Spectral moment ternary

Measurements such as these can be conducted to determine the three-body virial coefficients, M 12) and M 21) of collision-induced absorption. To that end, it is useful to measure the variation of yi (and also of yo> Eq. 3.6, where possible) with small amounts of gas 1 mixed with large amounts of the other gas 2, and with small amounts of 2 mixed with 1, to determine the ternary spectral moments M 12 and M 21 separately, with a minumum of interference from the weaker terms. In a mixture of helium and argon, for example, two different three-body coefficients can be determined, those of the He-Ar-Ar and the He-He-Ar complexes. 

Table 3.3. Spectral moments of the neon-argon liquid mixture along the coexistence curve measurement [107] compared with binary values calculated from first principles. (Calculated ternary moments are given in Table 3.2 above.)...

Table 3.7 also lists ternary spectral moments for a few systems other than H2-H2-H2. For the H2-He-He system, the pairwise-additive dipole moments are also known from first principles. The measured spectral moments are substantially greater than the ones calculated with the assumption of pairwise additivity - just as this was seen in pure hydrogen. For the other systems listed in the Table, no ab initio dipole surfaces are known and a comparison with theory must therefore be based on the approximate, classical multipole model. 

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. 

Summarizing, it may be said that virial expansions of spectral line shapes of induced spectra exist for frequencies much greater than the reciprocal mean free time between collisions. The coefficients of the density squared and density cubed terms represent the effects of purely binary and ternary collisions, respectively. At the present time, computations of the spectral component do not exist except in the form of the spectral moments see the previous Section for details. 

H2 He He rotovibrational band. The density dependence of the H2-He enhancement spectrum in the fundamental band of hydrogen has been measured previously, using a trace of hydrogen in helium of thousands of amagats [121, 175, 142] ternary moments were measured at room temperature. The measurements suggest again greater values of the spectral moments, Table 6.7. 

Very little is known about the irreducible ternary dipole components. An early estimate based on classical electrodynamics, hard-sphere interaction and other simplifying assumptions suggests very small, negative contributions to the zeroth spectral moment [402], namely —0.13 x 10-10 cm-1 amagat-3. 

Figure 1 Comparison of observed ( , ) and computed ternary spectral moments of collision-induced absorption of compressed hydrogen in the H2 fundamental band. The dashed curve represents the moments computed on the basis of the pairwise additive dipole components only. The solid line also accounts for the irreducible dipole components from Ref. [53]. (This figure is an update of Fig. 3.46.)...

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. 

At higher densities the shapes of most CILS spectra vary with density as it had been noticed since the first experimental studies [307, 308]. This fact reveals the presence of three-body and possibly higher CILS components. The onset of discernible many-body spectral components is best dealt with in the form of a virial expansion of the spectral moments [208,209,326] that at least in principle permits the separation of the binary, ternary, and so on spectral... 

Ternary moments have been computed for several systems of practical interest [314, 422]. Recent studies are based on accurate ab initio pair dipole surfaces obtained with highly correlated wavefunctions. Because not much is presently known about the irreducible ternary components, it is important to determine to what extent the measured three-body spectral components arise from pairwise-additive contributions [296, 299]. 

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