Doppler line width

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. 

Figure 9.3 Doppler limited laser line with twelve axial modes within the line width...

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. 

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. 

In order to dissipate the recoil energy Mossbauer was the first to use atoms in solid crystal lattices as emitters and also to cool both emitter and absorber. In this way it could be shown that the 7-ray emission from radioactive cobalt metal was absorbed by metallic iron. However, it was also found that if the iron sample were in any other chemical state, the different chemical surroundings of the iron nucleus produce a sufficient effect on the nuclear energy levels for absorption no longer to occur. To enable a search for the precisely required absorption frequency, a scan based on the Doppler effect was developed. It was noted that a velocity of 102 ms-1 produced an enormous Doppler shift and using the same equation (7) it follows that a readily attainable displacement of the source at a velocity of 1 cms-1 produces a shift of 108 Hz. This shift corresponds to about 100 line-widths and provides a reasonable scan width. 

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. 

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... 

The second factor involves the theory that defines the natural width of the lines. Radiations emitted by atoms are not totally monochromatic. With plasmas in particular, where the collision frequency is high (this greatly reduces the lifetime of the excited states), Heisenberg s uncertainty principle is fully operational (see Fig. 15.4). Moreover, elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. The natural width of spectral lines at 6000 K is in the order of several picometres. 

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... 

Second, we consider the diffuseness in gas-phase spectra.74- 78 An account of those aspects of gas-phase spectra that relate to electronic relaxation is only possible if the other causes of diffuseness are first made clear. We therefore summarize some of the characteristics of vibration-rotation spectra with special reference to a molecule like naphthalene at a vapor pressure of 1 mm76 The Doppler width of each line is 0.022 cm-1 the rotational line spacing can be as small as 0.0004 cm-1, or 50 lines per Doppler width the length of a sequence is 300 cm 1 and the average sequence spacing is 5 cm-1 for anthracene the average sequence spacing... 

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 data from Table 3.7 make it possible to make a few estimates. Let us consider a concrete example. If the length of the resonator is L = 2 m, the Doppler contour, say of a K2 molecule in the BlTlu state, contains about 11 axial modes, the distance between them being Au>i = ttc/L m 4 108 s-1. If we assume that the width of the Bennet dip is equal to the homogeneous line width, rBen T = 0.86 108s 1 (see... 

The Doppler-free two photon transition l3 —> 23S i at 1.23 x 1015 Hz2 [13] can be improved to an accuracy limited only by the natural line width of 1 MHz if recent techniques for the frequency counting in the optical region are used [20,21,22],... 

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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