Doppler linewidth

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. 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

Natural width of D lines 10 MHz Peak D2 cross section for Doppler linewidth 8.8 10 m2... 

Linewidth The spread in wavelengths or frequencies associated with a transition in an atom or molecule. There are three contributions natural linewidth associated with the lifetime of the transition pressure broadening associated with the presence with the other molecules nearby Doppler broadening associated with relative motion of the molecule and light source. 

In flames, only Doppler and, to a lesser extent, collisional broadening contribute significantly to the overall linewidth. 

Usually, mainly Doppler broadening determines the gain profile of a particular laser transition. Indeed, due to the different configurations achievable with gas lasers (namely, a large cavity length), the laser line can be narrower than the Doppler linewidth. Different experimental realizations of single-mode lasers are detailed elsewhere (Demtroder, 2(X)3). 

The spectral linewidths of fluorescence lines are determined in most spectral lamps by Doppler effect and pressure broadening and are therefore normally much broader than the natural linewidth, which is approached only by low-pressure hollow cathode lamps 23) operated at liquid helium temperatures. 

Since the single-mode laser linewidth is small compared to the absorption linewidth, one can probe the absorption profile by tuning the laser line across it, getting more information than by measuring the absorption coefficient averaged over the whole doppler width 6). 

With this technique the Doppler width could be reduced by two orders of magnitude below the natural linewidth, and spectral structures within the Doppler width could be resolved. Examples are the resolution of hyperfine structure components in an 12-beam using a single-mode argon laser (tunable within a few gigahertz) or the investigation of the upper state hfs-splitting in the atomic... 

In the case of a common upper level the fluorescence from this level due to excitation by the monochromatic wave will reflect this selective population with molecules having only velocity components inside the range Auz. Thus, observing the fluorescence in z direction on any transition from this upper level yields linewidths much smaller than the normal doppler width 322). In this way lines which are not resolved in normal fluorescence spectroscopy can be separated even if their frequency difference is much less than their doppler width 323). 

This method is specially suited for measurements of closely spaced Zeeman or Stark splitting and fine and hyperfine structures, which are separated only within their doppler linewidth 5 ). 

Fig. 24 Tunable-diode-laser spectrum of RQ0 of v9 of ethane. Trace (a) is the average of 250,000 scans and exhibits linewidths of 0.0022 cm-1 (the Doppler width is 0.0018 cm-1). Trace (b) results from the deconvolution of the data in trace (a) using a gaussian with a FWHM of 0.0022 cm-1 as a response function. Trace (c) is the Q branch calculated using a model that includes torsional splitting effects Av = 1.95 mk. Trace (c) is calculated for Av = 0.00075 cm-1, which is less than one-half the 300 K Doppler width.

Accuracy of the radiofrequency measurements of the classic 2S — 2P Lamb shift [15, 16, 23, 24, 25] is limited by the large (about 100 MHz) natural width of the 2P state, and cannot be significantly improved. New perspectives in reducing the experimental error bars of the classic 2S — 2P Lamb shift were opened with the development of the Doppler-free two-photon laser spectroscopy for measurements of the transitions between the energy levels with different principal quantum numbers. Narrow linewidth of such transi-... 

Linewidth is also affected by pressure broadening from collisions between atoms. Collisions shorten the lifetime of the excited state. The uncertainty in the frequency of atomic absorption and emission lines is roughly numerically equal to the collision frequency between atoms and is proportional to pressure. The Doppler effect and pressure broadening are similar in magnitude and yield linewidths of 10-3 to I0-2 nm in atomic spectroscopy. 

Doppler and pressure effects broaden the atomic lines by one to two orders of magnitude relative to their inherent linewidths. 

Figure 21-17 Relative bandwidths of hollow-cathode emission, atomic absorption, and a monochromator. Linewidths are measured at half the signal height. The linewidth from the hollow cathode is relatively narrow because the gas temperature in the lamp is lower than a flame temperature (so there is less Doppler broadening) and the pressure in the lamp is lower than the pressure in a flame (so there is less pressure broadening).

In most optical excitations the resolution is determined by the Doppler effect or the finite linewidth of the light source. The Doppler effect gives a typical frequency width of 1 GHz, and the width of the light source can be anywhere from 1 kHz to 30 GHz. We assume that these widths are larger than the radiative width. The photoionization cross sections from the ground states of H, alkali, and the alkaline earth atoms are given in Table 3.3. 20... 

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