The intensity of light scattering by monatomic gases is calculated by a new self-consistent-field method which is particularly suited to analyzing the effect of collective phenomena such as the fluctuations of the inner field. The polarizability density of atoms is introduced, and the properties of this space function are illustrated by an explicit quantum-mechanical calculation for the hydrogen atom. The Fourier coefficients of the polarizability density are combined with the Fourier coefficients of the particle density and are used as stochastic variables of the scattering system. The effective inner field for a specific particle configuration is obtained as an iterative solution of an integrodifferential equation, and is used for calculating the scattering intensity. This intensity is then averaged over all particle configurations. At ordinary pressures (αn≪1, α is atomic polarizability, n is the particle density) Rayleigh's scattering formula is confirmed, but at high pressures (αn→1) observable corrections to his formula are obtained. In particular, scattering is found depolarized contrary to Rayleigh's theory and to some recent work.
The phase space of a light quantum in a given volume is subdivided into ’’cells’’ of magnitude h3. The number of possible distributions of the light quanta of a macroscopically defined radiation over these cells gives the entropy and with it all thermodynamic properties of the radiation.
The depolarization ratio ρ for the single particle light scattering spectrum of a relativistic plasma with a displaced Maxwell velocity distribution is calculated to the lowest significant order in β = v/c. (c is the light velocity; v is the electron velocity.) It is found that ρ reaches the order of magnitude 0.1 if the temperature increases beyond 108 °K, and that the plasma temperature can be determined by one single polarization measurement without spectral decomposition of the scattered radiation.
The vibrational frequencies and normal coordinates of finite, straight, zigzag chains are calculated from an Urey-Bradley potential, the boundary effects being taken into account by a perturbation method. The dominant perturbation terms fall off with 1/N2 (N = number of C atoms) and are found to be negligible for N>5. The intensities of infrared and Raman bands are calculated without using the simplifications implied in ``bond moment'' and ``bond polarizability'' theories. All the vibrations are found inactive as fundamentals in infrared absorption. The Raman active vibrations produce branches of lines with relative intensities approximately 1, 1/9, 1/25..., 1/N2 and with line spacing rapidly decreasing with increasing N. The strong Raman line observed near 890 cm-1 cannot be assigned to a vibration of the carbon skeleton. One low-frequency vibration (v∼1150/N cm-1) perpendicular to the molecular plane should be Raman active. Its low intensity (it has not been observed so far) indicates cylindrical symmetry of the polarizability about the molecular axis.
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