Intercollisional dip

Beyond the binary systems. Spectroscopic signatures arising from more than just two interacting atoms or molecules were also discovered in the pioneering days of the collision-induced absorption studies. These involve a variation with pressure of the normalized profiles, a(a>)/n2, which are pressure invariant only in the low-pressure limit. For example, a splitting of induced Q branches was observed that increases with pressure the intercollisional dip. It was explained by van Kranendonk as a correlation of the dipoles induced in subsequent collisions [404]. An interference effect at very low (microwave) frequencies was similarly explained [318]. At densities near the onset of these interference effects, one may try to model these as a three-body, spectral signature , but we will refer to these processes as many-body intercollisional interference effects which they certainly are at low frequencies and also at condensed matter densities. 

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. 

The spectral profile of the intercollisional dip has been recorded as function of frequency, at constant densities, for a few gases and mixtures [130]. The lower part of Fig. 3.5 shows the low-frequency part of the spectral function, obtained for the 1 1 mixture of helium and argon at a total pressure of 160 atmospheres and room temperature [130]. The sudden drop in absorption below 10 cm-1 was seen to vary with density whereas, at the higher frequencies, no such variation of the shape is observed, other than the simple scaling of the entire profile with density squared. The time between collisions of He and Ar atoms is readily obtained as ti2 = 0.9 x 10-12 s. The product fxn equals unity for the... 

Fig. 3.5. Upper part The low-frequency portion of the spectral function for hydrogen at 140 atmospheres showing the intercollisional dip. Lower part The low-frequency portion of the spectral function for a 1 1 mixture of helium and argon at the total pressure of 160 atmospheres showing the intercollisional dip. Reproduced with permission from the National Research Council of Canada, from [130].

The most significant differences of the various profiles shown, Fig. 3.7, occur at the lowest frequencies. Albeit the measurements do not extend down to zero frequency, it seems clear that at the lowest frequencies the intercollisional process has affected the profiles. We notice the beginning of a dip similar to the ones seen in Fig. 3.5. At the higher densities the intercollisional wing of the inverted Lorentzian extends to much higher frequencies, the more so the higher the densities are the intercollisional dip persists to the highest densities. 

Similar results were also obtained for argon-krypton mixtures [252]. Apart from the low-frequency region of the intercollisional dip, the variation of the translational line shape is rather subtle reduced absorption profiles of a number of rare gas mixtures at near-liquid densities (up to 750 amagat) have been proposed which ignore these variations totally [252],... 

Liquids. The translational absorption profiles of a 2% solution of neon in liquid argon have been measured at various temperatures along the coexistence curve of the gas and liquid phases [107]. Figure 3.8 shows the symmetrized spectral function at four densities. At the lowest density (479 amagat for T = 145 K curve at top) the profile looks much like the binary spectral function seen in Fig. 3.2, especially the nearexponential wing for frequencies v > 25 cm-1. With increasing density the intercollisional dip develops at low frequencies, much like the dips seen at much lower densities in Fig. 3.5 - only much broader. 

An exception is the intercollisional dip which may be striking, especially in lines generated by isotropic overlap-induced dipoles rotational lines are less affected. 

The important point to be made here is that at low pressures, a few wavenumbers away from these narrow intercollisional features, the intensities of the spectra vary accurately as density squared. This important fact, which has been carefully verified on many occasions, indicates again the binary nature of the main parts of the spectra observed. The intercollisional dips show a variation with density that differs strikingly from that of the binary spectra. Here, we study the binary parts of the rotovibrational spectra the parts that show deviations from the density squared dependence will be considered below. 

At not too high gas densities (say 10 or 50 amagat), a large part of the induced rotovibrational spectra is demonstrably of a binary origin. (We may momentarily ignore small regions around the intercollisional dips where intensities do not follow a density square dependence.) In that sense, the spectra shown in Fig. 3.31 (and Fig. 3.37, etc.) may be considered the binary induced spectra of the rotovibrational bands. 

Intercollisional dip. In most examples of the rotovibrational spectra shown, one notices a fairly well developed dip at the Q transition frequency. 

Later studies showed the same phenomena in deuterium and deuterium-rare gas mixtures [335, 338, 305], and also in nitrogen and nitrogen-helium mixtures [336] in nitrogen-argon mixtures the feature is, however, not well developed. The intercollisional dip (as the feature is now commonly called) in the rototranslational spectra was identified many years later see Fig. 3.5 and related discussions. The phenomenon was explained by van Kranendonk [404] as a many-body process, in terms of the correlations of induced dipoles in consecutive collisions. In other words, at low densities, the dipole autocorrelation function has a significant negative tail of a characteristic decay time equal to the mean time between collisions see the theoretical developments in Chapter 5 for details. 

