Scattering by Molecules Independent Atom Approximation

Scattering by Molecules Independent Atom Approximation. The intensity of electrons scattered elastically by a molecule is in the Debye-Ehrenfest theory - obtained using the first Bom approximation for the scattering amplitudes and assuming that the atoms scatter independently. In the independent atom approximation applied today complex scattering amplitudes [see equation (4)] are used. 

For a rigid system of M atoms considered to be independent scattering centres, the intensity of electrons scattered elastically becomes  

If it is assumed that the inelastically scattered intensity is completely incoherent (see p. 26), the total intensity is given by  

Equation (21) is only valid for a rigid system. To include the interatomic vibrations the intensity expression must be replaced by 

In most cases Gaussian distance distributions are assumed, i.e. 

---