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Landau–Placzek ratio

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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, 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.

The Landau–Placzek ratio is defined as

R L P = I c 2 I B {\displaystyle R_{LP}={\frac {I_{c}}{2I_{B}}}}

where

  • I c {\displaystyle I_{c}} is the integral intensity of central Rayleigh peak
  • I B {\displaystyle I_{B}} is the integral intensity of Brillouin peak.

The Landau–Placzek formula provides an approximate theoretical prediction for the Landau–Placzek ratio,

R L P = c p − c v c v {\displaystyle R_{LP}={\frac {c_{p}-c_{v}}{c_{v}}}}

where

  • c p {\displaystyle c_{p}} is the specific heat at constant pressure
  • c v {\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., & Placzek, G. (1934). Structure of the undisplaced scattering line. Phys. Z. Sowiet. Un, 5, 172.
  3. Landau, L. D., Pitaevskii, L. P., Lifshitz, E. M., Electrodynamics of continuous media (Vol. 8). elsevier. Section 120, pp. 428-433.
  4. 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.
  5. Wait, P. C., & Newson, T. P. (1996). Landau Placzek ratio applied to distributed fibre sensing. Optics Communications, 122(4-6), 141-146.
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