The intercollisional dips of the Qi lines were seen at all densities where spectra could be recorded, even if hydrogen is dissolved in liquid argon, etc., but at the highest densities (e.g., pressurized liquids) certain deviations... 

Intercollisional dip. The line shape of the intercollisional dip has been modeled by an inverted Lorentzian as was explained on pp. 124ff. 

In recent molecular dynamics studies attempts were made to reproduce the shapes of the intercollisional dip from reliable pair dipole models and pair potentials [301], The shape and relative amplitude of the intercollisional dip are known to depend sensitively on the details of the intermolecular interactions, and especially on the dipole function. For a number of very dense ( 1000 amagat) rare gas mixtures spectral profiles were obtained by molecular dynamics simulation that differed significantly from the observed dips. In particular, the computed amplitudes were never of sufficient magnitude. This fact is considered compelling evidence for the presence of irreducible many-body effects, presumably mainly of the induced dipole function. 

We start with the basic relationships ( Ansatz ) of collision-induced spectra (Section 5.1). Next we consider spectral moments and their virial expansions (Section 5.2) two- and three-body moments of low order will be discussed in some detail. An analogous virial expansion of the line shape follows (Section 5.3). Quantum and classical computations of binary line shapes are presented in Sections 5.4 and 5.5, which are followed by a discussion of the symmetry of the spectral profiles (Section 5.6). Many-body effects on line shape are discussed in Sections 5.7 and 5.8, particularly the intercollisional dip. We conclude this Chapter with a brief discussion of model line shapes (Section 5.10). 

Relationship with the intercollisional dip. The cancellation effect described by the doubly primed spectral moments y(naab>", y, abb ", is of course related to the intercollisional interference process observed near zero frequency, Fig. 3.5. The important difference is that the spectral moments are ternary quantities by design while the intercollisional dip is affected by many-body processes. 

This concludes the theory of collision-induced line shapes of binary systems, that is the line shape that one might observe at gas densities that are not too high - with one exception near zero frequency the intercollisional dip will always be present, no matter how low the pressure may be. The absorption dip is a many-body effect and is not obtainable from a binary theory (Poll 1980). At low gas densities, the intercollisional process appears only over a very small frequency interval near zero, of the order of the mean collision frequency, and it can in general be readily distinguished from the binary profile which extends over a much greater range of frequencies. 

Intercollisional interference is a many-body process. Poll (1980) has pointed out that, no matter how low the gas densities actually are, this many-body effect will always have to be reckoned with, for principal reasons. In more practical terms, at low densities intercollisional dips are generally reasonably well separable from the intracollisional profiles, because intercollisional profiles are relatively sharp while intracollisional ones are rather diffuse. In other words, a reasonably clear distinction between binary and many-body profiles is straightforward in low-density recordings. For this reason, separate theoretical discussions of the intra-and intercollisional processes are convenient and quite natural. 

It is, therefore, interesting to point out that in a recent molecular dynamics study, shapes of intercollisional dips of collision-induced absorption were obtained. These line shapes are considered a particularly sensitive probe of intermolecular interactions [301]. Using recent pair potentials and empirical pair dipole functions, for certain rare-gas mixtures spectral profiles were obtained that differ significantly from what is observed... 

Figures 6.8 and 6.9 compare the computational results with the existing measurements. All measurements shown agree very closely with the fundamental theory except for the dips discernible in the measurements near 4160 cm-1, the so-called intercollisional dips [404, 238]. That feature arises from correlations of the induced dipoles in subsequent collisions. It cannot be described by a theory that considers binary interactions only.

Apart from the intercollisional dips (which are not accounted for in a binary theory) and the effects of the ortho-H2 contamination, the agreement between theory and measurement is generally better than 10%. 

Intercollisional dips were also observed in the S lines of the vibrational... 

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

Ternary spectral moments of collision-induced absorption in hydrogen gas are analyzed in the H2 fundamental band in terms of pairwise additive and irreducible contributions to the interaction-induced dipole moment, Eqs. (1 - 7) [51]. Numerical results show that irreducible dipole components, especially of the exchange quadrupole-induced ternary dipole component, are significant for agreement with spectroscopic measurements, such as ternary spectral moments (Fig. 1) [53], an observed diffuse triple transition 3<3i centered at 12,466 cm-1 [52, 54, 55], and the intercollisional dip in compressed hydrogen gas, pp. 188 -190. 

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