Profile wings

Bottom panel Observed and synthetic Ha profiles for HD 140283 (black 5760K, grey 5560 K). The data was retrieved from the VLT archive (observing date 2000-06-15), reduced using REDUCE and rectified using parabolic fits to the continua in adjacent orders. Notice the variable telluric features which somewhat suppress the blue wing. An effective temperature of 5560 K (best estimate of [3]) is clearly too low, 5760 K (derived from the UVES POP spectrum) too high. At a S/N of 150, observational systematic errors are thus of the order of at least 100 K. 

For still larger column densities, the damping wings completely overcome the contribution of the Doppler core to the EW (see Fig. 3.9) and we can take for the whole line profile A co A

[Pg.62]

For resonance lines, self-absorption broadening may be very important, because it is applied to the sum of all the factors described above. As the maximum absorption occurs at the centre of the line, proportionally more intensity is lost on self-absorption here than at the wings. Thus, as the concentration of atoms in the atom cell increases, not only the intensity of the line but also its profile changes (Fig. 4.2b) High levels of self-absorption can actually result in self-reversal, i.e. a minimum at the centre of the line. This can be very significant for emission lines in flames but is far less pronounced in sources such as the inductively coupled plasma, which is a major advantage of this source. 

Thus, spectral interferences in atomic spectroscopy are less likely than in molecular spectroscopy analysis. In any case, even the atomic lines are not completely monochromatic i.e. only one wavelength per transition). In fact, there are several phenomena which also bring about a certain broadening . Therefore, any atomic line shows a profile (distribution of intensities) as a function of wavelength (or frequency). The analytical selectivity is conditioned by the overall broadening of the lines (particularly the form of the wings of such atomic lines). 

Near the line centers, the spectral functions have sometimes been approximated by a Lorentzian. The far wings, on the other hand, may be approximated by exponential functions as Fig. 3.2 might suggest. However, better model profiles exist see Chapters 5 and 6 [421, 102, 320], Model profiles have been useful for fitting experimental spectra, for an extrapolation of measured profiles to lower or higher frequencies (which is often needed for the determination of spectral moments) and for a prediction of spectra at temperatures for which no measurements exist. We note that van der Waals dimer structures (which appear at low frequencies and low pressures) modify the Lorentzian-like appearance more or less, as we will see. 

The most significant differences of the various profiles shown, Fig. 3.7, occur at the lowest frequencies. Albeit the measurements do not extend down to zero frequency, it seems clear that at the lowest frequencies the intercollisional process has affected the profiles. We notice the beginning of a dip similar to the ones seen in Fig. 3.5. At the higher densities the intercollisional wing of the inverted Lorentzian extends to much higher frequencies, the more so the higher the densities are the intercollisional dip persists to the highest densities. 

Liquids. The translational absorption profiles of a 2% solution of neon in liquid argon have been measured at various temperatures along the coexistence curve of the gas and liquid phases [107]. Figure 3.8 shows the symmetrized spectral function at four densities. At the lowest density (479 amagat for T = 145 K curve at top) the profile looks much like the binary spectral function seen in Fig. 3.2, especially the nearexponential wing for frequencies v > 25 cm-1. With increasing density the intercollisional dip develops at low frequencies, much like the dips seen at much lower densities in Fig. 3.5 - only much broader. 

Figure 3.29 compares two line profiles obtained in the fit. The solid line represents the rotational line profile in the zero density limit (ii = 8.4 x 10-14 s, T2 = 5.1 x 10 14 s, from Fig. 3.28). The dashed line shows the profile at 185 amagat of argon (n = 8.94 x 10-14 s, 12 = 2.70 x 10-14 s). The amplitudes S are here arbitrarily set to unity, S = 1, in both cases so that the areas under the curves are equal. We note a very slight narrowing of the profiles near the line centers this is caused by ii which increases slightly with density. Moreover, the far wing intensities increase with increasing argon density which is related to the decreasing 12 values see the discussion of the properties of the BC profile, p. 271.

Fig. 3.51. Logarithmic plot of the normalized induced dipole moment correlation function, C(t), for hydrogen-argon mixtures at 165 K. Measurements at 90 amagat ( ) 450 amagat ( ) and 650 amagat (o). The broken lines at small times represents the portion of C(t) affected by the smoothing of the wings of the spectral profiles. Reproduced with permission by the National Research Council of Canada from [109].

It was widely believed that the main defect of classical line shape can approximately be corrected with the help of one of the various desym-metrization procedures proposed in the literature that formally satisfy Eq. 5. 73. However, it has been pointed out that the various procedures give rise to profiles that differ greatly in the wings [70]. While they are sufficient to generate the asymmetry, Eq. 5.73, the resulting desym-... 

For any given potential and dipole function, at a fixed temperature, the classical and quantum profiles (and their spectral moments) are uniquely defined. If a desymmetrization procedure applied to the classical profile is to be meaningful, it must result in a close approximation of the quantum profile over the required frequency band, or the procedure is a dangerous one to use. On the other hand, if a procedure can be identified which will approximate the quantum profile closely, one may be able to use classical line shapes (which are inexpensive to compute), even in the far wings of induced spectral lines a computation of quantum line shapes may then be unnecessary. 

The desymmetrization procedures are compared in Fig. 5.6 and Table 5.3, using the classical He-Ar profile at 295 K as an example (lowermost curve, solid thin line in the figure column 2 in the Table). The quantum profile is also shown for comparison (heavy solid line last column). At positive frequencies, all four procedures mentioned enhance the wing of the classical line shape toward that of the quantum profile. Specifically,... 

P-1 (dotted line column 3) approximates the quantum profile at the 2% level up to frequencies around 100 cm-1, but deteriorates quickly above roughly 200 cm-1 beyond the 10% level, rendering it less desirable for the analyses of measurements taken over a broad region of frequencies. For the positive frequency wing, the logarithmic slope of the P-1 profile is that of the classical profile, which is very different from that of the quantum profile. 

Of the four procedures considered, the Egelstaff procedure P-4 (scaled) is clearly the best approximation to the exact quantum profile. It results in the almost exact quantum profile from the classical profile, even far in the wing where intensities have fallen off to a small fraction of the peak intensity. In other words, quantum corrections based on the ideal gas approximation are the leading ones. Next are the extremely simple procedures P-2 and P-3. The widely used procedure P-1, on the other hand, leads to rapidly deteriorating wings and should be avoided, unless limited to a narrow frequency band near the line center. 

Specifically, an exact quantum profile of Ne-Ar pairs (which was in agreement with the measurement) was compared with an extended CAA profile computation, using the same input [71]. The approximation to the profile did not differ from the exact profile by more than 10% even in the far wing, where the intensities have dropped by nearly two orders of magnitude relative to the peak. Considering the extreme simplicity of the model, this agreement is remarkable. 

Related to this near absence of logarithmic curvature of the wings is the fact that the KO model is superior in describing line profiles resulting from overlap induction. The BC shape, on the other hand, shows more curvature in the wing, as this is needed for the modeling of profiles generated by low-order multipolar induction. Purely quadrupole-induced components are closely modeled by the BC shape. 

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