Scattering by a multi-electron atom

An atom with the atomic number Z contains Z electrons. The waves scattered by these Z electrons will contribute in different ways to the overall scattering by the atom, depending on which orbital they belong to. 

The waves scattered coherently by each of the electrons all have the same wavelength. Therefore, they will interfere. Hence, the total scattered amplitude is the sum of the amplimdes scattered by each electron. The electron scattering factor, which is the amplimde scattered by an electron, was denoted earlier by f. For a given electron it depends on how far its orbital extends (see equation [1.15]). Therefore, the coherent intensity can be written as  

The values of the scattering factors for the various atoms are compiled in the 

In the case of incoherent radiation, which would then indicate inelastic scattering or also Compton scattering, the wavelengths of the radiations emitted by the various electrons are different, depending on what orbital is considered. Therefore, there is no interference. The intensity scattered by the entire atom is the sum of the intensities scattered by each of the electrons and it is written  

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