On the Optical Properties of Solids. II

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Abstract
The absorption of light by a crystal due to atomic motion is calculated by first‐order perturbation theory in the approximation in which atoms are considered as charged mass points. The effect of each normal oscillator is shown to depend on the value of a sum over normal mode transformation coefficients which becomes identical with the dipole moment associated with the oscillator when the crystal is small compared to the longest absorbed wavelength. To get results in terms of frequency, this expression must be weighted by the density of states of the normal oscillators. The general results are evaluated for the case of a simple model of an ionic crystal; in addition to the strong absorption peak at the ``limiting frequency,'' peaks at frequencies corresponding to critical points of the constant energy surfaces in k space are shown to appear provided boundary conditions are taken into account, and the effects of crystal size are shown to enhance the importance of these subsidiary peaks. The bearing of these effects on other optical properties, and on the impurity problem, is discussed briefly.

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