Rayleigh ratio

https://doi.org/10.1351/goldbook.R05159
The quantity used to characterize the scattered intensity at the scattering angle \(\theta\), defined as \(R(\theta) = \frac{i_{\theta }\,r^{2}}{I\,f\,V}\), where \(I\) is the intensity of the incident radiation, \(i_{\theta}\) is the total intensity of scattered radiation observed at an angle \(\theta\) and a distance \(r\) from the point of scattering and \(V\) is the scattering volume. The factor \(f\) takes account of polarization phenomena. It depends on the type of radiation employed.
  1. For light scattering, dependent on the polarization of the incident beam, \(f=1\) for vertically polarized light, \(f = 1 - \cos^{2}\theta\) for horizontally polarized light and \(f = 1 + \frac{\cos^{2}\theta}{2}\) for unpolarized light.
  2. For small-angle neutron scattering, \(f=1\).
  3. For small-angle X-ray scattering, \(f \approx 1\), if \(\theta < \rm{ca.}\ 5\,°\).
Notes:
  1. The dimension of \(R(\theta)\) is \((\rm{length})^{-1}\).
  2. In small-angle neutron scattering the term cross-section is often used instead of \(R(\theta)\); the two quantities are identical.
  3. An alternative recommended symbol is \(R_{\theta}\).
Source:
Purple Book, 1st ed., p. 65 [Terms] [Book]