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] summarazing 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.[2]

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,[3][4]

${\displaystyle R_{LP}={\frac {c_{p}-c_{v}}{c_{v}}}}$

where

• ${\displaystyle c_{p}}$ is the specific heat at constant pressure
• ${\displaystyle c_{v}}$ is the specific heat at constant volume.

References

1. Landau, L. D., & Placzek, G. (1934). Struktur der unverschobenen Streulinie. Z. Phys. Sowjetunion, 5, 172-173.
2. Landau, L. D., Pitaevskii, L. P., Lifshitz, E. M., Electrodynamics of continuous media (Vol. 8). elsevier. Section 120, pp. 428-433.
3. Cummins, H. Z., & Gammon, R. W. (1966). Rayleigh and Brillouin scattering in liquids: the Landau—Placzek ratio. The Journal of Chemical Physics, 44(7), 2785-2796.
4. Wait, P. C., & Newson, T. P. (1996). Landau Placzek ratio applied to distributed fibre sensing. Optics Communications, 122(4-6), 141-146.