Landau–Placzek ratio

Landau–Placzek ratio is a ratio of the integrated intensity of Rayleigh scattering to the combined integrated intensity of Brillouin scattering of a triplet frequency spectrum of light scattered by homogenous liquids or gases. The triplet consists of two frequency shifted Brillouin scattering and a central unshifted Rayleigh scattering line split. The triplet structure was explained by Lev Landau and George Placzek in 1934 in a short publication,^[1][2] summarizing major results of their analysis. Landau and Placzek noted in their short paper that a more detailed discussion will be published later although that paper does not seem to have been published. However, a detailed discussion is provided in Lev Landau and Evgeny Lifshitz's book.^[3] The Landau–Placzek ratio is defined as

${\displaystyle R_{LP}=\frac{I_c}{2I_B}}$

where

• ${\displaystyle I_c}$ is the integral intensity of central Rayleigh peak
• ${\displaystyle I_B}$ is the integral intensity of Brillouin peak.

The Landau–Placzek formula provides an approximate theoretical prediction for the Landau–Placzek ratio,^[4][5]

${\displaystyle R_{LP}=\frac{c_p-c_v}{c_v}}$

where

• ${\displaystyle c_p}$ is the specific heat at constant pressure
• ${\displaystyle c_v}$ is the specific heat at constant volume.

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