Normalisation scattering cross sections

The INS intensity, 5 (g,fo), as calculated from the Scattering Law, Eq. (2.41), is related to the mean square atomic displacements, weighted by the incoherent scattering cross sections. What is required to calculate this quantity is the mean square atomic displacement tensor, Bi, and this can be obtained from the crystalline equivalent of L/ " ( A2.3), the normalised atomic displacements in a single molecule Eq. (4.20). This is and was introduced above, in Eq. (4.55). We have seen how... 

Looking back. Fig. 11.1 provides further confirmation of the validity of the incoherent approximation. The ratio, H/D, of the normalised areas of the bands near 400 cm is 9.8. The predicted ratio on the basis of their incoherent cross sections is 39.2 (= 80.27/2.05) in contrast, the ratio of their total scattering cross sections is 10.7 (= 82.03/7.64) in much better agreement with the experimental observation. 

Another commonly-used normalisation procedure is to use the relative flow technique. In this method the elastic differential cross section for a particular species may be obtained by comparing the scattered intensity under the same conditions with that from another target with a known cross section. It is important to ensure, for both the gas under study and the reference gas, that the electron flux density and distribution, the detector efficiency, and the target beam flux distribution are the same for both gases during the measurement. 

Since the absolute differential cross section for scattering by unpolarised electrons was not determined by Sohn and Hanne, they analysed their results using normalised state multipoles defined by... 

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