Peak absorption coefficient

Changing the base glass caused considerable changes in the -state mean life. To ascertain whether this was the result of variations in spontaneous emission matrix elements or radiationless transition probabilities, the peak absorption coefficient of the 4/9/2 —4F3/2 transition was plotted... 

Figure 35. In (a) and (b) are shown the change in peak absorption coefficient with decay time for 2 and 6 per cent Nd glasses, respectively [from Ref. (130)],...

Fig. 15. Plots of the peak absorption coefficients of the K = 0 lines of different J transitions for methylcyanide. The variation of intensity for the different K components is shown for the 7=6-5 transition. The inset gives the wavelength region in which the strongest rotational lines occur for various symmetric top molecules. The excitation temperature is assumed to be 150 °K...

In practice this relation is only an approximation because of the uncertainty of all of the parameters. Nevertheless it is still an useful estimation. For example CS2 m water should be measured. The ZnSe-IRE with a length of 50 mm, a thickness of 3 mm, and windows with an angle of 45 °, allow 12 reflections in the sample area. It is coated with a PDMS membrane (n w 1.4) of 20 Xm thickness. The band at 1521 cm (= 6.575 pm) with a peak absorption coefficient of 3100 L mol cm is evaluated. With Eq. 6.5-1 and 6.5-3 the pathlength is calculated to be (V 0.31 A = 24.5 pm. Within this spectral range the noise amplitude is measured as 0.001 absorbance units. The enrichment factor/yv//w is 66. 

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 ... 

Fig. 7.4. Part of the absorption spectrum of i 3/2(AZ) in a FZ natSi sample with [A/] 101B cm-3. The peak absorption coefficients of fines 1 (not shown) and 2 are 2.8 and 6cm 1, respectively, and line 3 is absent...

When V = V(f the centre frequency and maximum of the line profile, the peak absorption coefficient is given by... 

In applying this formula to the determination of the peak absorption coefficient, it is customary to combine with it the rotational partition function contribution kT/hB giving the term hB J/kT, (ref 3, p. 117). This equates to hvpd/IkT in linear and symmetric top molecules and replaces the fimn term in Equation 1.21, with becoming fj. This latter term takes into account the Boltzmann occupancy factor for that state fj = exp — [57(7 + )/kT]... 

At the line peak, when the absorption coefficient is maximum, v = Vq and the peak absorption coefficient is independent of pressure. 

Making the substitutions that gave Equation 1.34 now gives for the modified peak absorption coefficient a ax... 

Significance of the Peak Absorption Coefficient Functions for Quantitative Millimetre Wavelength Spectrometry... 

The peak absorption coefficient of OCS, 10 m", occurs at 462 GHz. This is by no means, however, the optimum working frequency due to the non-ideal behaviour of most MMW detectors. Commercial Schottky barrier mixer diode detectors show a quadratic roll-off in sensitivity at frequencies >100 GHz. If this is factored into Equation 6.1, the peak sample sensitivity occurs around 300 GHz, and the response is so flat that even at 100 GHz it has only fallen off by a factor of two. What is common to both curves is the dramatic fall-off in sample sensitivity at frequencies <100 GHz, reinforcing the point that the band 26-40 GHz is ill suited to high-sensitivity analytical spectroscopy. 

Figure 6.1 Peak absorption coefficient A and sample sensitivity B for OCS Plotted vs. frequency. B = 0.202 cmT at 300 K kT 200 cmT ...

MMW spectra possess a number of features that make direct readout of sample concentration from a measurement less than straightforward. Although the peak absorption coefficient of the sample may be determined in several ways itemised below. Equations 1.24 and 1.48 show that additional information about linewidth, temperature, occupation of vibrational states and even Doppler broadening is required to obtain the analyte concentration. Such calculations can be incorporated into any anal5dic program, but the parameters required are often not readily available in the literature and may need to be determined directly. 

Although some correction must still be made for changes in the linewidth broadening parameter, the calculations required are much less detailed. In particular, practical measurements are much simplified by exploiting the insensitivity of the peak absorption coefficient to pressure (Section 1.2). This technique becomes especially effective if combined with the line profile integration described in the next section. 

The peak absorption coefficient of the transition, 7max) if Doppler broadening is neglected, is given by... 

Concerning the intensity of rotational transitions, it should be briefly recalled that the formula for absorption coefficients involves the transition dipole moment. An important quantity often measured is the absorption coefficient at the resonant frequency Vq, called the peak absorption coefficient ot,, which results to be proportional to the transition moment ( (m /i K) ) as well as to frequency ... 

A useful quantitative measure of the intensity of a rotational transition is given by the peak absorption coefficient o, defined by... 

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