Ternary and many-body translational spectra

Above we have looked at the translational spectra of binary systems. These are obtainable experimentally at sufficiently low densities, especially when absorption of the infrared inactive gases is studied. An induced spectrum may be considered to be of a binary nature if the integrated intensity varies as density squared. In that case, the shape of the densities-normalized absorption coefficient, cc/q Q2, is invariant, regardless of the densities employed.  

With increasing density, N-body interactions with N = 3, 4,. .. may have a discernible effect on the total intensities as well as on the shape of the absorption profile. One may expect a ternary component, and at higher densities perhaps four-body, etc., spectral components that are superimposed with the binary spectrum. At the highest densities (e.g., liquids and pressurized fluids) every monomer may be assumed in permanent interaction with a substantial number of near neighbors. At intermediate densities, that is well below liquid densities, one may be 

We will look next at the variations of measured spectra due to many-body interactions. These manifest themselves in two different ways. One is a relatively sharp intercollisional dip near zero frequency. The other is a diffuse spectral component which leads to line narrowing. 

Intercollisional interference. We note that at the lowest frequencies the simple proportionality between absorption coefficient and product of gas densities breaks down. Under such conditions, certain many-body interactions affect the observations and modify the shape or intensities of the binary spectra, often quite strikingly. An example is shown in Fig. 3.3, a measurement of the absorption in a neon-xenon mixture in the microwave region, at the fixed frequency of 4.4 cm-1. Because of the frequency-dependent factor of g(v) that falls off to zero frequency as v2, absorption is extremely small at such frequencies, Eq. 3.2. As a consequence, it has generally been necessary to use sensitive resonator techniques for a measurement of the absorption at microwave frequencies 

This breakdown of the linear relationship between the absorption coefficient a and the product of densities, Q1Q2, indicates that the observed absorption is not a binary process. Specifically, for the case at hand, one can no longer assume that the measured absorption consists of an incoherent superposition of the pair contributions. Rather, the correlations of the dipoles that are induced in subsequent binary collisions lead to a partially destructive interference, an absorption defect that occurs if the product of the time T12 between Ne-Xe collisions, and microwave frequency, /, approaches unity [404], We note that for the spectra shown above, Figs. 3.1 and 3.2, the product fx 2 is substantially greater than unity at all frequencies where experimental data are shown and, consequently, incoherent superpositions of the waves arising from different induced dipoles occur. The intercollisional absorption defect is limited to low frequencies (Lewis 1980). 

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