Spatial structure of boson peak vibrations in glasses

Low-frequency Raman scattering in glasses in the region of the boson peak is described in terms of the vibration spatial correlation functions. It is shown that the frequency dependence of the light to vibration coupling coefficient $C\left(\omega \right)$ is determined by the vibration correlation length $l_{\omega }$ and the spatial dimensionality of the vibration eigenmodes. The linear law $C\left(\omega \right)\propto \omega$ for the boson peak which is found experimentally in many glasses corresponds in the model to 1D spatial geometry of vibration eigenmodes. The estimated amplitude of the boson peak in the Raman scattering is in good agreement with the experimental data in vitreous silica.