arbitrariness of the virtual orbitals may be utilized profitably in such a way that the convergence may be improved in the perturbation theory and the configuration interaction calculation based on the Hartree-Fock equation. It is hoped that the discussion presented here will also have some pedagogical value in furthering a sound understanding of the nature of virtual orbitals.A weak depolarized Rayleigh wing has been observed for liquid xenon and for several liquids composed of spherical-top molecules. The intensity contours for these liquids decrease exponentially with increasing frequency shift. This behavior is similar to that predicted for spectra of collision-induced scattering from gases.
Brillouin spectra of liquid CCl4 (at 20.0°C) have been investigated 20 scattering angles, from 40° to 145°. The spectra were excited by 6328-Å radiation from a He-Ne laser and analyzed with a pressure-scanned Fabry-Perot spectrometer. The measured frequency shifts and linewidths of the Brillouin component were used to determine velocities and attenuations of thermal waves in the frequency range 1.6–4.7 Gc/sec. A large dispersion (>10%) and corresponding change in attenuation were found, characteristic of a thermal relaxation process in this region. A broad new component in the spectrum of isotropic scattering was observed, which is also characteristic of a relaxation process. Analyses of these data were carried out in two ways: one is based on a simple extension of acoustic equations to light scattering, and the other, on Mountain's theory of light scattering in the region of a thermal relaxation. It is shown that the observed spectra and derived data agree with Mountain's theory in all respects. Also, from these data it was possible to evaluate the total internal specific heat CI = 11.6±0.3 cal/mole°C. Within experimental error, this relaxes in a single relaxation time τ = (6.5±0.5) × 10−11 sec.
Raman spectra of low-pressure methane gas both at room temperature and near condensation have been studied in the frequency range from 0 to 50 cm '. The spectra include two contributions: One is due to collision-induced scattering (CIS) and the other to an unresolved dimer rotational band. The latter component is most prominent at low temperatures. Both the dimer band and CIS spectrum have been computed for a Lennard-Jones interaction and point-dipole polarizability. At large frequency shifts ( & 20 cm ) it is suAicient to use classical collision dynamics to compute the CIS spectrum, but at lower shifts it is necessary to use quantum theory and add the dimer contribution to obtain good agreement with the experimental spectrum.From analysis of the spectra we determine that the fractional depolarized scattering from dimers is 10% at 300'K and 43% at 115'K. The shape of the far wing (20-50 cm ') provides a sensitive means of testing the form of the induced polarizability anisotropy. For methane, excellent agreement with experiment is obtained for the point-dipole model.
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