a) necessity to use a sufficiently short wavelength X-rays to check the formula of Compton shift;
b) independence of the magnitude of shift from the kind of substance;
c) existence of a undisplaced component in scattered radiation;
d) increase of the intensity of shifted component of scattered radiation with the decrease of material atomic number , as well as with the increase of scattering angle;
e) broadening of both of the components of scattered radiation.
a) Compton shift formula is derived under the assumption of scattering of photons by free electrons. The electrons in the material will be free, if their binding energy is much smaller than the energy transferred to them by the photons. That is why it is necessary to use a sufficiently short-wave radiation; b) because the scattering of photons derives on free-electrons; c) due to scattering of photons on strongly coupled electrons and nuclei; d) due to an increase of the number of electrons, which become free (see item “a”); e) due to scattering of photons on moving electrons.