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A method, based on classical physics, to utilize the first four even moments of the depolarized collision induced light scattering spectrum to derive an empirical model for the pair polarizability anisotropy of interacting molecules, with only one adjustable parameter, is described and applied to the spectra of Ne, Ar, Kr, Xe, and CH4. Good agreement with ab initio results in the literature is obtained and profiles calculated with these models are in excellent agreement with experiment.

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A new and computationally viable full quantum version of line shape theory is obtained in terms of a mixed Weyl symbol calculus. The basic ingredient in the collision-broadened line shape theory is the time dependent dipole autocorrelation function of the radiator-perturber system. The observed spectral intensity is the Fourier transform of this correlation function. A modified form of the Wigner-Weyl isomorphism between quantum operators and phase space functions (Weyl symbols) is introduced in order to describe the quantum structure of this system. This modification uses a partial Wigner transform in which the radiator-perturber relative motion degrees of freedom are transformed into a phase space dependence, while operators associated with the internal molecular degrees of freedom are kept in their original Hilbert space form. The result of this partial Wigner transform is called a mixed Weyl symbol. The star product, Moyal bracket and asymptotic expansions native to the mixed Weyl symbol calculus are determined. The correlation function is represented as the phase space integral of the product of two mixed symbols: one corresponding to the initial configuration of the system, the other being its time evolving dynamical value. There are, in this approach, two semiclassical expansionsone associated with the perturber scattering process, the other with the mixed symbol star product. These approximations are used in combination to obtain representations of the autocorrelation that are sufficiently simple to allow numerical calculation. The leading O(h 0 ) approximation recovers the standard classical path approximation for line shapes. The higher order O(h 1 ) corrections arise from the noncommutative nature of the star product.

The intensity profiles of some of the broad continuous absorption bands of oxygen in the near-infrared and visible regions were measured in the compressed gas over a range of pressures and temperatures. Three single electronic transitions (12 600, 10 600, 07620 Å) and three double transitions (6290, 5770, 4770 Å) were studied in detail. The asymmetry of the band profiles is shown to arise from a Boltzmann relation between the intensity distributions in the high and low frequency wings when the band origin is properly chosen. By assuming an appropriate rotational structure and broadening each rotational transition by a Boltzmann-modified dispersion curve the profiles of the bands could be reproduced with only minor discrepancies. These criteria, along with the well-known quadratic density dependence of the intensity, show that the bands are properly interpreted as collision-induced electronic transitions. The large width of the translational broadening functions required in the analysis indicates that the induction must be predominantly due to overlap interaction. No specific effects of (O2)2 complexes are identifiable in the spectra.