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.
- 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.
- For small-angle neutron scattering, \(f=1\).
- For small-angle X-ray scattering, \(f \approx 1\), if \(\theta < \rm{ca.}\ 5\,°\).
Notes:
- The dimension of \(R(\theta)\) is \((\rm{length})^{-1}\).
- In small-angle neutron scattering the term cross-section is often used instead of \(R(\theta)\); the two quantities are identical.
- An alternative recommended symbol is \(R_{\theta}\).