Spectral moment translational

Table 3.1 lists measured spectral moments of rare gas mixtures at various temperatures. (We note that absorption in helium-neon mixtures has been measured recently [253]. This mixture absorbs very weakly so that pressures of 1500 bar had to be used. Under these conditions, one would expect significant many-body interactions the measurement almost certainly does not represent binary spectra.) For easy reference below, we note that the precision of the data quoted in the Table is not at all uniform. Accurate values of the moments require good absorption measurements over the whole translational frequency band, from zero to the highest frequencies where radiation is absorbed. Such data are, however, difficult to obtain. Good measurements of the absorption coefficient a(v) require ratios of transmitted to incident intensities, /(v)//o, that are significantly smaller than unity and, at the same time, of the order of unity, i.e., not too small. Since in the far infrared the lengths of absorption paths are limited to a few meters and gas densities are limited to obtain purely... 

The translational spectra of pure liquid hydrogen have been recorded with para-H2 to ortho-H2 concentration ratios of roughly 25 75, 46 54 and 100 0, Fig. 3.9 [201, 202]. For the cases of non-vanishing ortho-H2 concentrations, the spectra have at least a superficial similarity with the binary translational spectra compare with the data shown for low frequencies (< 250 cm-1) of Fig. 3.10 below. A comparison of the spectral moments of the low-density gas and the liquid shows even quantitative agreement within the experimental uncertainties which are, however, substantial. 

For the rototranslational band, the spectral moment y2 has been shown to be related to the translational moments M , according to [292]... 

Higher-order classical moments have also been reported. We mention the classical expressions for the translational spectral moments M , with n = 0, 2, 4, and 6, for pairs of linear molecules given in an appendix of [204]. Spectral moments of spherical top molecules have been similarly considered [163, 205], We note that for n > 1, spectral moments show dynamic as well as static quantum correction, which become more important as the order n of the spectral moments is increased. The discussions on pp. 219, and Table 5.1, suggest that, even for the near-classical systems, quantum corrections may be substantial and can rarely be ignored. 

Hi-Ar-Ar rototranslational spectra. Tables 6.3 and 6.4 show the roto-translational spectral moments computed from first principles, with the advanced TT3 H2-Ar [228] and the HFD-C Ar-Ar interaction poten-... 

We have not attempted to exhibit in great detail the effects of the rotational excitations on the induced dipole components B and those of vibrational excitation on the interaction potential because this was done elsewhere for similar systems [151, 63,295,294], The significance of the j,f corrections is readily seen in the Tables and need not be displayed beyond that. The vibrational influence is displayed in Fig. 6.20 first and second spectral moments are strongly affected, especially at high temperatures, similar to that which was seen earlier for H2-He [294], Fig. 6.23. The close agreement of the measurements of the rotovibrational collision-induced absorption bands of hydrogen with the fundamental theory shown above certainly depends on proper accounting for the rotational dependences of the induced dipole moment, and of the vibrational dependences of the final translational states of the molecular pair. 

V. I. Bukhtoyarova and M. V. Tonkov. Intermolecular interactions in compressed gases from translational absorption spectra I Spectral moments of translation bands. Opt. Spectrosc., 43 27, 1977. 

M. Zoppi and G, Spinelli. Interaction induced translational Raman scattering of liquid argon The spectral moments. Phys. Rev. A, 33 939-945 (1986). 

In practice one can hardly ever evaluate all of the moments of a spectral density, but rather one evaluates only the first few, until the calculations become too difficult or lengthy. If only the first 2M moments are evaluated, then /(a) is never known uniquely, except in the special case that 1(a)) consists of discrete contributions at M or fewer frequencies. Nevertheless, one expects that the knowledge of even a few moments of a spectral density furnishes some useful constraints on the possible forms of /(a). The problem is to translate these moment constraints, and the other general properties of /(a), into useful forms. Several schemes for making use of this information are outlined in the next section. 

According to Eq. 3.5, yi may be considered the total absorption in the translational band. We, however, prefer to consider Mq the total intensity, Eq. 3.4 with n = 0, because the spectral function g(v) is more closely related to the emission (absorption) process than a(v). For rare gas mixtures, we have the relationships of Eqs. 3.7. In other words, yo may be considered a total intensity of the spectral function, g(v), and the ratio yi /yo is a mean width of the spectral function (in units of cm-1). Both moments increase with temperature as Table 3.1 shows. With increasing temperature closer encounters occur, which leads to increased induced dipole moments and thus greater intensities. 

Let us mention several papers by Ya.B. on various problems of molecular physics and quantum mechanics which have not been included in this volume. Among the problems considered are the peculiar distribution of molecules according to their oscillatory modes when the overall number of oscillatory quanta does not correspond to the temperature of translation [9], the influence of the nuclear magnetic moment on the diffusion coefficient [10] and on absorption of light by prohibited spectral lines [11],... 

Besides, the review could conditionally be divided in accord with another criterion, (a) In Sections III-V and VII we discuss so-called unspecific interactions, which take place in a local-order structure of various polar liquids, (b) In Sections VI-IX we also consider specific interactions [16]. These are directly determined by the hydrogen bonds in water, are reflected in the band centered at 200 cm-1, which is termed here the R-band, and is characterized by some spectral features in the submillimeter wavelength range (from 10 to 100 cm-1). Note that sometimes in the literature the R-band is termed the translational band, since the peak frequency of this band does not depend on the moment of inertia I of a water molecule. 

The translational motions and spin dynamics of conduction electrons in metals produce fluctuating local magnetic hyperfine fields. These couple to the nuclear magnetic moments, inducing transitions between nuclear spin levels and causing nuclear spin relaxation. The translational motions of electrons occur on a very rapid time scale in metals (<10 s), so the frequency spectrum of hyperfine field fluctuations is spread over a wide range of w-values. Only a small fraction of the spectral intensity falls at the relatively low nuclear resonance frequency (ojq 10 s ). Nevertheless, the interaction is so strong that this process is usually the dominant mode of relaxation for nuclei in metallic systems, either solid or liquid. 

For a material to act as an efficient solar energy absorber, it not only has to absorb over a broad spectral (energy) range, it also has to absorb the photons effectively. Hence, the electrOTiic transition dipole moment is a parameter of importance as it translates into both the molar extinction coefficient (solution)... 

Quantitatively, we expect the temporal response of a solvent to be governed by the dynamics of the translation and reorientation of its molecules. This response changes the interaction of the anisotropic charge distribution of the solute, as characterized by the multipole moments (dipole, quadrupole, etc.) of its charge distribution, with the multipole moments of the solvent molecules. In a polar solvent we can seek to relate the time scale of the solute s reorientation dynamics to the frequency dependence of the dielectric constant in the spectral region corresponding to nuclear motions. ... 

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