The theory of the Raman effect in crystals, in particular rock-salt

Abstract

The Raman effect in crystals is treated in this paper with the help of Placzek’s approximation. It consists of contributions of different orders with respect to the amplitudes of the vibrations; the first-order effect is a line spectrum depending only on the vibrations of infinite wavelength, the second-order effect is a continuous spectrum depending on combination frequencies of all pairs of branches of the lattice vibrations, each pair taken for the same wave vector. In highly symmetrical crystals like rock-salt the first-order effect is zero. The second order effect can be calculated for rock-salt with the help of the tables of the lattice frequencies published by Kellermann. It consists of thirty-six peaks, each belonging to a combination frequency. The superposition of these allows us to determine without any arbitrary assumption about the coupling constants, the frequency of the observable maxima in fair agreement with Krishnan’s measurements. By adapting three coupling constants one can also determine the relative intensities of the most prominent peaks and obtain a curve which in its main features agrees with the observed one. The results show that lattice dynamics can account quantitatively for the Raman effect in crystals and that Raman’s attacks against the theory are unfounded.