The Scattering of X-rays by Gases and Crystals

It is shown that, in exact agreement with the wave mechanical result worked out by Wentzel and Waller and Hartree, the Raman-Compton-Jauncey formula for the scattering of x-rays by an atom deduced on the basis of classical electrodynamics may be written I_φ=Iₑ²+Z-Σzr=1Eᵣ²\, where I_φ is the intensity scattered in a direction φ with the primary beam, Iₑ is the scattering from a single isolated electron as calculated by Thomson, Z is the atomic number, Eᵣ is the average amplitude of the waves scattered by the r-th electron in the atom and F is the true atomic structure factor as given by F=Σ₁ᶻEᵣ. This shows that the coherent scattering is proportional to F² and that the introduction of the average atomic structure factor F^' by Jauncey is unnecessary. On the basis of Eq. (A), theoretical formulas for the scattering of x-rays by gases and crystals are redeveloped and the results turn out to explain all the disagreement between theories proposed by Jauncey and the writer.