 nm for Hg), a flow cell with a volume of a few pi (optical path 0.1 to 1 cm) and a means of optical detection. This system is an example of a selective detector the intensity of absorption depends on the analyte molar absorption coefficient (see Fig. 3.13). It is thus possible to calculate the concentration of the analytes by measuring directly the peak areas without taking into account the specific absorption coefficients. For compounds that do not possess a significant absorption spectrum, it is possible to perform derivatisation of the analytes prior to detection. 

For most treatments, the spectral density, J(a>), Eq. 2.86, also referred to as the spectral profile or line shape, is considered, since it is more directly related to physical quantities than the absorption coefficient a. The latter contains frequency-dependent factors that account for stimulated emission. For absorption, the transition frequencies ojp are positive. The spectral density may also be defined for negative frequencies which correspond to emission. 

We note that in a classical formula Planck s constant does not appear. Indeed, the zeroth moment Mo of the spectral density, J (o), does not depend on h, as the combination of Eqs. 5.35 and 5.38 shows. On the other hand, the classical moment y of the absorption profile, a(cu), is proportional to /h because the absorption coefficient a depends on Planck s constant see the discussions of the classical line shape below, p. 246. In a discussion of classical moments it is best to focus on the moments Mn of the spectral density, J co), instead of the moments, yn, of the spectral profile. 

In other words, for tetrahedral molecules, these relationships differ from the ones used for the linear molecules, especially Eq. 4.18. As a consequence, we must rederive the relationships for the spectral line shape and spectral moments. If the intermolecular interaction potential may be assumed to be isotropic, the line shape function Vg(a> T), Eq. 6.49, which appears in the expression for the absorption coefficient a, Eq. 6.50, may still be written as a superposition of individual profiles,... 

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

The most time consuming parts of the forward model are the calculation of the absorption coefficients and the calculation of the radiative transfer. A spectral resolution of Av = 0.0005 cm 1 is considered necessary in order to resolve the shape of Doppler-broadened lines. To avoid repeated line-shape and radiative transfer calculations at this high resolution, two optimizations have been implemented ... 

Let us mention several papers by Ya.B. on various problems of molecular physics and quantum mechanics which have not been included in this volume. Among the problems considered are the peculiar distribution of molecules according to their oscillatory modes when the overall number of oscillatory quanta does not correspond to the temperature of translation [9], the influence of the nuclear magnetic moment on the diffusion coefficient [10] and on absorption of light by prohibited spectral lines [11],... 

Again, in HR-CS AAS these problems are essentially nonexistent for the same reasons as given above. Firstly, because of the relatively constant, very intense emission of the primary radiation source, there are no more weak lines that is, the same high SNR will be obtained on all analytical lines, regardless of their spectral origin. The only factors that will have an influence will be the absorption coefficient and the population of the low excitation level in case nonresonance lines are used. Secondly, because of the high resolution of the monochromator, and the visibility of the entire spectral environment of the analytical line in HR-CS AAS, potential spectral interferences can easily be detected, and in addition cannot influence the actual measurement, except in the rare case of direct line overlap. However, even in this case, HR-CS AAS provides an appropriate solution, as discussed in the previous section. 

Each spectral line is characterized by an absorption coefficient kp which exhibits a maximum at some central characteristic wavelength or wave number r 0 = l/ o and is described by a Lorentz probability distribution. Since the widths of spectral lines are dependent on collisions with other molecules, the absorption coefficient will also depend upon the composition of the combustion gases and the total system pressure. This brief discussion of gas spectroscopy is intended as an introduction to the factors controlling absorption coefficients and thus the factors which govern the empirical correlations to be presented for gas emissivities and absorptivities. 

The specific absorption coefficient of the dye K dye (cm ppm ) is the easiest to determine of all the optical parameters in this kind of problems. For dye concentrations which are not too high, one can expect that Lambert-Beer law is satisfied that is, the transmittance of an aqueous solution of the dye should follow an exponential decay with concentration. This means that a linear relationship exists between the absorbance of the samples and dye concentration for each measured wavelength. Spectral measurements of the transmittance of solutions of the dye (in the absence of catalyst) for different concentrations can be made on a spectrophotometer. The specific absorption coefficient for different wavelengths is the slope of a straight line fit to these data, divided by the length of the spectrophotometer test cell. 

In this method fluorescent intensities are calculated from first principles. The data needed for the calculation are (1) the spectral distribution (intensity vs. wavelength) of the primary beam from the x-ray tube, (2) mass absorption coefficients ju/p of all elements in the sample, and (3) fluorescent yields w of all elements. The calculations require that measured line intensities I from the unknown be converted into relative intensities R by comparison with pure metal standards. (Use of R rather than / values eliminates the need to know the wavelength-dependent efficiencies of reflection by the analyzing crystal and detection by the counter.)... 

The measured peak absorption coefficient, Kmax, for a discrete impurity transition depends on the oscillator strength of the transition and on the impurity concentration. The measured profile of a recorded line is the convolution product of its true profile by the instrumental function of the spectroscopic device used. It depends significantly on the ratio of the true FWHM of the line to the spectral resolution (the spectral band width) of the spectroscopic device. When this ratio is of the order of 3 or above, the measured FWHM can be considered as the true FWHM and the observed profile is close to the true profile. For lower values of this ratio, the measured FWHM increases steadily while the measured value of Kmax decreases, and it is assumed that when the ratio becomes l/3 or smaller, the measured FWHM is the spectral resolution and the measured profile the instrumental function. This effect is known as instrumental broadening. For isolated lines, the absorption coefficient can be integrated over the entire line to give an integrated absorption I A ... 

Measurement of the intensity differences of the 2p line at LHeT in intrinsic FZ silicon samples and the same samples after NTD with different doses have been made by Pajot and Debarre [202]. The peak absorption coefficient K2P i of the 2p i line was measured with a spectral resolution <)vs of 0.45 cm-1 (53 peV) and for the P concentrations introduced, the observed FWHM of 2p i was equal to 5i>s. For P concentrations up to 1 x 1015cm-3, the valid relationship for 5vs > 0.45 cm 1 is ... 

All these quantities are equivalent since they all depend on the same transition matrix element, although their units are not the same. The / value has the advantage of being a dimensionless quantity. With broad band illumination, the appropriate quantities are those which are integrated over the spectral feature, such as the / value or the Einstein coefficient. With narrow band illumination (i.e. a monochromatic source narrower than the spectral feature), it is appropriate to use a quantity which is defined point by point within the line profile, such as the absorption coefficient, the cross section, or the differential oscillator strength df/dE. 

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