Intercollisional interference

Of the four procedures considered, the Egelstaff procedure P-4 (scaled) is clearly the best approximation to the exact quantum profile. It results in the almost exact quantum profile from the classical profile, even far in the wing where intensities have fallen off to a small fraction of the peak intensity. In other words, quantum corrections based on the ideal gas approximation are the leading ones. Next are the extremely simple procedures P-2 and P-3. The widely used procedure P-1, on the other hand, leads to rapidly deteriorating wings and should be avoided, unless limited to a narrow frequency band near the line center. 

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. 

Line shape function. Given a mixture of two monatomic gases of densities Na/V and Nb/V in the volume V, with Na Nb- The dipole moment 

The brackets denote an ensemble average and p(t) is the total dipole moment. The translational motion of the atoms is treated classically and, in the spirit of the kinetic theory, the ensemble average is replaced by a time average, C(t) = (MO + T - 

With the assumption that the atomic masses are very different, m /mg l,a significant simplification is introduced. The atoms of type B may be assumed to be at rest in the laboratory frame and the relative velocities of the A-B encounters are equal to the velocities of A measured in the laboratory frame. The density of atoms of type B is assumed small enough so that the mean time tc between optical collisions of the type A-B is much longer than the mean duration zj of these collisions the density Na/V of atoms A is assumed small and collisions of the type A-A are neglegible. The range of the induced dipole falls off to insignificant values rapidly with increasing separation so that zc zj. 

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Van Kranendonk J. Intercollisional interference effects in pressure induced infrared spectra. Can. J. Phys. 46, 1173-9 (1968). 

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. 

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... 

Translational spectra involving molecules show similar dips, see as an example the upper part of Fig. 3.5 which was recorded with hydrogen at room temperature. A more refined treatment of the intercollisional process must take into account not only two arbitrarily selected consecutive collisions. Rather, correlations to all orders are important which render the intercollisional interference a many-body process, not exactly the three-body mechanism our simplified discussion above seems to suggest. 

Diffuse component due to three-body interactions. The intercollisional interference process is a many-body effect arising from the correlations of dipoles induced in consecutive collisions. This effect is limited to a certain narrow frequency band defined by ti2cv 1, that is to frequencies, cv,... 

Besides this intercollisional interference process, there are other three-body processes which at elevated densities affect the observable spectra over a much wider range of frequencies, virtually at all frequencies at which absorption may be observed. With increasing density, one will be able to discern binary, ternary, and perhaps higher-order spectral contributions (even if cvxi2 1). These are caused by the dipoles induced in systems consisting of N interacting atoms or molecules, with N > 2. 

J. C. Lewis. Intercollisional Interference - theory and experiment. In Phenomena Induced by Intermodular Interactions, G. Birnbaum, ed., p. 215, Plenum Press, New York, 1985. 

J. van Kranendonk. Intercollisional interference effects. In J. van Kra-nendonk, editor, Intermolecular Spectroscopy and Dynamical Properties of Dense Systems - Proceedings of the Int. School of Physics Enrico Fermi , Course LXXV, p.77, 1980. 

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. 

It has been argued that, in the low-density limit, intercollisional interference results from correlations of the dipole moments induced in subsequent collisions (van Kranendonk 1980 Lewis 1980). Consequently, intercollisional interference takes place in times of the order of the mean time between collisions, x. According to what was just stated, intercollisional interference cannot be described in terms of a virial expansion. Nevertheless, in the low-density limit, one may argue that intercollisional interference may be modeled as a sequence of two two-body collisions in this approximation, any irreducible three-body contribution vanishes. 

Computations. The kinetic theory of intercollisional interference is a classical theory. We briefly summarize the basic relationships needed for the computation of a line profile from Newtonian mechanics. 

Figure 6.14 compares the results of line shape computations based on the isotropic interaction approximation with the measurement by Hunt [187], This spectrum does not have many striking features because of the relatively high temperature of 300 K. We notice only a broad, unresolved Q branch and a diffuse Si(l) line of H2 is seen other lines such as Si(J) with J = 0, 2, 3,. .. are barely discernible. Various dips of the absorption at 4126, 4154 and 4712 cm-1 are caused by intercollisional interference, a many-body effect which is not accounted for in a binary theory. Roughly 90% of the Q branch (in the broad vicinity of 4150 cm-1) arises from the isotropic overlap induced dipole component (XL = 01). The anisotropic overlap component (XL = 21) is a little less than one-half as intense as the quadrupole induced term (XL = 23). These two components with X = 2 are responsible for the Si line structures superimposed on the broad isotropic induction component which is of roughly comparable intensity near the Si line center. 

Subsequently, a kinetic theory of intercollisional interference was developed (Lewis 1980 and 1985). The kinetic theory was based on the idea of pairwise additivity of intermolecular force and induced dipole moment. It traces the collisional history of an individual molecule of a highly diluted system. The traced molecule may be a vibrating molecule, surrounded by non-vibrating molecules, or else a dissimilar molecule of low concentration (gas mixtures). 

The development of the kinetic theory of intercollisional interference has stimulated extensive experimental, computational and other theoretical work which we will briefly consider (Lewis 1985). 

The induced dipole moment of the HD-X systems, with X = He, Ar, H2, HD, is well known from the fundamental theory, for the purely rotational bands and also for most fundamental bands [59]. To the induced dipole, the permanent dipole moment of HD has to be added vectorially, accounting for the linear variation with density which differs from the density variation of the induced dipole components [391]. According to the theory of intracollisional interference (as the process was called, to be distinguised from the intercollisional interference considered elsewhere in this monograph), interference occurs for those induced components that are of the same symmetry as the allowed dipole, namely A1A2AL = 0110 and 1010 [178, 179, 321, 389]. These induced components are always parallel or antiparallel to the allowed dipole, causing constructive or destructive interference. 

G. Bachet. Experimental observation of the intercollisional interference effect on the S(l) pure rotational line of the collision induced spectrum of the H2-He mixture. J. Physique Lett., 44 183, 1983. 

J. C. Lewis and J. van Kranendonk. Intercollisional interference effects in collision-induced light scattering. Phys. Rev. Lett., 24 802, 1970. 

J. W. Mactaggart and H. L. Welsh. Studies in molecular dynamics by collision-induced infrared absorption in H2-rare gas mixtures. I Profile analysis and the intercollisional interference effect. Can. J. Phys., 51 158, 1973. 

R. D. Mountain and G. Bimbaum. Molecular dynamics study of intercollisional interference in collision induced absorption in compressed fluids. J. Chem. Soc. Faraday Trans. 2, 83 1791, 1987. 

J. C. Lewis. Intercollisional Interference Effects. In J. van Kranendonk (ed.). Inter-molecular Spectroscopy and Dynamical Properties of Dense Systems—Proceedings of the International School of Physics Enrico Fermi," Course LXXV, North-Holland, Amsterdam, 1980, pp. 91-110. 

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