Spectra Doppler broadening

Two-photon spectroscopy may also be used to obtain highest-resolution spectra. Doppler broadening, which originates in the random motion of molecules in the gas phase, prevents individual rotational lines of a vibronic transition from being resolved in conventional spectroscopy. However, if two photons of extremely monochromatic light coming from exactly opposite directions are absorbed simultaneously, the Doppler shifts of the two photons just cancel each other and the Doppler broadening is eliminated. As... 

Here k is the Boltzmann constant and Ao is the Avogadro number. Whereas collision broadening is independent of the location of the line in the spectrum, Doppler broadening is proportional to wavenumber. For a particular molecule, at a low... 

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.

In conclusion, the observed spectrum of an isolated Doppler-broadened line, along with some well-known constants and the easily measured temperature, contains all the information needed to determine the response function. Application details for this method are available in the literature (Jansson, 1968, 1970). 

For simplicity, suppose that we have an emission spectrum consisting of a single, predominantly Doppler-broadened line. This spectrum may be taken as an approximation to the case of widely separated and nonoverlapping lines of equal intensity. Again for simplicity, now consider the typical emission spectrum to be continuous, not sampled. Thus q(x) is given by q(x) = q0 exp( —x2) for a typical line, where q0 is the peak height. We have chosen the abscissa to be measured in either wavelength or wave number relative to a typical line center. For illustrative purposes only, the x interval for the observation is taken to be 2 Ax. If the line is centered in this interval at x = 0, we can never have q(x) < exp ( — Ax2). 

Fig. 28 Pure rotational spectrum of C>2. Trace (a) is the S3 transition recorded at a pressure of 1.0 atm. Trace (b) is the result of deconvolving the S3 profile with a Voigt profile to remove most of the pressure broadening, Doppler broadening, and instrument effects. Trace (c) was calculated using a 0.035-cm-1 Gaussian profile and calculated spin splittings. The traces are scaled to the same height.

The relatively weak dependence on the ratio Ktat/ i abs suggests that the modification to our calculated results will not be great except at very early times. The effective temperature calculated for Model 10H, for example, is, without modification, within 15% of the values inferred from the spectrum (Suntzeff, private communication) on days 1.14 (13,600 K), 1.51 (12,700 K), and 1.85 (11,690 K). Figure 5 illustrates the effect for K<0 0.3, and 0.1. The latter corresponds to a color temperature one third greater than the effective emission temperature. Karp et a1. (1977) have considered the effect of Doppler broadened lines on the bound-bound opacity. For typical photospheric densities (1012 g cm-3) and temperatures (5000 K to 50,000 K) the line opacity is approximately 20% to 200% that of electron scattering (see their Table 3). This should keep the color temperature within about 20% of the effective emission temperature. 

Photon Correlation. Particles suspended in a fluid undergo Brownian motion due to collisions with the liquid molecules. This random motion results in scattering and Doppler broadening of the frequency of the scattered light. Experimentally, it is more accurate to measure the autocorrelation function in the time domain than measuring the power spectrum in the frequency domain. The normalized electric field autocorrelation function g(t) for a suspension of monodisperse particles or droplets is given by ... 

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 spectrum 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. 

A remarkable feature of these spectra is the resolution of individual rotational lines in such large molecules. [Note that the expanded spectrum in, for example, Figure 9.47(a) covers only 5000 MHz (0.17 cm-1)]. This is due partly to the very low rotational temperature (3.0 K for aniline and 2.2 K for aniline Ar), partly to the reduction of the Doppler broadening and partly to the very high resolution of the ring dye laser used. 

Figure 7.27 Doppler broadening spectrum from two detectors in coincidence as a function of the Doppler shift momentum in atomic units. MSSQ samples with 0% and 40% porogen are shown. The lead filter is used to stop the low energy third photon from reaching a detector. In that case, only two photon events are observed. Statistical errors are of the order of the line width and smaller.

Figure 1.18. Part of the two-photon spectrum of benzene at different resolutions a) vibrational structure of the S - S transition, b) Q branch of the most intense vibrational line (I4i) with a resolution 5v limited by the Doppler broadening, and c) elimination of the Doppler broadening which yields individual rotational lines (by permission from Neusser and Schlag, 1992).

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