Line width Doppler-broadened

Since At is of the order of 10-8 s, it can be calculated that the natural line width is about (10 -s nm). In practice this natural line width is broadened by several effects. These include the Doppler effect caused by the motion of absorbing atoms in their environment (usually a flame). At any given instance... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Of the four types of broadening that have been discussed, that due to the natural line width is, under normal conditions, much the smallest and it is the removal, or the decrease, of the effects of only Doppler, pressure and power broadening that can be achieved. 

In a skimmed supersonic jet, the parallel nature of the resulting beam opens up the possibility of observing spectra with sub-Doppler resolution in which the line width due to Doppler broadening (see Section 2.3.4) is reduced. This is achieved by observing the specttum in a direction perpendicular to that of the beam. The molecules in the beam have zero velocity in the direction of observation and the Doppler broadening is reduced substantially. Fluorescence excitation spectra can be obtained with sub-Doppler rotational line widths by directing the laser perpendicular to the beam. The Doppler broadening is not removed completely because both the laser beam and the supersonic beam are not quite parallel. 

Doppler broadening arises from the random thermal agitation of the active systems, each of which, in its own test frame, sees the appHed light field at a different frequency. When averaged over a Maxwellian velocity distribution, ie, assuming noninteracting species in thermal equilibrium, this yields a line width (fwhm) in cm C... 

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. 

The major requirement of the light source for atomic absorption is that it should emit the characteristic radiation (the spectrum) of the element to be determined at a half-width less than that of the absorption line. The natural absorption line width is about 10 4 (A), but due to broadening factors such as Doppler and collisional broadening, the real or total width for most elements at temperatures between 2000 ° and 3000 °K is typically 0.02 — 0.1 A. Hence, a high resolution monochromator is not required. 

Ideally, the emission line used should have a half-width less than that of the corresponding absorption line otherwise equation (8.4) will be invalidated. The most suitable and widely used source which fulfils this requirement is the hollow-cathode lamp, although interest has also been shown in microwave-excited electrodeless discharge tubes. Both sources produce emission lines whose halfwidths are considerably less than absorption lines observed in flames because Doppler broadening in the former is less and there is negligible collisional broadening. 

The second contribution to the line-width is Doppler broadening. While the transition energy AE may be constant, the frequency and therefore the energy of radiation increases if the molecule is approaching the source and decreases if the molecule is receding from the source. In terms of energy... 

Fig. 2. Absorption spectrum of CjHs obtained with the Zeeman-tuned He-Ne laser line at X = 3.39 fim. The dips in the transmission of magnetic field dependent laser intensity are due to different rotational transitions in CjHj, their width is determined by doppler broadening. (From Gerritsen, H.J., ref.

AxN, Axp, AxD, Axv line-profile half-widths in cm-1 for natural, pressure-broadened, Doppler-broadened, and combined Doppler-and pressure-broadened cases, respectively generally Ax = Av/c, where c is velocity of light... 

The data illustrated in Fig. 4(a) are methane absorption lines (0.02 cm-1 wide) observed with a four-pass Littrow-type diffraction grating spectrometer. For these data also, 256 points were taken. The data were obtained at low pressure, so that Doppler broadening is the major contributor to the true width of the lines. The straightforward inverse-filtered estimate with 15 (complex) coefficients retained is shown in Fig. 4(b). Figure 4(c) shows the restored function. The positions and intensities of the restored absorption... 

Besides the uncertainty broadening just discussed, there are other causes of line broadening which make line widths generally considerably greater than the natural width (3.88). The Doppler effect causes an apparent change in radiation frequency for molecules with a component of velocity cobs in the direction of observation of the radiation. Different molecules have different values of cobs and we get a Doppler broadened line. 

The use of CW tunable semiconductor lasers as a source in IR spectroscopy research makes possible a very great increase in resolving power over traditional IR grating spectrometers. IR studies with laser sources have been done on several gases (e.g., H20,NH3,SF6,N0). The laser line width is typically 1/100th the width of the Doppler-broadened absorption lines of the gases, so the fine details of the IR line shapes are... 

It is essential to correctly evaluate the absorption cross-section a relative to the laser line profile, the spectral resolution of the light collection optics, and the natural HO line width as influenced by Doppler, Voigt, or collisional broadening. The principles governing absorption measurements of HO over a distance through the atmosphere are discussed by Hiibler et al. (38). 

The measurements of 2s — Is transitions in magnetically trapped hydrogen have achieved a relative accuracy of one part in 1012 [21] by means of two-photon spectroscopy which eliminates the first-order Doppler broadening. It is hoped that this technique will allow the measurement of the Is — 2s transition with the accuracy limited only by the shape of the transition line dictated by quantum electrodynamics, i.e. to a few parts in 1015. Further, if the center of the Is — 2s line could be determined with the accuracy of a few parts in 103 of its width, the relative accuracy for this transition would increase to a few parts in 1018. 

The iT20Ne(6h — 5g) transition is an ideal case for a calibration line, because no Doppler broadening occurs from Coulomb deexcitation for the noble gas Ne as is the case for diatomic molecules like N2. Therefore, the line shape reflects exclusively the response of the spectrometer. The resolution achieved is 26 (seconds of arc), which is close to the theoretical limit of 22 for the chosen geometry. The line width of the TrN(5g — 4/) transition, measured to 50 , is dominated by Coulomb deexcitation [21]. 

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